MCP Math Server
Server Quality Checklist
Latest release: v1.0.0
- Disambiguation4/5
The tools are highly specialized with clear distinctions in their mathematical domains (e.g., arithmetic, trigonometry, statistics), and descriptions provide precise scopes. However, some overlap exists in areas like prime testing (e.g., multiple primality tests) and trigonometric functions (e.g., degrees vs. radians variants), which could cause minor confusion despite detailed descriptions.
Naming Consistency5/5Tool names follow a consistent snake_case pattern throughout, with clear verb_noun or descriptive noun structures (e.g., 'compute_pi_chudnovsky', 'is_prime', 'harmonic_mean'). There are no deviations in naming conventions, making the set predictable and readable.
Tool Count1/5With 641 tools, the count is extremely excessive for any coherent server purpose, far beyond the typical well-scoped range of 3-15 tools. This overwhelms the domain of 'MCP Math Server' and suggests a lack of focus, making it impractical for agent use due to information overload.
Completeness5/5The tool set is remarkably comprehensive, covering a vast array of mathematical domains from basic arithmetic to advanced number theory, statistics, and trigonometry. There are no apparent gaps; it includes CRUD-like operations, constants, algorithms, and utilities across all mentioned categories, ensuring complete coverage for mathematical computations.
Average 2.9/5 across 641 of 641 tools scored. Lowest: 1.5/5.
See the Tool Scores section below for per-tool breakdowns.
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- No high-severity vulnerability alerts
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This repository is licensed under Apache 2.0.
This repository includes a README.md file.
No tool usage detected in the last 30 days. Usage tracking helps demonstrate server value.
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How is the quality score calculated?
The overall quality score combines two components: Tool Definition Quality (70%) and Server Coherence (30%).
Tool Definition Quality measures how well each tool describes itself to AI agents. Every tool is scored 1–5 across six dimensions: Purpose Clarity (25%), Usage Guidelines (20%), Behavioral Transparency (20%), Parameter Semantics (15%), Conciseness & Structure (10%), and Contextual Completeness (10%). The server-level definition quality score is calculated as 60% mean TDQS + 40% minimum TDQS, so a single poorly described tool pulls the score down.
Server Coherence evaluates how well the tools work together as a set, scoring four dimensions equally: Disambiguation (can agents tell tools apart?), Naming Consistency, Tool Count Appropriateness, and Completeness (are there gaps in the tool surface?).
Tiers are derived from the overall score: A (≥3.5), B (≥3.0), C (≥2.0), D (≥1.0), F (<1.0). B and above is considered passing.
Tool Scores
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. However, it only mentions 'applications' without explaining what the tool does behaviorally (e.g., whether it performs computations, returns educational examples, or modifies data). It lacks critical details such as output format, error handling, or any side effects, leaving the agent with no understanding of the tool's operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a single sentence, but it is under-specified rather than efficiently informative. It front-loads the core idea ('Applications of Bézout's identity') but fails to provide necessary details. While not verbose, its brevity comes at the cost of clarity, making it inadequate for effective tool use.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical tool with 3 parameters, 0% schema coverage, no annotations, and no output schema, the description is severely incomplete. It does not compensate for the lack of structured data by explaining purpose, parameters, behavior, or output. This leaves the agent unable to understand or use the tool effectively in any context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters (a, b, applications) with 0% schema description coverage, meaning none are documented in the schema. The description does not explain what these parameters mean (e.g., that 'a' and 'b' are integers for Bézout's identity, or what 'applications' array should contain). Without any parameter semantics provided, the agent cannot correctly invoke the tool.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose2/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Applications of Bézout's identity in various mathematical contexts' which is tautological with the tool name 'bezout_applications' and only adds a domain/category tag. It lacks a specific verb (e.g., 'compute', 'analyze', 'demonstrate') and does not clarify what the tool actually does with the inputs (e.g., whether it calculates Bézout coefficients, solves equations, or provides examples). This makes it vague and minimally informative beyond restating the name.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines1/5Does the description explain when to use this tool, when not to, or what alternatives exist?
There is no guidance on when to use this tool versus alternatives. The description does not mention any context, prerequisites, or sibling tools (e.g., 'bezout_identity' which might compute the identity itself). Without such information, an agent cannot determine appropriate usage scenarios or differentiate it from related tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description reveals nothing about what the tool does behaviorally - whether it computes, validates, optimizes, or something else. It doesn't mention input constraints (e.g., positive integers), computational characteristics, error conditions, or what the output represents. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise (one sentence with parenthetical domain/category), but it's under-specified rather than efficiently informative. The single sentence doesn't waste words, but it also doesn't provide enough information. The domain/category annotation could be considered extraneous repetition since it's already implied by the tool name and context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a mathematical tool with 2 required parameters, 0% schema description coverage, no annotations, and no output schema, the description is completely inadequate. It doesn't explain what the tool computes, what the parameters mean, what the output represents, or when to use it. For a tool in a domain with many alternatives (Egyptian fractions), this leaves critical gaps in understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the schema provides no descriptions for the two parameters (numerator, denominator). The description adds absolutely no information about what these parameters represent, their valid ranges, or their relationship. For a mathematical tool with two required integer parameters, this leaves the agent guessing about their meaning and constraints.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose2/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Alternative greedy algorithm for Egyptian fractions (Fibonacci method)' which gives a general domain (Egyptian fractions) and method name (Fibonacci method), but it's vague about what the tool actually does. It doesn't specify the verb (e.g., 'compute', 'generate', 'find') or what output is produced. It distinguishes from siblings by mentioning 'Egyptian fractions' which appears in other tool names, but the purpose remains unclear.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines1/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Alternative greedy algorithm' but doesn't specify what it's an alternative to, when this method is preferred, or what other Egyptian fraction tools exist (like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction' in the sibling list). There's no context for appropriate usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does at a high level ('Generate a comprehensive identity verification report') without explaining what 'comprehensive' entails, what the output looks like, whether it's a read-only or mutating operation, or any performance characteristics. This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—just one sentence with a parenthetical note. It's front-loaded with the main action ('Generate a comprehensive identity verification report'), and there's no wasted text. However, the conciseness comes at the cost of completeness, as it lacks necessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity implied by 'comprehensive' and the lack of annotations, output schema, and parameter documentation, the description is severely incomplete. It doesn't explain what a 'report' entails, how verification is performed, or what the user can expect. For a tool with 2 parameters and no structured guidance, this description fails to provide the necessary context for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, and the tool description provides no information about what 'test_angles' or 'tolerance' mean, their expected formats, or how they affect the verification process. For example, it doesn't clarify if 'test_angles' is a list of angles, a range, or something else, or what 'tolerance' units are. With no parameter information in the description and low schema coverage, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose2/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Generate a comprehensive identity verification report' which is a clear verb+resource, but it's vague about what 'identity verification' means in the context of trigonometry. The parenthetical '(Domain: trigonometry, Category: identities)' adds some context but doesn't specify what trigonometric identities are being verified or how. It doesn't clearly distinguish from sibling tools like 'verify_identity' or 'verify_hyperbolic_identity'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines1/5Does the description explain when to use this tool, when not to, or what alternatives exist?
There is no guidance on when to use this tool versus alternatives. The description doesn't mention any prerequisites, constraints, or comparison with sibling tools like 'verify_identity' or 'verify_hyperbolic_identity'. It provides no context for when this tool is appropriate or when other tools might be better suited.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states it will 'provide general information' without specifying what that means - whether it returns solution methods, existence proofs, historical context, or mathematical properties. It doesn't mention any behavioral traits like computational complexity, limitations, or what format the information comes in. For a mathematical analysis tool with no annotations, this is completely inadequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise (one sentence plus domain/category tags), but this conciseness comes at the cost of being under-specified. The domain/category tags add some structure but don't provide meaningful operational guidance. While it's not verbose, it's also not sufficiently informative for the tool's complexity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
This is a mathematical analysis tool with 2 undocumented parameters, no annotations, no output schema, and multiple sibling tools in the same domain. The description is completely inadequate - it doesn't explain what the tool actually does, what parameters it needs, what behavior to expect, or how it differs from related tools. Given the complexity of Diophantine analysis and the complete lack of structured documentation, the description fails to provide necessary context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage, so both parameters (equation_type and kwargs) are completely undocumented in the schema. The description provides no information about what these parameters mean, what values equation_type accepts, what kwargs should contain, or how they affect the analysis. With 2 undocumented parameters and 0% schema coverage, the description fails to compensate by explaining parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose2/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Analyze a Diophantine equation and provide general information' which is a tautology - it essentially restates the tool name 'diophantine_analysis' as 'analyze a Diophantine equation'. While it adds 'provide general information', this is vague and doesn't specify what kind of analysis or information is provided. It doesn't distinguish this tool from sibling tools like 'count_solutions_diophantine', 'solve_linear_diophantine', or 'parametric_solutions_diophantine'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There are multiple sibling tools related to Diophantine equations (count_solutions_diophantine, solve_linear_diophantine, parametric_solutions_diophantine, solve_quadratic_diophantine, etc.), but the description doesn't explain what makes this 'analysis' tool different from those solution-focused tools. The domain/category tags are too broad to provide meaningful usage guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states 'Analyze comprehensive properties' without explaining what analysis means, what output to expect, whether it's read-only or has side effects, performance characteristics, or error conditions. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise with just one sentence plus domain/category tags. It's front-loaded with the main purpose statement. While efficient, it may be too brief given the lack of other documentation, but within itself, it wastes no words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of Farey sequence analysis, zero annotation coverage, 0% schema description coverage, and no output schema, the description is completely inadequate. It doesn't explain what 'comprehensive properties' means, what format results come in, or any behavioral aspects. This leaves the agent with insufficient information to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the single parameter 'n' is completely undocumented in the schema. The description provides no information about what 'n' represents (order of the Farey sequence? upper bound?), its valid range, or its semantic meaning. With zero coverage and no compensation in the description, this is a significant gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze comprehensive properties of Farey sequence F_n', which provides a verb ('analyze') and resource ('Farey sequence F_n'), but it's vague about what 'comprehensive properties' entails. It distinguishes from siblings by specifying the domain/category, but lacks specificity about what analysis is performed compared to other farey-related tools like 'farey_sequence' or 'farey_neighbors'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: farey_sequences' which gives some context, but offers no explicit when/when-not instructions or references to sibling tools for comparison, leaving usage decisions unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, and the description does not disclose any behavioral traits such as error handling, input validation, performance characteristics, or output format. It fails to compensate for the lack of structured metadata.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, consisting of a single sentence. However, the domain/category tags add minimal value and could be considered slightly verbose for the information conveyed.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, no output schema, and three parameters, the description is severely inadequate. It does not provide enough context for an agent to understand how to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description does not explain the parameters at all. It does not clarify what 'x_points', 'y_points', and 'x' represent, their relationships, or any constraints beyond the schema's basic types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool performs linear interpolation on a sequence of points, which is a clear purpose. However, it does not differentiate from sibling tools like 'linear_interpolate' or 'lagrange_interpolate', and the domain/category tags are redundant rather than clarifying.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description mentions domain and category but does not specify scenarios, prerequisites, or comparisons to other interpolation tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'analyze' but doesn't disclose what the tool actually does behaviorally - whether it computes values, applies inversion, returns analytical results, or something else. No information about output format, computational limits, or error conditions.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise - one sentence plus domain/category tags. It's front-loaded with the core purpose. However, the conciseness comes at the cost of completeness, making it under-specified rather than efficiently informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a tool with 2 parameters (0% schema coverage), no annotations, no output schema, and multiple overlapping sibling tools, the description is completely inadequate. It doesn't explain what analysis means, what parameters do, what results to expect, or when to choose this over similar tools.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so parameters are completely undocumented in the schema. The description provides no information about what 'function_name' should be (named multiplicative functions like Euler's totient, divisor function, etc.) or what 'range_end' controls (evaluation range, inversion limit). No parameter guidance whatsoever.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze multiplicative functions using Möbius techniques' which provides a general purpose (analyze with specific techniques). However, it's vague about what 'analyze' entails - computational properties, range evaluation, or inversion applications. The domain/category tags add context but don't clarify the specific action.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool versus alternatives. With sibling tools like 'mobius_function', 'mobius_function_range', 'mobius_inversion_formula', and 'apply_mobius_inversion', there's clear overlap but no differentiation. The description doesn't indicate whether this is for evaluation, inversion, or range analysis of multiplicative functions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description provides minimal behavioral information beyond the basic purpose. With no annotations provided, the description carries full burden but fails to disclose important traits: it doesn't mention whether this is a read-only or destructive operation, what permissions might be needed, computational complexity, convergence behavior, error handling, or what the output looks like. For a complex optimization tool with 9 parameters, this lack of behavioral context is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise - a single sentence with parenthetical domain/category information. There's no wasted verbiage, and it's front-loaded with the core purpose. However, for such a complex tool, this brevity comes at the cost of completeness, making it more under-specified than optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (9 parameters, optimization algorithm), complete lack of annotations, 0% schema description coverage, and no output schema, the description is severely inadequate. It doesn't explain what the tool returns, how to interpret results, error conditions, performance characteristics, or practical usage considerations. For a numerical optimization tool that likely returns convergence results or optimized parameters, this minimal description leaves the agent with insufficient guidance.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage for all 9 parameters, the description provides absolutely no information about parameter meanings, formats, or usage. It doesn't explain what 'f' and 'grad_f' should contain (function definitions? mathematical expressions?), what 'x0' represents (initial guess vector), or the significance of hyperparameters like beta1, beta2, epsilon. The description fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs 'Adam optimization (adaptive moment estimation)' for 'efficient training', which is a specific verb (optimize) with a resource (training process). It distinguishes from siblings by specifying a particular optimization algorithm (Adam) rather than generic operations like gradient descent or coordinate descent. However, it doesn't explicitly differentiate from other optimization siblings like gradient_descent or gradient_descent_momentum beyond naming the algorithm.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions 'efficient training' and the domain/category, it doesn't specify scenarios where Adam is preferred over other optimization methods available in the sibling list (like gradient_descent, gradient_descent_momentum, coordinate_descent, or nelder_mead). There's no mention of prerequisites, typical use cases, or comparison with other optimization approaches.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates random samples but does not describe the output format (e.g., list of integers), randomness characteristics (e.g., pseudorandom vs true random), performance implications, or error handling. For a statistical sampling tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's purpose. The domain and category tags are appended concisely. There is no unnecessary verbiage or structural fluff, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical sampling tool with 4 parameters, no annotations, no output schema, and 0% schema description coverage, the description is insufficient. It does not explain the output (e.g., sample format), parameter semantics, or behavioral traits like randomness seeding or error conditions. The description alone does not provide enough context for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 4 parameters with 0% description coverage, meaning none of the parameters are documented in the schema. The description does not mention any parameters, their meanings (e.g., 'n' as number of trials, 'p' as success probability), valid ranges, or default behaviors. This fails to compensate for the lack of schema documentation, leaving all parameters semantically undefined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Generate random samples from the binomial distribution', which clearly indicates the verb ('Generate random samples') and resource ('binomial distribution'). However, it does not differentiate from sibling tools like 'binomial_cdf' or 'binomial_pmf', which also operate on the binomial distribution but for different purposes (cumulative distribution function vs probability mass function). The domain/category tags add context but don't enhance the core purpose statement.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'binomial_cdf' or 'binomial_pmf', nor does it explain when random sampling is appropriate compared to calculating probabilities or distributions. There is no indication of prerequisites, typical use cases, or limitations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions analysis but doesn't disclose behavioral traits such as computational complexity, output format (e.g., returns convergence rate, boolean, or detailed report), error handling, or any side effects. This leaves significant gaps for an agent to understand how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences: one stating the purpose and another providing domain/category tags. It's front-loaded with the main action and avoids unnecessary verbosity, though the tags could be integrated more smoothly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical analysis tool), lack of annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain what the analysis entails, what results to expect, or how parameters influence the outcome, making it inadequate for effective tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters 'x' and 'max_terms' are undocumented in the schema. The description adds no meaning about these parameters—it doesn't explain what 'x' represents (e.g., a number to approximate), what 'max_terms' controls, or their constraints. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze convergence properties of continued fraction approximations', which provides a general purpose (verb+resource). However, it's vague about what specific convergence properties are analyzed (e.g., rate, stability, error bounds) and doesn't distinguish from sibling tools like 'convergence_comparison' or 'convergent_properties' that might handle related aspects.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The domain/category tags ('arithmetic', 'continued_fractions') imply context but don't specify use cases, prerequisites, or comparisons to siblings like 'continued_fraction_expansion' or 'cf_to_rational'. Usage is implied rather than clearly defined.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'random samples' but fails to describe key behaviors such as the output format (e.g., list of numbers), whether the seed parameter ensures reproducibility, or any performance considerations (e.g., large n values). This is inadequate for a tool with parameters and no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's function. It avoids unnecessary words and is front-loaded with the core action. However, the domain/category tags are somewhat redundant and could be omitted for better focus.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 3 parameters with 0% schema coverage, no annotations, and no output schema, the description is insufficient. It does not explain parameter meanings, output format, or behavioral traits, making it incomplete for effective use. The agent lacks critical information to invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the parameters (n, rate, seed) are documented in the schema. The description does not compensate by explaining what these parameters mean (e.g., n is sample size, rate is the distribution's rate parameter, seed controls randomness). This leaves all parameters semantically undefined, which is a critical gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Generate random samples from the exponential distribution', which provides a clear verb ('Generate') and resource ('random samples'), but it does not differentiate from sibling tools like 'exponential_cdf', 'exponential_pdf', or 'normal_sample'. The domain/category tags add context but do not enhance the core purpose statement.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools (e.g., 'exponential_cdf' for cumulative probabilities or 'normal_sample' for normal distribution samples). This leaves the agent without direction on appropriate contexts.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'Find path' and 'using mediant operations', but does not explain what the tool returns (e.g., a sequence of fractions, steps), any constraints (e.g., input validity, performance limits), or error conditions. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, consisting of a single sentence followed by domain/category tags. It avoids unnecessary verbosity and is front-loaded with the core purpose. However, the lack of detail makes it somewhat under-specified rather than optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a tool with 5 parameters, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not compensate for the missing structured information by explaining parameters, return values, or behavioral details, making it inadequate for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 5 parameters with 0% description coverage, and the tool description does not mention any parameters or their meanings. It fails to explain what 'start_p', 'start_q', 'end_p', 'end_q', and 'max_denom' represent (e.g., numerators and denominators of fractions, maximum denominator limit), leaving all parameters undocumented and unclear to the agent.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Find path through Farey sequence using mediant operations' which provides a general purpose (verb+resource). However, it lacks specificity about what 'path' means or how the mediant operations are applied, making it somewhat vague. It distinguishes from siblings by mentioning Farey sequences, but does not clearly differentiate from other Farey-related tools like 'farey_sequence' or 'farey_neighbors' beyond the 'path' concept.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category tags ('Domain: arithmetic, Category: farey_sequences'), which imply a mathematical context, but it does not provide explicit guidance on when to use this tool versus alternatives. There is no mention of prerequisites, specific use cases, or comparisons to sibling tools like 'farey_sequence' or 'mediant', leaving the agent with no clear usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the Carmichael number limitation, which is useful behavioral context about reliability. However, it doesn't describe what the tool returns (likely a boolean or probability), error conditions, performance characteristics, or what the 'k' parameter controls (iterations/confidence). The description adds some value but leaves critical behavioral aspects unspecified.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
Extremely concise - just one sentence plus domain/category tags. Every word earns its place: names the algorithm, states a key limitation, and provides classification. However, it's arguably too brief given the complete lack of parameter documentation and behavioral details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a primality testing tool with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain what the tool returns, how to interpret results, what the parameters mean, or when to use it versus sibling primality tests. The Carmichael number warning is helpful but insufficient for complete understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It provides no information about parameters 'n' (the number to test) or 'k' (likely iterations/confidence level with default 10). The description doesn't mention parameters at all, leaving them completely undocumented beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Fermat primality test' which names the algorithm, but it doesn't specify what the tool actually does (test if a number is prime using Fermat's method). It mentions 'can be fooled by Carmichael numbers' which is a limitation, not the purpose. The domain/category tags add context but don't define the tool's function.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives. The mention of Carmichael numbers implies a limitation, but doesn't specify when to choose this over other primality tests (like 'aks_primality_test', 'miller_rabin_test', or 'deterministic_miller_rabin' which are sibling tools). No prerequisites or context for usage are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool calculates, with no information about computational complexity, error handling, input constraints (e.g., positive integers, coprime requirements), or what the output represents. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise with two sentences. The first sentence states the purpose, and the second provides domain/category context. There's no wasted text, though it could be more informative. It's appropriately sized for a simple tool but lacks depth.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical tool with specialized domain), no annotations, 0% schema coverage, and no output schema, the description is insufficient. It doesn't explain the Frobenius number concept, input requirements, output format, or usage context. For a tool in a server with many mathematical functions, more completeness is needed to guide proper use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning the parameter 'denominations' is completely undocumented in the schema. The description adds minimal semantics by mentioning 'given denominations' but doesn't explain what denominations are (e.g., array of positive integers), their constraints, or examples. It doesn't compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose ('Calculate the Frobenius number for given denominations') which is clear at a high level, but it doesn't specify what the Frobenius number is or what 'denominations' refer to (e.g., coin denominations in the coin problem). It distinguishes from siblings by mentioning the domain and category, but the purpose remains somewhat vague without domain knowledge.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but doesn't explain what problem this solves, what the input represents, or when an agent should choose this over other mathematical tools. No explicit when/when-not or alternative tools are referenced.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the method (Gaussian elimination) without detailing behavioral traits such as numerical stability, handling of singular matrices, error conditions, or output format. This is inadequate for a tool performing a complex mathematical operation with potential pitfalls.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. It efficiently includes domain and category without unnecessary elaboration. However, the lack of essential details (e.g., parameter info, behavioral traits) means it could be more informative while remaining concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of Gaussian elimination (a numerical method with potential issues like singularity or rounding errors), no annotations, 0% schema coverage, and no output schema, the description is severely incomplete. It fails to address critical aspects like input validation, error handling, or result interpretation, making it inadequate for safe and effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the input schema provides no descriptions for parameters. The description does not add any semantic information about 'matrix_a' or 'vector_b', such as expected formats (e.g., 2D array for matrix, 1D array for vector), data types, or constraints (e.g., square matrix). This leaves parameters completely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve a system of linear equations Ax = b using Gaussian elimination.' It specifies the mathematical operation (solve), the resource (system of linear equations), and the method (Gaussian elimination). However, it does not differentiate from potential siblings like 'matrix_solve_2x2' or 'matrix_solve_3x3', which might handle specific matrix sizes, so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain (linear_algebra.matrices) and category (general), but does not specify when to use this tool versus alternatives (e.g., for general matrices vs. small fixed sizes, or compared to other solvers like 'matrix_solve_2x2'). There is no explicit when/when-not or named alternatives, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'calculate basic Fourier coefficients', which hints at a computational operation, but doesn't disclose behavioral traits like whether it's read-only, if it has side effects, error handling, or performance characteristics. The description is too minimal to adequately inform an agent about how the tool behaves beyond its stated purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two short sentences and no wasted words. It is front-loaded with the core purpose. However, the parenthetical domain/category could be integrated more smoothly, but overall it's efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of harmonic analysis with 3 undocumented parameters, no annotations, and no output schema, the description is incomplete. It doesn't explain what the tool returns, how parameters interact, or any constraints (e.g., array lengths must match). For a tool with mathematical computations, more context is needed to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, and the tool description provides no information about what these parameters mean (e.g., what 'fundamental_freq' represents, how 'harmonics' and 'amplitudes' arrays relate). The description fails to compensate for the lack of schema documentation, leaving parameters entirely unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze harmonic content and calculate basic Fourier coefficients', which provides a general purpose but lacks specificity about what 'analyze' entails or what 'basic' means. It distinguishes from siblings by mentioning 'Domain: trigonometry, Category: wave_analysis', but this is vague and doesn't clearly differentiate from other wave-related tools like 'fourier_coefficients_basic' or 'wave_amplitude_analysis' in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
There are no explicit guidelines on when to use this tool versus alternatives. The domain/category tags imply a context of trigonometry and wave analysis, but this is too broad to guide selection among the many sibling tools in those categories. No exclusions, prerequisites, or comparisons are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only mentions the forecasting method without details on output format, error handling, computational limits, or side effects. This is inadequate for a tool with 6 parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the key information (method and domain). It avoids redundancy and is appropriately sized, though it could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (6 parameters, no annotations, no output schema), the description is insufficient. It does not explain the return values, error conditions, or practical usage, leaving significant gaps for a forecasting tool in a crowded sibling set.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters are undocumented in the schema. The description adds no information about what 'data', 'period', 'alpha', etc., represent or their valid ranges, failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool performs 'Holt-Winters exponential smoothing forecast with trend and seasonality', which specifies the method and domain (timeseries analysis). However, it does not differentiate from sibling tools like 'exponential_smoothing' or 'moving_average_forecast', leaving the purpose somewhat vague in context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or exclusions, leaving the agent without usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It fails to describe any behavioral traits such as what the tool returns (e.g., a boolean, an explanation), error handling, performance characteristics, or any side effects. The description is minimal and doesn't compensate for the lack of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and to the point, consisting of a single sentence that states the tool's purpose and includes domain/category information. It's front-loaded with the main action, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of prime constellations and the lack of annotations, output schema, and low parameter coverage, the description is incomplete. It doesn't provide enough context for a user to understand what the tool does, how to use it correctly, or what to expect in return, making it inadequate for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'pattern' of type array of integers. The description doesn't add any meaning beyond the schema—it doesn't explain what the pattern represents (e.g., differences between primes), valid formats, or constraints. This leaves the parameter semantics largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose as checking if a pattern is admissible for prime constellations, which is clear but somewhat vague. It specifies the domain (arithmetic) and category (prime_patterns), but doesn't explain what 'admissible' means or what constitutes a prime constellation, leaving the exact functionality ambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description doesn't mention any prerequisites, constraints, or sibling tools that might be related (like 'prime_constellations' or 'prime_triplets' in the list), leaving the user without context for appropriate application.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description mentions 'Generate random samples', implying a read-only operation that produces output, but it does not disclose any behavioral traits such as whether the tool is deterministic (e.g., with a seed parameter), what the output format is, or any performance considerations. This leaves significant gaps for a tool with 4 parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately sized and front-loaded with the core purpose in a single sentence. It avoids unnecessary details and is efficient, though it could be slightly more informative without losing conciseness. Every sentence (only one) earns its place by stating the tool's function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a statistical sampling tool with 4 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not provide enough context for an AI agent to understand how to use the tool effectively, such as explaining parameter roles, output format, or usage scenarios. This is inadequate for a tool with multiple inputs and no structured output documentation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the 4 parameters (n, mean, std, seed) are documented in the schema. The description does not add any meaning beyond the schema—it does not explain what these parameters represent, their units, constraints, or default behaviors. For example, it does not clarify that 'n' is the sample size, 'mean' and 'std' define the distribution, or 'seed' controls randomness. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Generate random samples from the normal distribution', which specifies the verb ('Generate random samples') and resource ('normal distribution'), making the purpose clear. However, it does not distinguish this tool from sibling tools like 'uniform_sample' or 'binomial_sample', which also generate random samples from different distributions, leaving the differentiation vague.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('probability') and category ('general'), but this does not help an AI agent decide between this tool and other sampling tools like 'uniform_sample' or 'exponential_sample'. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does ('Find the smallest primitive root modulo n') but provides no information about error conditions (what happens if n has no primitive roots), computational characteristics, input constraints (must n be positive? prime?), or output format. This is inadequate for a tool with mathematical constraints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise - a single sentence plus domain/category tags. It's front-loaded with the core functionality. However, the conciseness comes at the cost of completeness; while there's no wasted text, the description may be too brief for adequate tool understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given that there are no annotations, no output schema, and 0% schema description coverage for the single parameter, the description is insufficiently complete. A mathematical tool for finding primitive roots needs more context about input constraints, error handling, and output format. The description doesn't address these critical aspects, making it inadequate for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the parameter 'n' is completely undocumented in the schema. The description mentions 'modulo n' which gives some context that n is the modulus, but doesn't explain what values are valid (must be integer > 1? prime? odd?), what happens with invalid inputs, or the mathematical meaning of 'primitive root modulo n'. This minimal information doesn't adequately compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Find the smallest primitive root modulo n' which clearly indicates the verb ('Find') and resource ('primitive root modulo n'). However, it doesn't differentiate from sibling tools like 'all_primitive_roots' which would return all primitive roots rather than just the smallest one. The domain/category tags are helpful but don't improve the core purpose statement.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There's no mention of when this tool is appropriate, what prerequisites might be needed (e.g., n must be a prime or have primitive roots), or when to choose other tools like 'all_primitive_roots' from the sibling list. The domain/category tags don't provide usage guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does without any information about side effects, performance, error handling, or output format. For a computational tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise with a single sentence and domain/category tags, making it front-loaded and efficient. However, the brevity leads to under-specification rather than optimal conciseness, as it lacks necessary details for full understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical computation), lack of annotations, no output schema, and low schema description coverage, the description is incomplete. It doesn't cover behavioral aspects, parameter details, or output expectations, making it inadequate for effective tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'window' but doesn't explain what 'data' represents or the expected format (e.g., time series array). It adds minimal value beyond the schema, failing to compensate for the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose as 'Compute rolling variance over a window' with domain/category tags, which is clear but vague. It specifies the verb ('Compute'), resource ('rolling variance'), and scope ('over a window'), but doesn't differentiate from sibling tools like 'variance' or 'rolling_std' beyond the domain/category hints. This makes it adequate but not specific enough for sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: timeseries, Category: analysis', which implies context but doesn't specify scenarios, prerequisites, or exclusions. With many sibling tools for statistical analysis, this lack of explicit usage guidelines leaves the agent without clear direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. The description only states what the tool does without any information on side effects, performance, error handling, or output format. For a tool with no annotations and no output schema, this lack of behavioral detail is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a single sentence that directly states the tool's purpose and context. It is front-loaded and wastes no words, though it could benefit from additional detail. The structure is efficient but under-specified.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of time series analysis, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It fails to explain parameters, output, or behavioral aspects, making it insufficient for effective tool use in this context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It does not mention the parameters 'data' and 'period' at all, leaving their meaning and usage completely undocumented. This is inadequate given the schema's lack of descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose as 'Measure strength of seasonal component in time series' which is clear but somewhat vague. It specifies the domain and category, but does not differentiate from sibling tools like 'detect_seasonality' or 'seasonal_decompose' which likely have related functions. The verb 'measure' is specific, but the scope and method are not detailed.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives. The description mentions the domain and category, but does not indicate prerequisites, typical use cases, or comparisons to sibling tools such as 'detect_seasonality' or 'seasonal_decompose'. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It fails to describe what the tool does (e.g., generates prime numbers), its output format, performance characteristics beyond 'better asymptotic complexity', or any side effects. This leaves critical behavioral information unspecified.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, consisting of a single sentence that identifies the algorithm and its complexity, followed by domain/category tags. It is front-loaded with the algorithm name, but could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It does not explain what the tool returns, how to interpret results, or provide enough context for effective use, especially compared to other prime-related tools in the sibling list.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description does not explain the 'limit' parameter's meaning (e.g., upper bound for prime generation). Without any parameter details in the description, it does not compensate for the low schema coverage, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool implements the 'Sieve of Atkin' algorithm, which is a modern sieve with better asymptotic complexity, and provides domain/category context. However, it does not specify the exact verb (e.g., 'generate primes up to a limit') or clearly distinguish it from sibling tools like 'sieve_of_eratosthenes' or 'incremental_sieve', making the purpose somewhat vague.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description offers no guidance on when to use this tool versus alternatives. It does not mention any specific use cases, prerequisites, or comparisons with other prime-generation tools in the sibling list, leaving the agent with no usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does ('Compare performance') without detailing how it behaves—e.g., whether it runs algorithms, outputs metrics, requires computational resources, or has side effects. This is inadequate for a tool with potential performance implications.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. However, it could be more structured by including key details like parameters or usage context, but it efficiently states the core purpose without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of comparing sieve algorithms, the description is incomplete. No annotations, output schema, or detailed parameter info are provided. The description lacks essential context such as what 'performance' includes, output format, or behavioral traits, making it insufficient for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'limit' with 0% description coverage. The description does not mention parameters at all, failing to explain what 'limit' means (e.g., upper bound for sieve analysis, number of iterations). With low schema coverage, the description does not compensate, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Compare performance of different sieve algorithms' which provides a clear verb ('Compare') and resource ('performance of different sieve algorithms'), but it's vague about what 'performance' entails (e.g., speed, memory usage, accuracy). It distinguishes from siblings by specifying 'sieve algorithms' (Domain: arithmetic, Category: sieve_algorithms), but lacks specificity on which algorithms or metrics are compared.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify prerequisites, context, or exclusions. With many sibling tools available (e.g., sieve_of_eratosthenes, sieve_of_atkin), there is no indication of when this comparative analysis is preferred over individual sieve tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the domain (numerical) and category (series), but does not disclose critical behavioral traits such as input format for the function 'f' and 'derivatives', error handling, computational limits, or output format. This leaves significant gaps for an AI agent.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. It uses only one sentence with no wasted words, making it efficient. However, the domain/category parenthetical adds little value and could be integrated more smoothly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (5 required parameters, 0% schema coverage, no annotations, no output schema), the description is incomplete. It does not compensate for the lack of structured data, failing to explain parameters, behavior, or output. This makes it inadequate for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not explain any of the 5 required parameters ('f', 'derivatives', 'a', 'x', 'n'). It fails to add meaning beyond the schema, leaving parameters completely undocumented. For example, it does not clarify that 'derivatives' should be an array of derivative expressions or what 'n' represents (order of expansion).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool computes a Taylor series expansion of a function around a point, which is a clear purpose. However, it does not differentiate from sibling tools like 'maclaurin_series' (which is a special case of Taylor series) or 'power_series', making it somewhat vague in context. The domain/category tags add minimal value.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. For example, it does not mention when to prefer 'taylor_series' over 'maclaurin_series' (which expands around zero) or other series tools like 'sin_series' or 'cos_series'. The description lacks any context for selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions generating random samples but does not specify output format (e.g., array of numbers), randomness characteristics (e.g., pseudorandom, reproducibility with seed), or any side effects. For a tool with parameters like 'seed' for reproducibility, this lack of detail is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and it efficiently communicates the core function. However, it could be improved by including key usage details without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (4 parameters, no annotations, no output schema), the description is incomplete. It does not explain the parameters, output format, or behavioral traits like randomness control. For a statistical sampling tool, this lack of detail makes it inadequate for users to understand how to invoke it correctly or interpret results.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters (n, a, b, seed) are documented in the schema. The description does not add any meaning beyond the schema; it does not explain what 'n' (sample size), 'a' and 'b' (distribution bounds), or 'seed' (random seed) represent. This leaves all parameters undocumented, failing to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Generate random samples from the uniform distribution', which provides a clear verb ('Generate') and resource ('random samples'), but it is vague about the specific mechanism or context. The domain and category tags ('Domain: probability, Category: general') add some context but do not differentiate it from sibling tools like 'random_array', 'random_float', or 'random_int', which also generate random values. It lacks specificity to distinguish it clearly from these alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention any prerequisites, constraints, or comparative contexts with sibling tools such as 'random_array', 'random_float', or 'random_int'. Without such information, users must infer usage based on the tool name and parameters alone, which is insufficient for effective tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It fails to mention any behavioral aspects such as input validation (e.g., vector dimensions, numeric types), error handling, computational complexity, or output format. This leaves critical operational details unspecified.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence, followed by domain and category. It avoids unnecessary details, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a vector projection operation, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks essential details such as the mathematical formula, return type (e.g., vector or scalar), error conditions, and examples, making it inadequate for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate by explaining parameters. It does not describe 'vector_a' and 'vector_b' beyond their names, failing to clarify their roles (e.g., which is projected onto which), expected formats (e.g., numeric arrays), or constraints (e.g., same length). This adds minimal value over the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose as 'Project one vector onto another' with a domain and category, which is clear but vague. It specifies the verb ('Project') and resource ('vector'), but does not distinguish it from sibling tools like 'scalar_projection' or 'vector_rejection' that might perform related operations, leaving the exact mathematical operation ambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks explicit instructions, prerequisites, or comparisons to sibling tools such as 'scalar_projection' or 'vector_rejection', leaving the agent without context for selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool does, without any information on error handling (e.g., invalid base or number formats), output format, performance, or side effects. This leaves critical behavioral aspects undocumented.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence followed by domain/category tags. It is front-loaded with the core functionality. However, the domain/category tags are redundant with context and could be considered minor waste, but they do not significantly detract from clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 3 parameters with 0% schema coverage, no annotations, and no output schema, the description is insufficient. It does not explain parameter semantics, behavioral traits, or output format. For a tool performing arithmetic in arbitrary bases, more context is needed to use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not explain the parameters at all. It mentions 'two numbers' and 'a specified base' but does not clarify that 'num1' and 'num2' are strings (likely representing numbers in the given base) or what valid ranges or formats are for 'base'. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Add two numbers in a specified base.' It specifies the verb ('Add'), resources ('two numbers'), and a key constraint ('in a specified base'), which distinguishes it from generic addition tools. However, it does not explicitly differentiate from its sibling 'add' (which likely adds numbers in base 10 by default), leaving some ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('number_systems'), but this is too vague to inform usage decisions. There is no mention of when to choose this over the sibling 'add' tool or other base-related tools like 'base_conversion'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, and the description fails to disclose any behavioral traits. It doesn't mention computational complexity, input constraints (e.g., range of n), error handling, or output format. For a tool with no annotations, this leaves the agent with insufficient information about how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose and algorithm type. It's front-loaded with the essential information and wastes no words, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a primality test algorithm, no annotations, 0% schema coverage, and no output schema, the description is severely incomplete. It lacks details on parameters, behavior, output, and usage context, making it inadequate for an agent to effectively use the tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description provides no information about the parameter 'n'. It doesn't explain what 'n' represents (e.g., integer to test), valid ranges, or constraints. With one undocumented parameter, the description fails to compensate for the lack of schema details.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs the AKS primality test, which is a specific algorithm for determining if a number is prime. It distinguishes itself from simpler primality tests like 'is_prime' or 'miller_rabin_test' by mentioning it's deterministic and polynomial-time, though it doesn't explicitly contrast with siblings.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like 'is_prime', 'miller_rabin_test', or 'deterministic_miller_rabin'. The description only states what the algorithm is, not its practical application or trade-offs compared to other primality tests available.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'Analyze aliquot sequence' but doesn't specify what the analysis returns (e.g., sequence terms, cycle detection, length), whether it has computational limits, or error handling. This leaves significant gaps in understanding the tool's behavior for an AI agent.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a single sentence and parenthetical tags, making it easy to parse. However, it could be more front-loaded by specifying the output or key behaviors upfront to improve utility for an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks details on return values, error conditions, performance characteristics, and how parameters affect the analysis, making it insufficient for a tool with mathematical complexity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'starting from n' which clarifies the 'n' parameter, but doesn't explain 'max_steps' (e.g., its purpose as a limit on iterations, default behavior, or implications). With two parameters and no schema descriptions, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze aliquot sequence starting from n' which provides a clear verb ('Analyze') and resource ('aliquot sequence'), but it's somewhat vague about what 'analyze' entails (e.g., compute terms, detect cycles, etc.). It distinguishes from siblings by specifying 'aliquot sequence' (a mathematical concept), but doesn't explicitly differentiate from similar tools like 'collatz_sequence' or 'digital_sum_sequence' beyond the domain/category tags.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description includes domain and category tags ('Domain: arithmetic, Category: special_numbers'), which imply a mathematical context, but there's no mention of prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'collatz_sequence' or 'digital_sum_sequence' that also analyze sequences.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool 'finds' primitive roots, implying a read-only operation, but does not specify output format (e.g., list of integers), computational complexity, or error handling for invalid inputs (e.g., when 'n' has no primitive roots). For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated in the first sentence. The domain/category tags are brief and relevant. There is no wasted verbiage, making it efficient, though it could benefit from additional clarifying details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of modular arithmetic, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what primitive roots are, the return values, or edge cases, which are essential for an AI agent to use the tool correctly in this mathematical context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description does not add any semantic information about 'n', such as its meaning (modulus), constraints (e.g., must be positive integer > 1), or examples. With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose ('Find all primitive roots modulo n') with a specific verb ('Find') and resource ('primitive roots modulo n'), which is clear. However, it does not distinguish this tool from its sibling 'primitive_root' (singular), leaving ambiguity about whether this tool returns all roots versus a single root. The domain/category tags add context but don't clarify this distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention the sibling tool 'primitive_root', nor does it specify conditions like when 'n' must be prime or have primitive roots, or any prerequisites for usage. The agent is left without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the calculation but doesn't describe key behaviors: whether it requires exactly one of period or frequency, how it handles invalid inputs (e.g., negative values), the output format (e.g., radians per second), or error conditions. This leaves significant gaps in understanding how the tool operates beyond the basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence. The domain and category in parentheses add context without verbosity. However, the lack of elaboration on parameters or usage slightly undermines efficiency, as the agent may need to infer or test details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (3 parameters, no annotations, no output schema), the description is incomplete. It doesn't explain the input constraints (e.g., period and frequency are likely mutually exclusive), the output (angular velocity in what units?), or error handling. For a calculation tool with multiple parameters and no structured guidance, this leaves too much undefined for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate for undocumented parameters. It only mentions 'period or frequency' without explaining their roles, units, or interdependencies (e.g., mutual exclusivity). The 'unit' parameter and its enum values ('seconds', 'hz') are not addressed, leaving the agent to guess their meaning and how they relate to the calculation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool calculates angular velocity from period or frequency, which clarifies the purpose. However, it's somewhat vague about the exact mathematical relationship (e.g., ω = 2π/T or ω = 2πf) and doesn't explicitly differentiate from sibling tools like 'frequency_from_period' or other trigonometric/conversion tools, leaving room for ambiguity in sibling tool selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (trigonometry) and category (angle_conversion), but doesn't specify scenarios, prerequisites, or exclusions (e.g., whether it handles only positive values, specific units beyond the schema). Without explicit when/when-not instructions, the agent must infer usage from context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions applying Möbius inversion but doesn't describe what the tool returns, whether it's a read-only computation or has side effects, error conditions, or performance characteristics. For a mathematical tool with three parameters, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence plus domain/category tags. It's front-loaded with the core action and wastes no words. However, this conciseness comes at the cost of completeness, as it omits necessary details about parameters and usage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical transformation tool with three undocumented parameters, no annotations, and no output schema, the description is inadequate. It doesn't explain what the tool returns, how to interpret results, or provide examples. The agent would struggle to use this tool correctly without additional context or experimentation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the three parameters ('formula', 'n', 'description') are documented in the schema. The description only vaguely references 'a function defined by a formula' without explaining what the formula format should be, what 'n' represents, or how the optional 'description' parameter is used. This fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Apply Möbius inversion to a function defined by a formula' which provides a clear verb ('Apply Möbius inversion') and resource ('function defined by a formula'), but it's somewhat vague about what constitutes a 'formula' and doesn't distinguish from siblings like 'mobius_function' or 'mobius_inversion_formula'. The domain/category tags add context but don't fully clarify the specific purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description doesn't mention prerequisites, typical use cases, or how it differs from related tools like 'mobius_function' or 'mobius_inversion_formula'. The agent must infer usage from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool does without describing how it behaves: it does not mention whether it returns a boolean, a proof, or an error for invalid inputs; it does not discuss computational limits, performance, or side effects. This leaves critical behavioral aspects unspecified.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence directly states the tool's purpose, and the second provides domain/category context without unnecessary elaboration. Every word serves a clear purpose, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of verifying a mathematical postulate, the description is insufficient. There are no annotations, no output schema, and the input parameter is undocumented. The description does not explain what the tool returns or how it handles edge cases, leaving significant gaps for an AI agent to understand and use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not add any parameter semantics. It mentions 'given n' but does not explain what n represents (e.g., an integer greater than 1), its valid range, or how it is used in verifying the postulate. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Verify Bertrand's postulate for given n.' It specifies the verb ('verify'), the mathematical concept ('Bertrand's postulate'), and the required input ('given n'). However, it does not explicitly differentiate from sibling tools, as there are no obvious alternatives for verifying this specific postulate in the list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('prime_conjectures'), which implies usage in mathematical contexts. However, it does not specify when to use this tool versus alternatives (e.g., general prime-checking tools like 'is_prime'), nor does it outline prerequisites or constraints (e.g., valid ranges for n).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe how it behaves—e.g., what 'best' means (e.g., closest approximation within denominator limit), whether it returns a single fraction or sequence, error handling, or computational characteristics. This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with domain/category tags—and front-loaded with the core purpose. There's no wasted text, but it might be overly terse given the complexity of the tool. It earns points for efficiency but loses some for potential under-specification.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical approximation with Farey sequences), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the tool returns, how approximations are selected, or any behavioral nuances, making it inadequate for effective use by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, and the tool description adds no information about what 'target' and 'max_denom' mean. Without any parameter semantics in the description, it fails to compensate for the lack of schema descriptions, leaving parameters undocumented and unclear in purpose.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Find best rational approximation using Farey sequences' which provides a clear verb ('Find best rational approximation') and method ('using Farey sequences'), distinguishing it from general approximation tools. However, it doesn't specifically differentiate from sibling tools like 'best_rational_approximation' (which appears to be a similar tool) or other approximation methods in the list, making the purpose somewhat vague in context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), but this doesn't help an AI agent decide between this tool and other approximation or Farey-related tools in the sibling list. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('perform bilinear interpolation') without describing how it behaves: no information on error handling, performance, numerical stability, or output format. For a tool with 10 parameters and no annotations, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with a parenthetical note—and front-loaded with the core purpose. There is no wasted verbiage; every word contributes to defining the tool's domain and category.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (10 parameters, no annotations, no output schema), the description is severely incomplete. It doesn't explain the mathematical operation, parameter meanings, expected output, or any behavioral aspects. For a numerical interpolation tool with many inputs, this minimal description is inadequate for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 10 parameters with 0% description coverage, and the tool description provides no information about any parameters. It doesn't explain what x, y, x1, x2, y1, y2, f11, f12, f21, f22 represent or their roles in bilinear interpolation. This leaves the agent with no semantic understanding beyond the parameter names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform bilinear interpolation for 2D grid data', specifying the verb ('perform'), resource ('bilinear interpolation'), and domain ('2D grid data'). It distinguishes from siblings like 'linear_interpolate' by specifying the 2D grid context, though it doesn't explicitly contrast with them.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance through the parenthetical '(Domain: numerical, Category: interpolation)', which implies it's for numerical interpolation tasks. However, it doesn't specify when to use this tool versus alternatives like 'linear_interpolate', 'cubic_spline_interpolate', or 'lagrange_interpolate' from the sibling list, nor does it mention prerequisites or constraints.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the method ('Binary remainder method') but doesn't disclose behavioral traits like what the output looks like (fraction list? string representation?), whether it handles improper fractions, error conditions, or computational characteristics. For a mathematical decomposition tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with domain/category annotations. It's front-loaded with the core purpose. However, it's arguably too brief given the lack of other information, bordering on under-specification rather than optimal conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of Egyptian fraction decomposition, no annotations, no output schema, and 0% schema coverage for two parameters, the description is incomplete. It doesn't explain the algorithm's behavior, output format, or parameter semantics, leaving significant gaps for the agent to operate effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description doesn't mention the parameters at all, failing to explain what 'numerator' and 'denominator' represent (e.g., positive integers, proper/improper fractions) or any constraints. With two undocumented parameters, the description adds no value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool performs 'Binary remainder method for Egyptian fraction decomposition', which gives a general purpose (Egyptian fraction decomposition using a specific method). However, it's vague about what this method entails compared to other Egyptian fraction tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction' in the sibling list. It doesn't clearly differentiate itself from these alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus other Egyptian fraction tools. The description only mentions the domain and category, but offers no explicit when/when-not instructions or alternatives. The agent must infer usage from the method name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'calculate' but doesn't specify whether this is a read-only computation, what the output format might be, or any constraints like input validation or error handling. For a tool with three parameters and no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a single sentence and includes domain/category tags, which are efficient. However, it could be more front-loaded with critical details; the tags might be better integrated or omitted if not essential. Overall, it's brief but under-specified rather than perfectly structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (involves mathematical sequences with three parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It fails to explain the tool's behavior, parameter meanings, or expected results, making it inadequate for an AI agent to use effectively without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the parameters (coeffs, initial, n) are documented in the schema. The description does not add any meaning to these parameters—it doesn't explain what coeffs represent (e.g., recurrence coefficients), what initial conditions are expected, or what n signifies (e.g., term index). This leaves the parameters largely unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool calculates a Binet-style formula for sequences using characteristic roots, which gives a general purpose. However, it's vague about what specific sequence or recurrence it handles, and it doesn't differentiate from sibling tools like 'solve_linear_recurrence' or 'fibonacci', which might be related. The domain and category tags add some context but don't fully clarify the exact function.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools such as 'solve_linear_recurrence' or 'fibonacci_sequence'. This leaves the agent without clear direction on appropriate contexts for invocation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool calculates without mentioning input constraints (e.g., valid ranges for k, n, p), error handling, performance characteristics, or output format. This is insufficient for a tool with three parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage or unnecessary information, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical calculation with three parameters, no annotations, and no output schema, the description is incomplete. It lacks essential details such as parameter meanings, constraints, example usage, and what the output represents. This makes it inadequate for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not add any parameter semantics. It fails to explain what k, n, and p represent (e.g., k = number of successes, n = trials, p = probability of success) or their valid ranges. With three undocumented parameters, this is a critical gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the cumulative distribution function (CDF) of the binomial distribution.' It specifies the verb ('calculate'), resource ('CDF'), and domain ('probability, Category: general'). However, it does not explicitly differentiate from sibling tools like 'binomial_pmf' or 'binomial_sample,' which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify use cases, prerequisites, or comparisons to related tools such as 'binomial_pmf' or 'normal_cdf.' This leaves the agent without clear usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It only states what the tool calculates without mentioning input constraints (e.g., valid ranges for k, n, p), error handling, or output format. This is inadequate for a tool with three parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's purpose. It is front-loaded and wastes no words, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical tool with three parameters, no annotations, and no output schema, the description is insufficient. It does not cover parameter semantics, behavioral traits, or usage guidelines, making it incomplete for effective agent operation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not explain the parameters k, n, and p beyond what the schema provides (their types). It fails to add meaning such as k being the number of successes, n the number of trials, and p the probability of success, which is crucial for correct usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool calculates the binomial PMF, which is a specific probability function, but it does not differentiate from sibling tools like binomial_cdf or binomial_sample. It mentions the domain and category, which adds some context but doesn't clearly distinguish its unique purpose among related tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like binomial_cdf or binomial_sample. The description lacks any context about appropriate scenarios, prerequisites, or exclusions, leaving the agent without usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('Check tangency relationship') without describing any behavioral traits—such as whether it's a read-only operation, what the output format might be, error conditions, or computational constraints. This is inadequate for a tool with parameters and no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose and includes domain/category context. There is no wasted verbiage, and it is front-loaded with the core functionality. This efficiency is appropriate for a mathematical tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (4 parameters, no annotations, no output schema), the description is incomplete. It lacks essential details: parameter meanings, behavioral traits, output expectations, and usage guidelines. While conciseness is good, the description does not provide enough context for an agent to use the tool effectively without additional external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description provides no information about the four integer parameters (p1, q1, p2, q2). It does not explain what these parameters represent (e.g., numerators and denominators of fractions defining Ford circles) or their constraints. With zero coverage and no compensatory details, the description fails to add value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check tangency relationship between two Ford circles.' It specifies the verb ('Check'), resource ('tangency relationship'), and domain context ('Ford circles', 'arithmetic', 'farey_sequences'). However, it does not explicitly differentiate from sibling tools like 'ford_circle_properties' or 'ford_circles', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit when/when-not instructions or references to sibling tools. This leaves the agent without practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'calculate' but doesn't disclose behavioral traits such as whether it's read-only or mutative, computational complexity, error handling, or output format. For a tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first phrase. The domain/category tags add relevant context without unnecessary elaboration. However, it could be more structured by explicitly separating purpose from usage hints.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of mathematical constant calculations, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't cover input examples, output format, error cases, or computational limits, making it inadequate for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the tool description doesn't explain what 'identity' means (e.g., a string like 'e^(iπ)+1=0' or 'π≈3.14'). Without schema descriptions, the description fails to compensate by clarifying parameter semantics, leaving the agent guessing about valid inputs.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Calculate mathematical constant relationships and identities' with domain/category context, which clarifies the general purpose. However, it's vague about what specific relationships or identities it calculates (e.g., π vs e, Euler's identity) and doesn't distinguish it from sibling tools like 'verify_identity' or 'comprehensive_identity_verification' that might overlap in functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives. The domain/category tags ('arithmetic', 'mathematical_constants') give some implied context, but there's no mention of prerequisites, limitations, or comparisons to sibling tools like 'verify_identity' or 'comprehensive_identity_verification' that might handle similar tasks.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It fails to do so, offering no information on what the tool returns (e.g., convergence rates, error bounds), computational characteristics (e.g., complexity, limitations), or side effects. This leaves the agent with no understanding of the tool's behavior beyond its name.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted text, making it efficient for quick comprehension, though this brevity contributes to gaps in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of mathematical analysis tools, no annotations, 0% schema description coverage, and no output schema, the description is severely incomplete. It does not explain what properties are analyzed, how results are returned, or any behavioral context, making it inadequate for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, meaning the schema provides no parameter documentation. The description adds no semantic information about parameters, such as what 'cf' (continued fraction array) or 'target' (optional target value) represent, their expected formats, or usage examples, failing to compensate for the schema's lack of detail.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze properties of continued fraction convergents.' It specifies the verb ('analyze'), resource ('properties of continued fraction convergents'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools like 'cf_convergence_analysis' or 'convergents_sequence', which are closely related, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools such as 'cf_convergence_analysis' or 'convergents_sequence', leaving the agent without direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does ('Calculate numeric derivative') without any behavioral traits such as computational complexity, error handling, precision limitations, or output format. It lacks critical information needed for an agent to understand how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Calculate numeric derivative using forward difference method (Domain: calculus, Category: general).' It uses only one sentence with no wasted words, efficiently conveying the core purpose and context. Every part of the description earns its place by adding value.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical computation tool with 3 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to provide necessary context such as parameter explanations, behavioral details, or output information, making it inadequate for an agent to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters (func, x, h) have descriptions in the schema. The description does not add any meaning beyond the schema—it doesn't explain what 'func' represents (e.g., a mathematical expression as a string), what 'x' is (the point at which to compute the derivative), or what 'h' is (the step size, though it has a default). This leaves parameters undocumented and unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate numeric derivative using forward difference method.' It specifies the verb ('calculate'), resource ('numeric derivative'), and method ('forward difference'), which is specific. However, it doesn't explicitly distinguish from sibling tools like 'derivative_backward' or 'derivative_central', which are likely similar methods, so it misses full sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('calculus') and category ('general'), but this is too vague to help an agent choose between this and other derivative methods (e.g., backward or central differences) or other calculus tools. There are no explicit when-to-use or when-not-to-use instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does without any behavioral traits such as error handling (e.g., for negative numbers or non-integer inputs), performance characteristics, or output format. This leaves critical gaps for an agent to understand how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Reverse the digits of a number.' This single sentence clearly conveys the core purpose without any wasted words. The additional domain and category information in parentheses is minimal and does not detract from clarity, making it efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a digital operation with potential edge cases), lack of annotations, no output schema, and poor parameter coverage, the description is incomplete. It does not address what the tool returns, how it handles inputs like negative numbers or zero, or any behavioral nuances, making it inadequate for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description adds no information about the parameter 'n'. It does not explain what 'n' represents (e.g., an integer whose digits will be reversed), valid ranges, or handling of edge cases. With low schema coverage, the description fails to compensate, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Reverse the digits of a number.' It specifies the verb ('reverse') and resource ('digits of a number'), making the function unambiguous. However, it does not differentiate from siblings like 'digit_sort' or 'palindromic_numbers', which might involve similar digit manipulations, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('digital_operations'), but this is too vague to inform usage decisions among the many sibling tools in similar categories. No explicit when/when-not or alternative tools are named.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the domain (arithmetic) and category (mobius_functions) but doesn't disclose behavioral traits like what the tool returns (values, formulas, or analysis results), computational complexity, error conditions, or whether it performs read-only analysis versus mutation. The description is too vague about the actual behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two brief clauses, though the parenthetical domain/category information could be considered redundant if available elsewhere. It's front-loaded with the core purpose, but could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical tool with 3 parameters, no annotations, no output schema, and 0% schema coverage, the description is inadequate. It doesn't explain what the tool returns, how parameters interact, or provide examples of typical use cases. The domain/category tags don't compensate for the missing operational details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage for 3 parameters, the description provides no information about parameters. It doesn't explain what 'n', 'function_type', or 'power' represent, their valid ranges, or how they affect the analysis. The description fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze divisor functions using Möbius inversion techniques' which provides a general purpose (analyzing divisor functions) and method (Möbius inversion). However, it doesn't specify what kind of analysis is performed (e.g., computing values, verifying properties, or transforming functions) or distinguish it from sibling tools like 'divisor_count', 'divisor_sum', or 'mobius_inversion_formula'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools related to divisors, Möbius functions, and arithmetic operations, there's no indication of when this specific inversion technique is appropriate versus other divisor analysis tools or the general 'mobius_inversion_formula' tool.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. It mentions 'find common denominators' which implies a read-only calculation, but doesn't specify what the tool actually returns (just the LCM? a list of suitable denominators? something else?), whether there are size/complexity limitations, or what happens with invalid inputs. For a tool with zero annotation coverage, this leaves significant behavioral questions unanswered.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two brief sentences. The first sentence states the purpose, and the second provides domain/category context. There's no wasted verbiage, though the information density could be higher by being more specific about the actual function. The structure is front-loaded with the core purpose first.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given 1 parameter with 0% schema coverage, no annotations, no output schema, and a mathematical tool that could have various interpretations, the description is insufficiently complete. It doesn't explain what the tool returns, how to interpret results, what mathematical operation it performs (LCM calculation? finding denominators meeting certain criteria?), or provide examples. For a tool in a domain with multiple sibling tools, more specificity is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage, so the description must compensate. It mentions 'denominators' in the context of finding common denominators, which aligns with the 'denominators' parameter name, but provides no additional semantic information about what the array should contain (unit fractions? any denominators?), expected format, constraints, or examples. The description adds minimal value beyond what's obvious from the parameter name.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Find common denominators for Egyptian fraction operations' which provides a general purpose (finding common denominators) and domain context (Egyptian fractions). However, it's vague about the specific operation - it doesn't specify whether this calculates LCMs, finds suitable denominators for addition/subtraction, or performs another specific function. The mention of 'operations' is ambiguous without specifying which operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain (Egyptian fractions) and category, it doesn't indicate what specific problem this solves, what prerequisites exist, or when to choose this over other Egyptian fraction tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction' that appear in the sibling list. No explicit when/when-not guidance is provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions analysis but does not specify what properties are examined (e.g., length, uniqueness, optimality), the output format, or any constraints like input validation. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise, consisting of a single sentence followed by domain and category tags. It is front-loaded with the main purpose, though the tags could be integrated more smoothly. There is no wasted text, making it efficient, but it lacks depth that might be necessary for clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of Egyptian fractions, no annotations, no output schema, and low schema coverage, the description is incomplete. It does not compensate for missing structured data by explaining what properties are analyzed, the return values, or usage scenarios. This makes it inadequate for effective tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'denominators' as an array of integers. The description does not explain what this parameter represents (e.g., a list of denominators in an Egyptian fraction), its expected format, or any constraints (e.g., positive integers, sorted). Without this semantic context, the parameter remains poorly defined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze properties of an Egyptian fraction decomposition,' which provides a clear verb ('analyze') and resource ('Egyptian fraction decomposition'). However, it does not distinguish from sibling tools like 'egyptian_fraction_decomposition' or 'egyptian_expansion_lengths,' making it vague about what specific properties are analyzed. The domain and category tags add context but do not refine the purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With siblings such as 'egyptian_fraction_decomposition' and 'shortest_egyptian_fraction,' there is no indication of when this analysis tool is appropriate, leaving usage entirely implied. This lack of explicit context reduces its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool calculates, with no information about error handling, input validation, performance characteristics, or output format. For a mathematical computation tool with zero annotation coverage, this is a significant gap in behavioral transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and it efficiently communicates the core functionality. The structure is clear and to the point.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to address key aspects like parameter details, behavioral traits, or return values. For a tool performing a vector norm calculation, this leaves too many unknowns for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('vector') with 0% schema description coverage. The description does not add any meaning beyond the schema—it does not explain what the vector represents, its expected format (e.g., numeric values), dimensionality, or constraints. With low schema coverage and no compensatory details in the description, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Euclidean norm (L2 norm) of a vector.' It specifies the mathematical operation (calculate), the resource (Euclidean norm/L2 norm), and the input (a vector). However, it does not distinguish this from sibling tools like 'chebyshev_norm' or 'manhattan_norm', which are also vector norm calculations, so it lacks sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (linear_algebra.vectors) and category (general), but this is generic context rather than explicit usage instructions. There is no mention of when to choose Euclidean norm over other norms or related vector operations, nor any prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the mathematical method (Möbius inversion) but doesn't describe what the tool returns (e.g., a single integer value, a formula, or an error for invalid inputs), computational complexity, or edge cases (e.g., handling of n ≤ 0). This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The domain and category tags are included but don't add unnecessary verbosity. However, the lack of additional useful information (e.g., usage guidelines or parameter details) means it could be more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical derivation tool with no annotations, no output schema, and poor parameter documentation, the description is incomplete. It doesn't explain the return value, error conditions, or how it differs from related tools. For a tool performing a non-trivial mathematical operation, this level of detail is inadequate for an agent to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, documenting only that 'n' is an integer. The description adds no information about parameter semantics—it doesn't explain what 'n' represents (e.g., a positive integer for which to compute the totient), valid ranges, or constraints. With low schema coverage, the description fails to compensate, leaving the parameter poorly defined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Derive Euler's totient function using Möbius inversion', which specifies the mathematical operation (derive) and the function (Euler's totient). However, it doesn't clearly distinguish this from sibling tools like 'euler_totient' (which likely computes the totient directly) or 'mobius_inversion_formula' (which likely performs the inversion generally). The domain/category tags add context but don't clarify the specific purpose relative to alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description doesn't mention prerequisites, typical use cases, or comparisons to sibling tools like 'euler_totient' or 'mobius_inversion_formula'. Without this, an agent must infer usage from the name and description alone, which is insufficient for informed tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It fails to describe any behavioral traits: it does not specify what 'neighbors' means (e.g., immediate left/right fractions), the output format, error handling for invalid inputs, or computational characteristics. This leaves the agent with insufficient information to predict the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage. However, the parenthetical domain/category note, while potentially useful, is somewhat redundant with the tool name and could be integrated more seamlessly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical tool with three parameters), lack of annotations, and no output schema, the description is incomplete. It fails to explain key aspects: what 'neighbors' are, the output structure, input constraints, and mathematical context. While conciseness is good, the description does not provide enough information for an agent to use the tool effectively without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the three parameters (p, q, n) are documented in the schema. The description adds no parameter semantics—it does not explain that p/q is the fraction and n is the order of the Farey sequence, nor does it clarify constraints (e.g., p and q coprime, n positive). This leaves parameters entirely unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the neighbors of a fraction in a Farey sequence.' It specifies the verb ('Find'), resource ('neighbors of a fraction'), and domain context ('Farey sequence'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'farey_sequence' or 'farey_fraction_between', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context about typical use cases (e.g., mathematical analysis, approximation problems) or prerequisites (e.g., valid fraction inputs). Without such information, an agent must infer usage from the tool name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only mentions what the tool analyzes (properties of Ford circles) but doesn't disclose any behavioral traits such as computational complexity, output format, whether it's read-only or has side effects, error conditions, or performance characteristics. For a tool with no annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with a single sentence that states the core purpose, followed by domain/category metadata in parentheses. There's no wasted verbiage, and the main purpose is front-loaded. However, the parentheses content could be integrated more smoothly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has no annotations, no output schema, and 0% schema description coverage for its single parameter, the description is incomplete. It doesn't explain what properties are analyzed beyond tangency, what the output looks like, or what the parameter 'n' means. For a mathematical tool with specific domain knowledge required, this leaves significant gaps for an AI agent to understand how to use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% schema description coverage, meaning the parameter is completely undocumented in the schema. The description provides no information about what 'n' represents (e.g., maximum denominator, sequence index, or other context). The description fails to compensate for the complete lack of parameter documentation in the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze properties of Ford circles including tangency relationships', which provides a general purpose (analyze properties) and resource (Ford circles). However, it's vague about what specific properties are analyzed beyond tangency relationships, and it doesn't differentiate from sibling tools like 'ford_circles' which might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain (arithmetic) and category (farey_sequences) in parentheses, but this doesn't constitute practical usage guidance. There's no mention of prerequisites, when-not-to-use scenarios, or explicit alternatives among the many sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'basic' and 'common waveforms,' hinting at limitations, but fails to disclose critical behavioral traits such as supported waveform types, computational constraints, error handling, or output format. This leaves significant gaps in understanding the tool's operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the purpose. There is no wasted text, making it efficient, though it could benefit from additional clarifying details without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (Fourier analysis), lack of annotations, 0% schema coverage, and no output schema, the description is insufficient. It does not explain what the tool returns, how results are structured, or any assumptions about input validity, leaving the agent with inadequate information for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'waveform' and 'n_terms' undocumented. The description does not add any semantic details about these parameters, such as valid waveform strings or the meaning of 'n_terms.' This lack of information fails to compensate for the schema's deficiencies.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Calculate basic Fourier series coefficients for common waveforms,' which provides a clear verb ('Calculate') and resource ('Fourier series coefficients'). However, it does not differentiate from sibling tools like 'fourier_series_approximation' or 'harmonic_analysis,' leaving the scope vague regarding what 'basic' and 'common waveforms' entail.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes a domain ('trigonometry') and category ('wave_analysis'), which imply context but do not explicitly state when to use this tool versus alternatives. No guidance is provided on prerequisites, limitations, or specific scenarios for application, resulting in minimal usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the tool computes an approximation, which implies it is a read-only operation, but does not disclose any behavioral traits such as computational complexity, accuracy limitations, or output format. For a tool with 5 parameters and no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. The domain/category tags are somewhat redundant but do not significantly detract. It is appropriately sized for a tool with this complexity, with no wasted sentences.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (5 parameters, no annotations, no output schema), the description is incomplete. It does not explain what the tool returns, how the approximation is computed, or any constraints on inputs. The lack of parameter semantics and behavioral transparency makes it inadequate for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the 5 parameters are documented in the schema. The description does not add any meaning to parameters like 'f', 'period', 'n_terms', 'x', or 'n_samples'. It fails to compensate for the lack of schema documentation, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Compute Fourier series approximation of periodic function', which provides a clear verb ('Compute') and resource ('Fourier series approximation'). However, it does not distinguish from sibling tools like 'fourier_coefficients_basic' or 'harmonic_analysis', and the domain/category tags add minimal value. The purpose is clear but lacks sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain and category, but this does not help an agent choose between this and related tools (e.g., 'fourier_coefficients_basic', 'harmonic_analysis', or 'maclaurin_series'). There is no explicit or implied context for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. However, it only states what the tool does ('Find intersection points') without describing how it behaves—e.g., whether it returns all intersection points, handles degenerate cases, requires specific input formats, or has error handling. This minimal information is inadequate for a tool with complex inputs, warranting a score of 1.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose without unnecessary words. It is front-loaded with the core functionality, making it efficient and easy to parse, which aligns perfectly with the criteria for a score of 5.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (two nested object parameters with 0% schema coverage, no annotations, and no output schema), the description is severely incomplete. It fails to explain input requirements, behavioral traits, or output format, leaving critical gaps for an AI agent to use the tool correctly. This inadequacy results in a score of 1.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two required parameters ('circle1' and 'circle2') as nested objects. The description does not add any meaning beyond the schema—it does not explain what properties these circles should have (e.g., center coordinates, radius) or how to structure them. With no parameter information in the description to compensate for the schema gap, the score is 1.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Find intersection points') and resource ('two circles'), specifying the domain (geometry) and category (general). It distinguishes this tool from siblings like 'geom_line_intersection' or 'geom_segment_intersection' by focusing on circles, but does not explicitly differentiate from other circle-related tools (e.g., 'geom_circle_area'), making it a 4 rather than a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify prerequisites, typical use cases, or when other tools might be more appropriate. This lack of explicit usage context results in a score of 2.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions efficiency but fails to disclose critical behavioral traits such as computational complexity, memory usage, error handling, or output format. For a tool with three parameters and no output schema, this lack of transparency is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise, consisting of a single sentence that efficiently conveys the core idea. It is front-loaded with the main purpose and includes domain/category tags. However, it could be more structured by explicitly separating purpose from context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (three parameters, no output schema, no annotations), the description is incomplete. It does not explain the algorithm's behavior, parameter roles, or expected results. For a mathematical tool with specific inputs, more detail is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not explain what 'current_primes', 'current_limit', or 'new_limit' represent, their constraints, or how they interact. This leaves the semantics unclear and fails to compensate for the schema's lack of descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool is an 'incremental sieve for extending existing sieve results efficiently', which provides a vague purpose. It specifies the domain (arithmetic) and category (sieve_algorithms), but does not clearly distinguish it from sibling tools like 'sieve_of_eratosthenes' or 'segmented_sieve', nor does it explicitly state what resource (e.g., prime numbers) it operates on. This leaves the purpose somewhat ambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions efficiency but does not specify scenarios, prerequisites, or exclusions. With many sibling tools related to sieves and primes, the lack of comparative context makes it unclear when this tool is the appropriate choice.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'iterative_sequences' in the category, hinting at iterative behavior, but doesn't specify details like convergence criteria, output format (e.g., list of numbers), error handling for invalid inputs, or computational limits. This leaves significant gaps for a tool that likely involves iterative calculations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a single sentence and domain/category tags, making it easy to parse. However, it's under-specified rather than optimally concise—it could benefit from a bit more detail without becoming verbose. The structure is front-loaded with the core purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and two parameters, the description is incomplete. It doesn't explain the iterative process, output format, error conditions, or relation to sibling tools. For a mathematical sequence generator, more context is needed to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter details. The description only mentions 'a number with given digit count', which partially explains 'n' and 'digits' but lacks specifics: what ranges are valid? Are digits the length of n? Does n need to be positive? It adds minimal meaning beyond the bare parameter names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool generates a Kaprekar sequence for a number with given digit count, which provides a basic purpose. However, it's vague about what a Kaprekar sequence entails (e.g., iterative rearrangement of digits) and doesn't distinguish from siblings like 'kaprekar_numbers' or 'kaprekar_constant', which are related but different operations. The domain/category tags add context but don't clarify the specific behavior.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description doesn't mention prerequisites (e.g., valid input ranges), exclusions, or comparisons to sibling tools like 'kaprekar_numbers' (which might list Kaprekar numbers) or 'kaprekar_constant' (which might compute the constant). Usage is implied only by the name and basic description.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool computes a Maclaurin series expansion but doesn't describe any behavioral traits such as computational limits, error handling, output format, or performance characteristics. The description is minimal and lacks details on what the tool actually returns or how it behaves, which is insufficient for a tool with three parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a single sentence, but it's not optimally structured. It front-loads the core purpose but includes parenthetical clarifications and tags that could be integrated more smoothly. While not verbose, the lack of parameter or usage details makes it feel under-specified rather than efficiently informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical series computation with three parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain the parameters, return values, or behavioral context needed for effective use. The description alone is inadequate for a tool of this nature, failing to provide necessary operational details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has three parameters (derivatives, x, n) with 0% schema description coverage, meaning none are documented in the schema. The description adds no information about these parameters—it doesn't explain what 'derivatives' represents (e.g., list of derivative values?), what 'x' is used for, or what 'n' signifies (e.g., number of terms?). This leaves all parameters semantically undefined, failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute Maclaurin series expansion (Taylor series around x=0)', which specifies the verb ('compute') and resource ('Maclaurin series expansion'). It distinguishes from siblings by mentioning the specific type of series (Maclaurin vs. other series tools like binomial_series, power_series, or taylor_series), though it doesn't explicitly contrast them. The domain and category tags add context but don't fully differentiate from all siblings.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('numerical') and category ('series'), but doesn't specify scenarios, prerequisites, or exclusions. For example, it doesn't clarify when to choose this over 'taylor_series' or other series-related tools in the sibling list, leaving usage entirely implicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states what the tool does but provides no information about error handling, performance characteristics, computational complexity, or what happens with invalid inputs. For a calculation tool with zero annotation coverage, this represents a significant gap in behavioral transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise - a single sentence followed by domain/category tags. It's front-loaded with the core functionality and wastes no words. However, the brevity comes at the cost of completeness, making it efficient but potentially underspecified.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a calculation tool with no annotations, no output schema, and 0% parameter schema coverage, the description is inadequate. It doesn't explain what the tool returns, what format the output takes, what errors might occur, or provide any examples. The domain/category tags add minimal context but don't compensate for the missing information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage for the single parameter 'n', and the description provides no additional information about what 'n' represents. While it mentions 'n×n magic squares', it doesn't clarify valid ranges, constraints, or the mathematical meaning of 'n' in this context. For a tool with one parameter and zero schema coverage, the description should compensate but doesn't.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Calculate magic constants for n×n magic squares' which provides a clear verb ('Calculate') and resource ('magic constants'), but it's somewhat vague about what 'magic constants' specifically are. It distinguishes from siblings by mentioning 'magic squares' (a specific domain), but doesn't explicitly differentiate from other mathematical calculation tools in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags ('arithmetic', 'special_numbers') imply a mathematical context, there's no explicit mention of when this tool is appropriate, what prerequisites exist, or what other tools might be better for related calculations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the operation without detailing output format, error handling, performance implications, or any side effects. This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise, consisting of a single sentence that directly states the tool's purpose. It is front-loaded with the core action and includes domain/category tags efficiently, with no wasted words or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (2 parameters, 0% schema coverage, no annotations, no output schema), the description is severely incomplete. It lacks essential details on parameter semantics, behavioral traits, and expected outputs, making it insufficient for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters 'matrix' and 'scalar' are undocumented in the schema. The description adds no semantic information about these parameters, such as matrix format, scalar type constraints, or examples, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Multiply') and resource ('a matrix by a scalar value'), making the purpose specific and understandable. However, it does not explicitly differentiate from sibling tools like 'scalar_multiply' or 'element_wise_multiply', which could cause ambiguity in tool selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('linear_algebra.matrices') and category ('general'), but these are generic and do not specify usage context, prerequisites, or exclusions, leaving the agent without clear selection criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states the method (Cramer's rule) and domain, but fails to describe critical behaviors: input format expectations (e.g., string arrays for numbers), error handling (e.g., singular matrices), output format, or computational constraints. This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that efficiently conveys the core purpose, method, and domain/category. It is front-loaded with essential information and has no wasted words, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (solving linear equations), lack of annotations, 0% schema coverage, and no output schema, the description is severely incomplete. It omits parameter details, behavioral context, usage guidelines, and output expectations, making it inadequate for an agent to use the tool correctly without guesswork.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate by explaining parameters. It does not mention matrix_a or vector_b at all, nor their semantics (e.g., matrix_a as a 2x2 array, vector_b as a 2-element array), expected formats, or examples. This leaves both parameters undocumented, failing to add any meaning beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: solving a 2x2 system of linear equations using Cramer's rule, with the domain and category specified. It uses specific verbs ('solve') and resources ('2x2 system of linear equations'), but does not explicitly differentiate from sibling tools like matrix_solve_3x3, which is a similar tool for 3x3 matrices.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify prerequisites, limitations (e.g., only for 2x2 matrices), or when to choose other tools like matrix_solve_3x3 or gaussian_elimination. This leaves the agent without clear usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates without mentioning any behavioral traits like computational complexity, error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves beyond the basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's function without unnecessary words. It is appropriately sized for a simple mathematical tool, though it could be more front-loaded by immediately highlighting key details like parameter roles.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a mathematical function with 3 parameters), no annotations, no output schema, and low schema description coverage, the description is incomplete. It does not explain the return value, error conditions, or practical usage context, making it inadequate for an agent to fully understand how to invoke and interpret results.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, meaning the schema provides no semantic information. The description does not add any meaning about the parameters (x, mean, std), such as what they represent, their units, or typical values. This fails to compensate for the low schema coverage, leaving parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool calculates the probability density function (PDF) of the normal distribution, which clarifies the verb ('calculate') and resource ('PDF of normal distribution'). However, it does not distinguish this from sibling tools like 'normal_cdf' (cumulative distribution function) or 'normal_sample' (sampling from normal distribution), leaving the specific purpose vague relative to alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('probability') and category ('general'), but this is too generic to help an agent choose between this and other statistical or probability tools in the sibling list, such as 'normal_cdf' or 'exponential_pdf'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions analyzing properties but doesn't disclose behavioral traits such as what the tool returns (e.g., numerical results, plots, or error handling), computational complexity, or any limitations (e.g., assumptions of simple harmonic motion). This leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, with no wasted words. It efficiently states the purpose and context in a single sentence. However, it could be more front-loaded with key details, but overall it's appropriately sized.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (5 parameters, no annotations, no output schema), the description is incomplete. It doesn't explain what the tool outputs, how parameters interact, or any assumptions (e.g., linear damping). For a tool with multiple inputs and no structured guidance, more context is needed to ensure proper use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It lists parameters (amplitude, frequency, phase, damping, mass) but doesn't explain their meanings, units, or roles in the analysis. Without this, users may not understand how to provide correct inputs, making the tool less usable.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze simple harmonic motion and oscillation properties', which provides a general purpose (analyzing oscillations) but lacks specificity about what analysis it performs (e.g., calculating period, energy, or other derived properties). It distinguishes from siblings by mentioning its domain (trigonometry) and category (applications), but doesn't clearly differentiate its exact function from other mathematical tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description mentions 'Domain: trigonometry, Category: applications', which implies a context but doesn't specify scenarios, prerequisites, or comparisons to other tools like 'spring_oscillation' or 'harmonic_analysis' in the sibling list. Usage is implied rather than stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the mathematical domain and category, but does not describe computational behavior such as performance characteristics (e.g., for large n/k), error handling, or output format. The description is minimal and lacks details on what the tool returns or how it operates beyond the basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence plus domain/category tags—with no wasted words. It is front-loaded with the core purpose. However, it is arguably too brief, lacking necessary details for a tool with no annotations and low schema coverage, which slightly reduces its effectiveness despite the efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical partition counting), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain the output (e.g., integer count, possible errors), parameter constraints, or behavioral traits. The domain/category tags add some context but are insufficient for a tool that requires more detailed guidance for correct use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It explains that n and k are integers used for counting partitions, but does not specify their meaning (e.g., n is the integer to partition, k is the maximum number of parts), valid ranges (e.g., non-negative), or constraints (e.g., k ≤ n). This leaves significant gaps in understanding parameter semantics beyond basic types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose ('Count partitions of n into at most k parts'), which is clear but somewhat vague. It specifies the mathematical operation (counting partitions) and the parameters (n, k), but does not differentiate from sibling tools like 'distinct_partitions' or 'restricted_partitions' that also deal with partitions. The domain/category tags are helpful but not part of the core purpose statement.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'distinct_partitions' or 'restricted_partitions', nor does it explain the difference between 'at most k parts' and other partition types. There is no context on typical use cases or constraints, leaving the agent to infer usage from the name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'Analyze periodic structure' but does not specify what the analysis entails, what the output might look like, or any constraints like input validation or performance characteristics. This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two parts: the core function and domain/category. It is front-loaded with the main purpose, but the domain/category annotation adds minimal value and could be considered slightly redundant in this context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of analyzing periodic continued fractions, no annotations, no output schema, and 0% schema description coverage, the description is inadequate. It lacks details on input semantics, expected output, or behavioral traits, making it incomplete for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'numbers' of type array of integers. The description does not explain what 'numbers' represents (e.g., coefficients of a quadratic irrational, a sequence of continued fraction terms) or provide any semantic context, failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze periodic structure of quadratic irrational continued fractions' which provides a specific verb ('Analyze') and resource ('periodic structure of quadratic irrational continued fractions'), but it does not distinguish from sibling tools like 'continued_fraction_expansion' or 'cf_convergence_analysis', making the purpose somewhat vague in context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description includes a domain and category ('Domain: arithmetic, Category: continued_fractions'), but this is too general to offer practical usage instructions or distinguish it from other continued fraction tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does ('Analyze phase relationships') without any information on how it behaves—such as whether it performs calculations, returns data, requires specific inputs beyond parameters, or has side effects. This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with domain and category annotations. It is front-loaded with the core purpose and wastes no words. Every part of the description earns its place by providing essential context without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of wave analysis, the lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not explain what the tool returns, how to interpret results, or provide any behavioral context. For a tool with parameters and mathematical operations, this leaves critical gaps in understanding its functionality.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not mention parameters at all. With two parameters ('phase_diff' and 'frequency'), one required, the description fails to add any meaning beyond the schema. It does not explain what these parameters represent, their units, or how they relate to the analysis, leaving them completely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze phase relationships between waves' with domain and category context. It specifies the verb ('Analyze') and resource ('phase relationships between waves'), making the intent unambiguous. However, it does not differentiate from sibling tools like 'wave_amplitude_analysis' or 'wave_interference', which are related but not explicitly contrasted.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('wave_analysis'), which implies context, but does not specify scenarios, prerequisites, or exclusions. With many sibling tools in wave analysis and trigonometry, the lack of explicit usage guidelines leaves the agent to infer applicability.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool 'finds' numbers, implying a read-only operation, but doesn't specify output format, performance characteristics, error handling, or computational complexity. For a mathematical computation tool with two parameters, this lacks necessary behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point—one sentence plus domain/category tags. It's front-loaded with the core functionality. However, the specialized term 'pluperfect digital invariant numbers' without explanation reduces clarity, slightly undermining efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and two parameters for a specialized mathematical tool, the description is incomplete. It doesn't explain the mathematical concept, parameter roles, return format, or error conditions. The domain/category tags add minimal context, leaving significant gaps for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'up to limit' and includes 'power' in parentheses, hinting at the two parameters, but doesn't explain what 'limit' and 'power' represent mathematically, their valid ranges, or how they interact. This insufficiently compensates for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool finds 'pluperfect digital invariant numbers up to limit' with domain/category context, which clarifies the mathematical operation. However, it doesn't specify what 'pluperfect digital invariant numbers' are (a specialized term) or how they differ from similar sibling tools like 'armstrong_numbers' or 'narcissistic_numbers', leaving the purpose somewhat vague for non-experts.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description includes domain/category tags ('arithmetic', 'special_numbers'), but this doesn't help differentiate it from many sibling tools in the same categories (e.g., 'armstrong_numbers', 'happy_numbers'). There's no mention of prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It fails to describe key behaviors: what the output format is (e.g., list of numbers), whether there are constraints on inputs (e.g., n and s must be positive integers), or any error handling. The description is too sparse to inform the agent about how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two sentences, but it's under-specified rather than efficiently informative. The first sentence states the purpose clearly, but the second adds limited value with domain/category tags that don't enhance tool understanding. It could benefit from more detail without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical sequence generator with 2 parameters), no annotations, and no output schema, the description is incomplete. It lacks essential details: output format, input constraints, and behavioral traits. While the purpose is clear, the tool's full context isn't adequately covered for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema only indicates n and s are integers without explaining their meaning. The description adds minimal semantics: 'first n s-gonal numbers' implies n is the count of numbers to generate and s is the polygon sides. However, it doesn't clarify valid ranges (e.g., s >= 3 for polygonal numbers) or provide examples, leaving significant gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n s-gonal numbers.' It specifies the verb ('Generate'), resource ('s-gonal numbers'), and scope ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'polygonal_number' or 'centered_polygonal_number', which might handle similar figurate numbers.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('figurate_numbers'), which gives some context, but offers no explicit guidance on when to use this tool versus alternatives like 'polygonal_number' (which might check if a number is polygonal) or other sequence generators. No prerequisites or exclusions are stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'evaluate' but doesn't disclose behavioral traits such as what the tool returns (e.g., a numeric sum, convergence status, error handling), performance characteristics, or any limitations (e.g., convergence radius, numerical stability). The description is too minimal to inform safe or effective use.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise with a single sentence and no wasted words. However, it's overly terse—under-specification reduces clarity rather than enhancing efficiency. It could benefit from slightly more detail without becoming verbose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a power series evaluation tool with 3 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain the mathematical operation, expected inputs, output format, or any edge cases. For a tool that likely performs numerical computation, this leaves too many gaps for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description only mentions 'coefficients' generically without explaining their role (e.g., coefficients of the power series terms) or the meaning of 'x' and 'x0' (e.g., evaluation point and center of expansion). It fails to compensate for the lack of schema documentation, leaving parameters largely unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Evaluate power series with given coefficients' which provides a basic verb+resource combination. However, it's vague about what 'evaluate' means (e.g., compute sum, convergence, etc.) and doesn't distinguish it from sibling tools like 'power_series_sum' or 'taylor_series', which appear related. The domain/category tags add minimal context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives like 'power_series_sum' or 'taylor_series' is provided. The description only mentions the domain and category, which doesn't help an agent decide between similar tools. There's no mention of prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool approximates π(x), implying a computational or mathematical operation, but does not disclose behavioral traits like accuracy, performance characteristics, or error handling. This is a significant gap for a tool with no structured annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the purpose directly. The domain and category tags are efficiently appended, though they might be redundant if already implied by the tool's context. No unnecessary sentences are present.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not explain what the approximation entails, how results are returned, or any limitations, making it inadequate for a tool with mathematical complexity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description does not add any parameter semantics. It mentions 'x' in the function notation but provides no details on its meaning, valid range, or units. With one undocumented parameter, the description fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool approximates the prime counting function π(x), which is a clear purpose. However, it does not differentiate from sibling tools like 'prime_count' or 'prime_counting_sieve', which might serve similar or overlapping purposes in prime number analysis. The domain and category tags add context but don't enhance specificity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description lacks any mention of prerequisites, constraints, or comparisons to sibling tools such as 'prime_count' or 'prime_counting_sieve', leaving the agent without usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'analyze' but does not disclose behavioral traits such as whether this is a read-only operation, if it has side effects, performance characteristics, or error handling. The description is too brief to offer meaningful insights beyond the basic action, leaving significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise, consisting of a single sentence followed by domain/category annotations. It is front-loaded with the main purpose and avoids unnecessary words. However, the brevity leads to under-specification, as it omits important details that would enhance usability without adding verbosity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of prime density analysis, the description is incomplete. There are no annotations, no output schema, and low schema coverage (0%). The description does not explain what the tool returns (e.g., density values, statistical summaries) or how to interpret results. For a mathematical tool with two parameters, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters 'limit' and 'interval_size' are undocumented in the schema. The description does not add any meaning to these parameters—it does not explain what they represent, their units, valid ranges, or how they interact. With two required parameters and no clarification, the description fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Analyze prime density in intervals', which provides a verb ('analyze') and resource ('prime density in intervals'), but it's vague about what 'analyze' entails (e.g., compute, compare, visualize). It distinguishes from siblings by specifying the domain and category, but this is minimal differentiation. The purpose is clear enough to understand the general function but lacks specificity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category annotations ('Domain: arithmetic, Category: prime_analysis'), which imply usage in arithmetic contexts for prime analysis, but it provides no explicit guidance on when to use this tool versus alternatives like 'density_analysis' or 'prime_gaps_analysis' among the siblings. There are no instructions on prerequisites, constraints, or comparisons to other tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'sieve-generated primes', hinting at a computational method, but doesn't describe output format, performance characteristics, error handling, or side effects. For a tool with one parameter and no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two sentences, but the second sentence is a domain/category tag that adds minimal value. It's front-loaded with the core purpose, though slightly vague. There's no wasted verbiage, but it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (prime gap analysis), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what the tool returns, how it processes the 'limit', or any algorithmic details. For a mathematical tool with siblings offering similar functions, more context is needed to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'limit' undocumented. The description adds no information about this parameter—it doesn't explain what 'limit' means (e.g., upper bound for primes, number of gaps to analyze) or its expected range/units. With low schema coverage, the description fails to compensate, leaving the parameter's purpose unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze prime gaps using sieve-generated primes', which provides a verb ('Analyze') and resource ('prime gaps'), but it's vague about what 'analyze' entails (e.g., compute gaps, find patterns, or something else). It distinguishes from siblings by mentioning 'sieve-generated primes', but many sibling tools involve primes (e.g., 'prime_gap', 'prime_gaps_analysis'), so differentiation is weak. The domain/category tags add context but don't clarify the specific action.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention prerequisites, typical use cases, or compare it to sibling tools like 'prime_gap' or 'prime_gaps_analysis'. The agent must infer usage from the name and description alone, which is insufficient for effective tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description mentions 'analyze' but doesn't specify what kind of analysis is performed, what the output format might be, whether this is a computational or theoretical analysis, or any behavioral constraints. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise - a single sentence plus domain/category tags. It's front-loaded with the core purpose. However, the domain/category tags might be redundant if the server already categorizes tools. The description could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the mathematical nature of the tool, 1 undocumented parameter, no annotations, and no output schema, the description is incomplete. It doesn't explain what the tool actually returns, how the error analysis is performed, or what mathematical context is assumed. For a tool about the Prime Number Theorem (a sophisticated mathematical concept), more context would be helpful for proper usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (x) with 0% schema description coverage, meaning the parameter is completely undocumented in the schema. The description doesn't mention the parameter at all, providing no semantic information about what 'x' represents (e.g., upper bound, input value, precision parameter). With 0% schema coverage, the description fails to compensate for the missing parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose as 'Analyze the error in Prime Number Theorem approximation' which specifies the verb (analyze) and resource (error in Prime Number Theorem approximation). However, it doesn't distinguish this tool from sibling tools like 'approximation_error' or 'convergence_comparison' that might also analyze errors in mathematical approximations. The domain/category tags provide some context but don't clarify uniqueness.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There are many sibling tools related to approximation errors, prime numbers, and mathematical analysis, but the description doesn't indicate when this specific tool is appropriate versus tools like 'approximation_error', 'prime_counting_function', or 'convergence_comparison'. No usage context, prerequisites, or exclusions are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'explore connections' but does not reveal any behavioral traits such as computational complexity, output format, whether it performs heavy computations, or if it has any side effects. The description is too vague to inform the agent about what to expect beyond the high-level topic.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no unnecessary verbosity or redundant information. However, it could be more structured by including key details about parameters or usage, but as a standalone statement, it is efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity implied by the Riemann Hypothesis and Farey sequences, the description is insufficient. There are no annotations, no output schema, and the single parameter is undocumented. The description does not cover what the tool returns, how results are presented, or any limitations. For a tool dealing with advanced mathematical concepts, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, and the tool description does not mention parameters at all. This leaves the parameter completely undocumented—the agent has no idea what 'n' represents (e.g., sequence length, precision, or index). With low schema coverage, the description fails to compensate by explaining parameter meaning or usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose is to 'Explore connections between Farey sequences and the Riemann Hypothesis', which provides a general domain (arithmetic) and category (farey_sequences). However, it lacks specificity about what kind of exploration it performs (e.g., computational analysis, theoretical insights, or visualization) and how it differs from sibling tools like 'farey_sequence' or 'farey_sequence_properties'. The verb 'explore' is vague compared to more precise alternatives like 'analyze', 'compute', or 'visualize'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify prerequisites, typical use cases, or when other tools might be more appropriate. For example, it doesn't clarify if this is for theoretical exploration, numerical computation, or educational purposes, leaving the agent to guess based on the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'placeholder implementation' which hints at limited functionality but doesn't clarify what that means operationally. It doesn't describe what the tool actually returns (simplified expression, success/failure, error handling), performance characteristics, or limitations of the 'basic' simplification.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and front-loaded with the core purpose. However, the parenthetical elements '(placeholder implementation)' and '(Domain: trigonometry, Category: identities)' add clutter without providing clear value. The structure could be improved by integrating the domain/category information more naturally or removing redundant elements.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a tool with no annotations, no output schema, and 0% parameter documentation, the description is inadequate. It doesn't explain what constitutes a valid trigonometric expression, what simplification techniques are applied, what the output looks like, or how this differs from other trigonometric tools. The 'placeholder implementation' note creates uncertainty rather than providing useful context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage for the single 'expression' parameter, the description provides no additional semantic information. It doesn't specify what format the expression should be in (textual, mathematical notation), what trigonometric functions are supported, or any constraints on the input. The description fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool performs 'Basic trigonometric expression simplification' which provides a general purpose, but it's vague about scope and methods. It doesn't specify what types of simplifications it performs (e.g., identities, angle reduction, factoring) or what qualifies as 'basic'. The parenthetical '(placeholder implementation)' further obscures the actual functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided about when to use this tool versus the many sibling trigonometric tools (e.g., verify_identity, pythagorean_identity, sum_difference_formulas, double_angle_formulas, half_angle_formulas). The domain/category tags ('Domain: trigonometry, Category: identities') are generic and don't help differentiate this specific simplification tool from other identity-related tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. It only states what the tool analyzes without describing what the analysis produces, whether it performs calculations, simulations, or returns specific values like period or frequency. No information about output format, computational behavior, or limitations is provided.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with just one sentence plus domain/category tags. It's front-loaded with the main purpose statement. However, the extreme brevity comes at the cost of completeness rather than being efficiently informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a 4-parameter physics analysis tool with no annotations and no output schema, the description is inadequate. It doesn't explain what the tool returns, how it uses the parameters, or what kind of analysis it performs. The domain/category tags add minimal context but don't compensate for the missing behavioral and output information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage and 4 parameters (3 required), the description provides no information about parameter meanings. It doesn't explain what 'mass', 'spring_constant', 'amplitude', or 'phase' represent in the context of spring oscillation analysis, leaving these completely undocumented beyond their names in the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze spring-mass oscillation system' which provides a clear verb ('Analyze') and resource ('spring-mass oscillation system'), but it's somewhat vague about what specific analysis it performs. It distinguishes itself from siblings by specifying a physics/trigonometry application domain, though many siblings are also mathematical tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: trigonometry, Category: applications' which gives some context but doesn't specify what makes this tool unique among the many mathematical siblings or when it would be preferred over other oscillation or physics-related tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool does ('test... using basic statistical measures') without detailing what 'basic statistical measures' entail, how results are interpreted, whether it's a read-only analysis, error handling, or output format. This leaves critical behavioral aspects unspecified, making it inadequate for informed tool selection.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: a single sentence that directly states the tool's purpose and includes domain/category tags. It is front-loaded with essential information and has no wasted words, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of statistical testing, lack of annotations, no output schema, and incomplete parameter documentation, the description is insufficient. It omits details on behavior, parameters, and results, leaving gaps that hinder effective tool use. While concise, it does not provide the completeness needed for a tool with analytical functions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('data') with 0% description coverage, and the tool description does not mention parameters at all. It fails to explain what 'data' should contain (e.g., a time series array), expected format, or constraints. With no parameter information in the description and low schema coverage, it does not add meaningful semantics beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Test time series for stationarity using basic statistical measures.' It specifies the verb ('test'), resource ('time series'), and method ('basic statistical measures'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., 'detect_trend' or 'differencing'), which are related but not identical, keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance: it mentions the domain ('timeseries') and category ('analysis'), implying context for when to use it. However, it does not specify when to choose this tool over alternatives (e.g., 'detect_trend' or 'autocorrelation'), nor does it outline prerequisites or exclusions. This lack of explicit guidance limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'for analysis' which suggests a read-only calculation, but doesn't specify whether this is a pure mathematical function, what the output format is, or any constraints on inputs. The description is too minimal to provide adequate behavioral context for a tool with 2 parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise - just one sentence plus domain/category tags. While efficient, it may be too brief given the lack of parameter explanation. The structure is clear with the main purpose stated first, but could benefit from more complete information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a 2-parameter mathematical tool with no annotations, 0% schema description coverage, and no output schema, the description is inadequate. It doesn't explain the mathematical operation, parameter meanings, expected output format, or any edge cases. The domain/category tags help minimally, but don't compensate for the missing core information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'digit powers' but doesn't explain what 'n' and 'power' parameters represent. It doesn't specify whether 'n' is the number whose digits are processed, what digit power calculation means mathematically, or any constraints on parameter values.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Calculate sum of digit powers for analysis' which gives a general purpose (verb+resource), but it's vague about what 'digit powers' means mathematically and doesn't distinguish from sibling tools like 'digit_sum' or 'digit_product'. The domain/category tags add some context but don't clarify the specific operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools performing digit operations (digit_sum, digit_product, digital_root, etc.), there's no indication of when this specific digit power sum calculation is appropriate versus other digit manipulation tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'Measure strength' but does not disclose behavioral traits like output format, computational complexity, or any side effects. For a tool with no annotations, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, with no wasted words. It efficiently states the purpose and includes domain/category tags, though it could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (time series analysis), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not provide enough information for an agent to understand how to use it effectively or interpret results.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description does not add any parameter details. It does not explain what 'data' represents (e.g., time series values, required length, format) or any constraints, failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Measure strength of trend component in time series', which provides a clear verb ('Measure') and resource ('trend component in time series'), but it does not differentiate from siblings like 'detect_trend' or 'detrend'. The domain/category tags add context but don't refine the purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives such as 'detect_trend' or 'detrend'. The description lacks any context about prerequisites, scenarios, or exclusions, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what is calculated, with no information about input validation (e.g., vector dimensions, numeric format), error handling, performance characteristics, or output format. For a mathematical tool with three vector parameters, this lack of behavioral context is inadequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded with the core purpose in a single sentence. Every word earns its place: 'Calculate' (verb), 'triple vector product a×(b×c)' (specific operation), and 'Domain: linear_algebra.vectors, Category: general' (context). There is zero wasted text or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical operation with three vector inputs), lack of annotations, 0% schema description coverage, and no output schema, the description is severely incomplete. It doesn't address input requirements, output format, error conditions, or mathematical assumptions (e.g., vector dimensionality). For a tool with three undocumented parameters, this is inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the three parameters (vector_a, vector_b, vector_c) have descriptions in the schema. The tool description adds no parameter semantics beyond naming them in the mathematical expression 'a×(b×c)'. It doesn't explain what constitutes valid vectors (e.g., numeric arrays, required dimensions, format expectations), leaving parameters completely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the triple vector product a×(b×c)', specifying the mathematical operation and domain (linear_algebra.vectors). It distinguishes from sibling tools like 'cross_product' and 'triple_scalar_product' by focusing on the specific triple vector product operation. However, it doesn't explicitly differentiate from all siblings beyond naming the operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain (linear_algebra.vectors) and category (general), but gives no explicit when-to-use instructions, no prerequisites, and no comparison to alternatives like 'cross_product' or 'triple_scalar_product'. The agent must infer usage from the operation name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'collect data' but doesn't disclose behavioral traits like whether this is a read-only operation, computational complexity, memory usage, or output format. The description is minimal and lacks essential context for a tool that likely involves significant computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with domain/category annotations. It's front-loaded with the core purpose. However, it's arguably too brief for a tool with computational complexity and multiple parameters, bordering on under-specification rather than optimal conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, no output schema, and a sibling-rich context with similar tools, the description is incomplete. It doesn't explain what data is returned, how it's structured, performance considerations, or differentiation from siblings. For a mathematical data collection tool, this leaves critical gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'up to limit' which partially explains the 'limit' parameter, but doesn't clarify its meaning (e.g., upper bound for prime search). It doesn't mention the 'return_all_pairs' parameter at all, leaving its purpose undocumented. The description adds minimal value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Collect[s] data about twin prime conjecture up to limit' which provides a general purpose (collecting data on a specific mathematical conjecture). However, it's vague about what specific data is collected (e.g., twin prime pairs, counts, gaps) and doesn't distinguish from similar sibling tools like 'twin_prime_pairs' or 'twin_prime_gaps' that might handle related data.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('arithmetic, prime_conjectures') but doesn't specify prerequisites, constraints, or compare to sibling tools like 'twin_prime_pairs' or 'twin_prime_gaps' that might serve overlapping purposes.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('verify identities') without explaining how it performs the verification, what the output looks like, or any constraints (e.g., numerical precision, domain restrictions). This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted text, though it could benefit from additional context to improve clarity and completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of verifying mathematical identities, the lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain the verification process, output format, or any behavioral nuances, making it inadequate for effective tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the input schema provides no descriptions for parameters 'x' and 'tolerance'. The tool description adds no information about what these parameters represent (e.g., that 'x' is the input value for the identity, 'tolerance' is the numerical precision threshold). This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool's purpose as 'Verify inverse hyperbolic function identities', which is a clear verb+resource combination. However, it does not distinguish this tool from sibling tools like 'verify_hyperbolic_identity' or 'verify_identity', leaving ambiguity about its specific scope within the broader verification tools available.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('trigonometry') and category ('inverse_hyperbolic'), but this is insufficient to inform the agent about specific use cases, prerequisites, or comparisons with sibling tools like 'verify_hyperbolic_identity' or 'comprehensive_identity_verification'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. It only states what the tool does mathematically without describing how it behaves: no information about computational complexity, error handling, output format, or limitations (e.g., range constraints for n and k). This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence plus domain/category tags—with zero wasted words. It's front-loaded with the core purpose and efficiently includes mathematical context. Every element earns its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical complexity, two undocumented parameters, no annotations, and no output schema, the description is incomplete. It identifies the mathematical problem but omits critical details: how results are returned, any constraints on inputs, or what the output represents (e.g., a list of powers or just existence). This leaves significant gaps for an agent to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters n and k are completely undocumented in the schema. The description adds no parameter semantics beyond mentioning 'number' and 'k-th powers'—it doesn't explain what n and k represent, their valid ranges, or examples. With two required parameters and zero coverage, this is insufficient.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Express a number as sum of k-th powers (Waring's problem).' It specifies both the verb ('express') and the mathematical operation, and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools that might involve power-related computations (like 'power_series' or 'sum_digit_powers'), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the mathematical domain ('additive_number_theory') but gives no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools. Users must infer usage from the mathematical context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool analyzes amplitude and phase, implying a read-only computation, but does not detail output format, error conditions, or computational limits. For a tool with no annotations, this leaves significant behavioral gaps, such as whether it returns a single value, a report, or has any side effects.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the purpose, followed by domain and category in parentheses. There is no wasted verbiage, and the structure is efficient. However, it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (wave analysis with 3 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what the analysis entails, the output format, or any behavioral nuances. For a computational tool with undocumented parameters and no structured output, this description is insufficient to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, meaning no parameter details are provided in the schema. The description does not add any parameter semantics—it does not explain what 'amplitude', 'frequency', or 'phase' represent, their units, or valid ranges. This fails to compensate for the low schema coverage, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'Analyze amplitude and phase of a general sinusoidal wave', which provides a clear verb ('Analyze') and resource ('amplitude and phase of a general sinusoidal wave'). However, it does not differentiate from sibling tools like 'amplitude_from_coefficients' or 'phase_shift_analysis', making it somewhat vague in comparison. The domain and category annotations add context but do not enhance specificity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('wave_analysis'), which implies context but does not specify scenarios, prerequisites, or exclusions. Without explicit when-to-use instructions or named alternatives, the agent lacks clear usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It fails to describe any behavioral traits: it does not explain what algorithm is used (e.g., moving average, STL), whether the operation is destructive or reversible, what the output format is (e.g., deseasonalized series, residuals), or any error handling. This leaves the agent with insufficient information to understand the tool's behavior beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence with no wasted words. The domain and category tags are efficiently appended. However, the brevity comes at the cost of completeness, as it omits necessary details for a tool with no annotations or output schema.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of time series analysis, lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to address key aspects such as the algorithm, output format, error conditions, or usage context. While concise, it does not provide enough information for an agent to effectively use this tool in practice.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'time series' and 'seasonal component', which loosely relate to the 'data' and 'period' parameters, but does not explain their semantics (e.g., 'data' as an array of time series values, 'period' as the seasonal cycle length). Without details on units, constraints, or examples, the description adds minimal value beyond the schema's structural information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Remove seasonal component from time series' with the domain and category specified. It uses a specific verb ('Remove') and identifies the resource ('seasonal component from time series'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'detect_seasonality' or 'seasonal_decompose', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites (e.g., needing detected seasonality first), exclusions, or comparisons to siblings such as 'detect_seasonality' or 'seasonal_decompose'. The domain and category tags offer minimal contextual hints but no explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does without explaining how it behaves—e.g., whether it returns a boolean, an error for invalid inputs, performance characteristics, or mathematical assumptions (like the probabilistic nature of Fermat tests). This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that states the core purpose followed by domain/category tags. There is no wasted text, and it efficiently communicates the essential information in a structured manner.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a primality test tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain the tool's behavior, parameter meanings, return values, or error handling, making it insufficient for an AI agent to use the tool effectively without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (n and a) with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'base a' but does not explain what 'n' represents (likely the number to test) or the roles, constraints, or expected ranges of either parameter. It adds minimal value beyond the schema, failing to compensate for the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Fermat primality check for base a.' It specifies the verb ('Perform'), resource ('Fermat primality check'), and scope ('for base a'), making it understandable. However, it does not explicitly differentiate from its sibling 'fermat_primality_test', though the distinction might be implied by the parameter focus.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('primality_tests'), which gives some context. However, it lacks explicit instructions on when to use this tool versus alternatives (e.g., 'fermat_primality_test' or other primality tests like 'aks_primality_test'), prerequisites, or limitations, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does, without mentioning any behavioral traits such as error handling, numerical stability, input validation, or output format. For a mathematical interpolation tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. It efficiently conveys the core purpose and domain/category. However, it could be more structured by separating purpose from context or adding brief usage notes.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical interpolation with three parameters), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on behavior, parameters, output, and usage context, making it inadequate for an AI agent to confidently invoke the tool without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the three parameters (x_points, y_points, x) are documented in the schema. The description doesn't add any parameter semantics beyond what's implied by the tool name—it doesn't explain what these arrays represent, their required lengths, or the meaning of 'x'. This leaves parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Lagrange polynomial interpolation through given points.' It specifies the verb ('perform'), resource ('Lagrange polynomial interpolation'), and scope ('through given points'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling interpolation tools like 'linear_interpolate' or 'cubic_spline_interpolate' beyond mentioning 'Lagrange' specifically.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('numerical') and category ('interpolation'), which gives some context, but doesn't specify when to use Lagrange interpolation versus other interpolation methods available among siblings (like linear or cubic spline interpolation). No prerequisites, alternatives, or exclusions are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what the tool does ('Find prime constellations') without explaining how it behaves: no information about output format, performance characteristics, error conditions, or whether it's computationally intensive. This is inadequate for a tool with parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences. The first sentence states the core purpose, and the second provides domain/category context. There's no wasted verbiage, though the structure could be improved by front-loading more specific guidance about parameter usage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 2 required parameters with 0% schema description coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain what prime constellations are, how patterns should be specified, what the output looks like, or any limitations. For a mathematical tool with potentially complex input semantics, this leaves too many gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. The description mentions 'specified pattern' which hints at the 'pattern' parameter, but doesn't explain what format the pattern should take (e.g., array of offsets like [0,2,6] for prime triplets) or what 'limit' means (e.g., maximum number of constellations to find). It adds minimal value beyond the bare parameter names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find prime constellations of specified pattern.' It includes a specific verb ('Find'), resource ('prime constellations'), and domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'prime_triplets' or 'prime_quadruplets' that might handle specific constellation patterns, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('prime_patterns'), but doesn't specify what constitutes a 'prime constellation' pattern, when this tool is appropriate compared to other prime-related tools, or any prerequisites for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does without any information on performance, limitations, error handling, or output format. For a tool with no annotations, this lack of behavioral context is a significant gap, leaving the agent unaware of how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information is brief and does not detract from clarity. There is no wasted verbiage, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of finding automorphic numbers (which involves mathematical computation), the description is insufficient. There are no annotations, no output schema, and minimal parameter semantics. The description does not explain what automorphic numbers are, how they are returned, or any computational limits, making it incomplete for effective tool use by an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'limit' with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'up to a limit' but does not clarify what 'limit' represents (e.g., maximum value, count), its valid range, or units. This adds minimal value beyond the schema, failing to compensate for the low coverage and leaving the parameter poorly understood.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all automorphic numbers up to a limit.' It specifies the verb ('find'), resource ('automorphic numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly distinguish this tool from its sibling 'is_automorphic_number', which tests individual numbers, leaving room for ambiguity in sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('digital_operations'), but this is generic and does not help an agent decide between this tool and its sibling 'is_automorphic_number' or other related tools. There are no explicit instructions on prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the conversion action without any details about error handling (e.g., invalid digits for the base), performance, input constraints (e.g., base range limits), or output format. This is inadequate for a tool with parameters and no structured safety hints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence followed by domain/category tags—with zero wasted words. It front-loads the core purpose immediately. Every part earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 2 required parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It doesn't address parameter details, behavioral aspects, or output expectations. For a conversion tool with potential complexity (e.g., base validation, digit parsing), this leaves significant gaps for an AI agent to infer correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'base representation string' and 'decimal number', which loosely relate to the 'digits' and 'base' parameters, but doesn't explain what 'digits' represents (e.g., a string of characters in the given base) or any constraints (e.g., base must be between 2 and 36). This adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert a base representation string to decimal number.' It specifies the verb ('Convert'), resource ('base representation string'), and outcome ('decimal number'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'base_conversion' or 'decimal_to_base', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools (e.g., 'base_conversion', 'binary_to_decimal', 'decimal_to_base'), there's no indication of how this tool differs or when it's appropriate. The domain/category tags are generic and don't offer practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does without explaining how it behaves: it doesn't mention what the analysis entails (e.g., calculation method, output format), whether it's a read-only operation, error handling, or any constraints. This leaves critical behavioral traits unspecified, making it inadequate for informed tool selection.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. Every word earns its place with no redundancy or fluff, making it easy to parse and front-loaded with the core functionality. This efficiency is ideal for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical analysis tool with two parameters), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't explain the analysis process, expected results, or any behavioral aspects. While conciseness is high, the tool requires more context for effective use, such as what the output represents or any mathematical assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has two parameters (freq1, freq2) with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'two interfering waves' which implies these parameters represent frequencies, but it doesn't specify units (e.g., Hz), valid ranges, or interpretation (e.g., which is primary). This adds minimal meaning beyond the parameter names, insufficient to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze beat frequency from two interfering waves.' It specifies the verb ('analyze'), resource ('beat frequency'), and context ('from two interfering waves'), making the intent unambiguous. However, it doesn't differentiate from siblings like 'wave_interference' or 'frequency_from_period', which are related but not identical, so it doesn't fully distinguish from alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('trigonometry') and category ('wave_analysis'), which implies a context but doesn't explicitly state when to use this tool versus alternatives like 'wave_interference' or 'frequency_from_period'. There's no mention of prerequisites, exclusions, or specific scenarios, leaving the agent to infer usage based on the name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. It mentions the mathematical domain and category but doesn't describe important behavioral aspects: what the tool returns (e.g., series terms, approximation), convergence conditions, error handling, or computational characteristics. For a mathematical tool with three parameters, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with a single sentence containing the core operation and two contextual tags. There's no wasted verbiage, and the mathematical formula is front-loaded. However, the brevity comes at the cost of completeness, making it more under-specified than optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical complexity, three undocumented parameters, no annotations, and no output schema, the description is incomplete. It identifies the operation but doesn't explain parameter roles, return format, mathematical constraints, or relationship to similar tools. The agent would struggle to use this tool correctly without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description provides zero information about the three parameters (x, alpha, n). With 0% schema description coverage and no parameter explanations in the description, the agent has no semantic understanding of what these parameters represent or how they relate to the binomial series expansion. This is inadequate for a tool with three required parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute binomial series expansion (1+x)^n' with the specific mathematical operation and formula. It distinguishes itself from siblings like 'binomial_cdf' or 'binomial_pmf' by focusing on series expansion rather than probability distributions. However, it doesn't explicitly differentiate from potential series-related siblings like 'power_series' or 'maclaurin_series'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with 'Domain: numerical, Category: series' which implies usage context but doesn't specify when to use this tool versus alternatives like 'power_series' or 'taylor_series'. No explicit when/when-not instructions or named alternatives are provided, leaving the agent with insufficient guidance for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what is calculated, with no information about input constraints (e.g., valid ranges for n and s), error conditions, computational characteristics, or output format. This leaves significant behavioral aspects undocumented.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with zero wasted words. The single sentence directly states the calculation purpose, and the parenthetical domain/category adds useful context without verbosity. This is appropriately front-loaded and efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. While concise, it fails to address key contextual elements: parameter meanings/constraints, behavioral characteristics, output format, or differentiation from related tools. For a mathematical calculation tool with two parameters, this leaves too many gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'nth' and 's-gonal' which correspond to the n and s parameters, but doesn't explain what these parameters represent (e.g., n is position/index, s is number of sides/polygon type) or any constraints (e.g., must be positive integers). This adds minimal semantic value beyond parameter names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth centered s-gonal number.' It specifies the verb ('calculate') and resource ('centered s-gonal number'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'centered_hexagonal_number' or 'polygonal_number', which are related figurate number calculations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category hint ('figurate_numbers') suggests a mathematical context, there's no explicit mention of when this specific centered polygonal calculation is appropriate compared to regular polygonal numbers or other centered figurate tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does without any details on behavior, such as output format (e.g., list of rationals), error handling (e.g., for invalid input), computational limits, or side effects. This leaves the agent with insufficient information to predict how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain and category tags. There is no wasted verbiage or redundancy, making it efficient for quick comprehension. The structure is clear and to the point.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with 1 parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It fails to address key contextual elements: what the output looks like (sequence format), any behavioral traits (e.g., handling of edge cases), or parameter details. The description alone is insufficient for an agent to use the tool effectively without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('cf') with 0% description coverage, meaning the schema provides no semantic information. The description does not compensate by explaining what 'cf' represents (e.g., an array of integers defining the continued fraction coefficients), its constraints (e.g., non-negative, finite length), or examples. This leaves the parameter's meaning and usage unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate sequence of convergents for a continued fraction.' It specifies the verb ('generate'), resource ('sequence of convergents'), and domain context ('continued fraction'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'cf_convergence_analysis' or 'convergent_properties', which could handle related aspects of convergents, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('continued_fractions'), but this is too vague to inform selection among the many sibling tools in the same domain, such as 'cf_convergence_analysis' or 'convergent_properties'. There are no explicit instructions on use cases, prerequisites, or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. However, it only states the operation ('Divide two vectors element-wise') without any behavioral details: it doesn't mention error handling (e.g., division by zero, mismatched vector lengths), output format, numerical precision, or side effects. For a mathematical operation tool with no annotation coverage, this is inadequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: a single sentence with domain and category annotations. It's front-loaded with the core operation and wastes no words. Every part ('Divide two vectors element-wise') directly contributes to understanding the tool's purpose, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, 2 parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It lacks essential context: behavioral traits (error handling, output), parameter details (vector format, constraints), and usage guidelines. While concise, it doesn't provide enough information for reliable tool invocation in a computational context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (vector_a, vector_b) with 0% description coverage in the schema. The description adds no parameter semantics beyond naming them implicitly ('two vectors'). It doesn't explain what the vectors represent, expected formats (e.g., arrays of numbers as strings), constraints (e.g., same length), or examples. With low schema coverage, the description fails to compensate, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Divide two vectors element-wise' with the domain 'linear_algebra.vectors' and category 'general'. It specifies the verb ('Divide') and resource ('two vectors') with the operation type ('element-wise'), making the purpose unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'divide' (which might be scalar division) or 'element_wise_multiply', though the 'element-wise' qualifier provides some implicit distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't specify scenarios, prerequisites, or exclusions. For example, it doesn't clarify if vectors must be same length, handle zero-division cases, or when to choose this over scalar division tools. With many sibling tools (e.g., 'divide', 'element_wise_multiply'), the lack of comparative guidance is a significant gap.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('using Farey sequence properties') but does not describe key behavioral traits such as error handling (e.g., what happens if inputs are invalid or if no fraction exists), performance characteristics, or output format. This leaves significant gaps in understanding how the tool behaves in practice.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no unnecessary information, and it efficiently communicates the core function without waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical tool with 4 parameters, no annotations, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral details, or output expectations. While it states the purpose, it lacks the necessary context for an agent to use the tool effectively, especially in a server with many sibling tools where differentiation is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 4 parameters (p1, q1, p2, q2) with 0% description coverage, meaning the schema provides no semantic information. The description does not explain what these parameters represent (e.g., numerators and denominators of two fractions), their constraints (e.g., q1 and q2 must be non-zero), or their relationships. This lack of parameter semantics makes it difficult for an agent to invoke the tool correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find a fraction between two given fractions using Farey sequence properties.' It specifies the verb ('Find'), resource ('a fraction'), and method ('using Farey sequence properties'), making it understandable. However, it does not explicitly distinguish this tool from sibling tools like 'farey_mediant_path' or 'farey_neighbors', which are also related to Farey sequences, so it misses full sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), but does not specify scenarios, prerequisites, or exclusions. For example, it does not indicate if the input fractions must be in reduced form or if there are constraints on the range, leaving the agent with no usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool performs Fisher's exact test but does not disclose behavioral traits such as output format, error handling, computational limits, or assumptions (e.g., small sample sizes). This is inadequate for a statistical inference tool with zero annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The additional context (Domain: statistics, Category: inference) is brief and relevant. There is no wasted text, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on parameters, output values (e.g., p-value, odds ratio), and usage context. This is insufficient for effective tool invocation by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 5 parameters (a, b, c, d, alpha) with 0% description coverage in the schema. The description does not add any meaning beyond the schema—it does not explain what a, b, c, d represent (e.g., counts in a 2x2 table) or the role of alpha (significance level). This fails to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Fisher's exact test for 2x2 contingency tables to test association between two categorical variables.' It specifies the statistical test, the table format, and the goal (testing association). However, it does not explicitly differentiate from sibling tools like 'chi_square_test' or 'proportion_test', which might also handle categorical data analysis, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (statistics) and category (inference), but does not specify scenarios, prerequisites, or comparisons to siblings like 'chi_square_test' or 'proportion_test'. This leaves the agent without clear usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool does ('analyze gaps'), with no information on output format, computational complexity, error handling, or side effects. For a tool with no annotations, this is a significant gap in behavioral transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted language or unnecessary elaboration, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of mathematical analysis tools, no annotations, no output schema, and low parameter schema coverage, the description is insufficient. It lacks details on what the analysis entails, the format of results, and parameter meaning, leaving critical gaps for the agent to operate effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, and the tool description does not explain what 'n' represents (e.g., order of the Farey sequence, upper bound). Without any parameter semantics in the description, the agent lacks essential context to use the tool correctly, failing to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze gaps between consecutive fractions in Farey sequence.' It specifies the verb ('analyze'), resource ('gaps'), and domain context ('Farey sequence'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'farey_sequence' or 'farey_neighbors', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic, Category: farey_sequences') but offers no explicit instructions on prerequisites, typical use cases, or comparisons with related tools like 'farey_sequence' or 'farey_neighbors'. This leaves the agent without clear direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool solves a system but doesn't disclose behavioral traits such as input format expectations (e.g., string format for congruences), error handling, performance characteristics, or output structure. The description is too sparse to guide the agent effectively on how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two short phrases, but it's under-specified rather than efficiently informative. The first phrase states the purpose clearly, but the second adds minimal value (domain/category). While not verbose, it lacks necessary details, making it less helpful than a more complete yet still concise description would be.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of solving CRT systems, the description is incomplete. No annotations, no output schema, and 0% schema description coverage mean the agent lacks critical information about input format, output structure, error conditions, and limitations. The description doesn't compensate for these gaps, making it inadequate for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no parameter information. It mentions 'congruences' implicitly but doesn't explain what they are, their required format (e.g., 'x ≡ a mod m' strings), or examples. With one required parameter and no schema descriptions, the description fails to compensate, leaving the agent guessing about input semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve generalized CRT system allowing non-coprime moduli.' It specifies the verb ('solve'), resource ('generalized CRT system'), and key capability ('allowing non-coprime moduli'). However, it doesn't explicitly differentiate from its sibling 'crt_solve' (which likely handles only coprime moduli), missing full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('modular_arithmetic'), but offers no explicit advice on when to use this tool versus alternatives like 'crt_solve'. There's no mention of prerequisites, constraints, or typical use cases, leaving the agent with insufficient context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool does without mentioning any behavioral aspects such as error handling (e.g., invalid input formats), performance characteristics, or output format. This leaves significant gaps in understanding how the tool behaves in practice.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and domain. There is no wasted verbiage or unnecessary elaboration, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical calculation with two parameters), lack of annotations, 0% schema coverage, and no output schema, the description is insufficient. It does not cover parameter semantics, behavioral traits, or output details, leaving the agent with inadequate information to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two required string parameters ('p1' and 'p2'). The description does not explain what these parameters represent (e.g., coordinate formats like '(x,y)' or 'x,y'), their expected syntax, or any constraints. This fails to compensate for the lack of schema documentation, making parameter usage ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Euclidean distance between two 2D points.' It specifies the verb ('calculate'), resource ('Euclidean distance'), and domain/context ('geometry, general'). However, it does not explicitly differentiate from sibling tools like 'geom_distance_3d' or 'geom_manhattan_distance', which would require a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance by mentioning the domain ('geometry, Category: general'), but it does not specify when to use this tool versus alternatives (e.g., 'geom_distance_3d' for 3D points, 'geom_manhattan_distance' for Manhattan distance). There are no explicit instructions on prerequisites, limitations, or comparisons to siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the domain and category but fails to describe critical behaviors: what happens if lines are parallel (no intersection), the format of the output (e.g., coordinates), error handling, or computational assumptions. This leaves significant gaps for a tool with two complex input parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first phrase. The additional context ('Domain: geometry, Category: general') is brief but relevant. There is no wasted text, though it could be more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (two nested object parameters, no schema descriptions, no output schema, no annotations), the description is incomplete. It lacks details on parameter formats, output structure, error conditions, and mathematical assumptions. While concise, it does not compensate for the missing structured information, making it insufficient for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two nested object parameters ('line1', 'line2') completely undocumented. The description does not add any parameter semantics—it does not explain what constitutes a 'line' (e.g., two points, slope-intercept form) or the expected structure. This is inadequate for a tool with complex, undefined inputs.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find intersection point of two lines in 2D space.' It specifies the verb ('Find'), resource ('intersection point'), and domain ('2D space'), making it easy to understand. However, it does not differentiate from sibling tools like 'geom_segment_intersection' or 'geom_circle_intersection', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage context by mentioning 'Domain: geometry, Category: general,' but it does not explicitly state when to use this tool versus alternatives (e.g., for lines vs. segments or circles). No guidance on prerequisites, edge cases (e.g., parallel lines), or alternatives is given, leaving the agent with insufficient direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the algorithm (ray casting) but does not disclose behavioral traits such as input format expectations (e.g., coordinate strings), performance characteristics, edge cases (e.g., points on polygon boundaries), or output format. This leaves significant gaps for a tool with two required parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first clause. It efficiently includes the algorithm and domain/category without unnecessary details. However, it could be more structured by explicitly separating purpose from context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (geometry algorithm with two parameters), lack of annotations, no output schema, and 0% schema coverage, the description is incomplete. It does not cover parameter semantics, behavioral details, or output expectations, making it inadequate for reliable tool invocation without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description provides no information about the parameters 'point' and 'polygon'. It does not explain what these parameters represent (e.g., coordinate formats like 'x,y' for point, array of vertices for polygon), their expected data types, or constraints. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a point is inside a polygon' with the specific algorithm 'ray casting'. It distinguishes itself from siblings by specifying the domain (geometry) and category (general), but does not explicitly differentiate from potential similar geometry tools (e.g., geom_polygon_area, geom_distance) in terms of when to use this specific check.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description mentions the domain and category, but does not specify scenarios, prerequisites, or comparisons to sibling tools (e.g., geom_polygon_area for area calculations). Usage is implied by the purpose statement alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates area but does not describe output format, error handling, or computational constraints (e.g., precision, valid vertex ranges). This is inadequate for a tool with three parameters and no output schema, as it leaves key behavioral traits unspecified.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The domain/category tags add minimal but relevant context without verbosity. However, it could be more structured by explicitly separating purpose from usage notes, though it avoids unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (three parameters with 0% schema coverage, no output schema, no annotations), the description is incomplete. It does not explain parameter formats, return values, or error conditions, which are essential for correct tool invocation. The domain/category tags provide some context but are insufficient for a tool with undocumented inputs and outputs.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters p1, p2, p3 undocumented. The description mentions 'three vertices' but does not explain what these parameters represent (e.g., coordinates in a specific format like 'x,y'), their units, or constraints. This fails to compensate for the lack of schema documentation, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the area of a triangle given three vertices.' It specifies the verb ('calculate'), resource ('area of a triangle'), and input type ('three vertices'). However, it does not differentiate from sibling tools like 'geom_polygon_area' or 'geom_circle_area' beyond the domain/category tags, which is a minor gap.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: geometry, Category: general' but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if this is for 2D triangles only or how vertices should be formatted, leaving usage ambiguous.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool performs optimization but doesn't disclose behavioral traits like convergence criteria (implied by 'tolerance' and 'max_iterations' in schema), output format, error handling, or performance characteristics. The description adds minimal context beyond the name, leaving key operational details unspecified.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. It avoids redundancy and wastes no words, though it could be more informative. The structure is clear but minimalistic.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (numerical optimization with 5 parameters), lack of annotations, 0% schema coverage, and no output schema, the description is inadequate. It doesn't explain what the tool returns, how it behaves, or how to interpret results. For a tool with significant parameter and behavioral complexity, this leaves too many gaps for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the 5 parameters (f, a, b, tolerance, max_iterations) are documented in the schema. The description adds no information about parameter meanings, expected formats (e.g., 'f' as a string representing a function), or usage constraints. This leaves parameters entirely unexplained, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform golden section search for univariate function optimization.' It specifies the verb ('perform'), resource ('golden section search'), and domain/category ('univariate function optimization'). However, it doesn't explicitly differentiate from sibling tools like 'gradient_descent' or 'coordinate_descent' which are also optimization methods, though the 'univariate' qualifier provides some implicit distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('numerical') and category ('optimization'), but doesn't specify scenarios where golden section search is preferred over other optimization methods (e.g., for unimodal functions, when derivatives are unavailable). There's no mention of prerequisites or limitations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the domain and category, but doesn't disclose behavioral traits such as what 'all inverse hyperbolic functions' entails (e.g., which functions are included), any constraints (e.g., valid input ranges for x), or the output format. This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two sentences, but the second sentence ('Domain: trigonometry, Category: inverse_hyperbolic') adds little practical value and feels like metadata rather than helpful guidance. It's front-loaded with the core purpose, but could be more structured to include essential details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical tool with no annotations, no output schema, and 0% schema coverage), the description is incomplete. It doesn't explain what 'all inverse hyperbolic functions' means, the return format, or any mathematical constraints, making it inadequate for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It only mentions 'a given x' without explaining what x represents (e.g., a real number, any numeric input) or any semantic details. This adds minimal value beyond the schema, failing to address the coverage gap adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate all inverse hyperbolic functions for a given x.' It specifies the verb ('calculate') and resource ('inverse hyperbolic functions'), and distinguishes it from siblings like 'asinh' (which calculates only one function). However, it doesn't explicitly differentiate from other inverse hyperbolic siblings (e.g., 'acosh', 'atanh'), which are listed separately, so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with 'Domain: trigonometry, Category: inverse_hyperbolic,' but this is vague and doesn't help the agent decide when to use this tool versus alternatives like 'asinh' or 'acosh'. No explicit when-to-use, when-not-to-use, or alternative tools are mentioned, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'relative tolerance comparison' but fails to disclose critical behavioral traits such as the algorithm used (e.g., |a-b| <= max(rel_tol*max(|a|,|b|), abs_tol)), edge cases (e.g., handling of NaN or infinity), or return format (e.g., boolean). This leaves significant gaps for a comparison tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence with no wasted words, and it front-loads the core purpose. However, the inclusion of domain/category tags in parentheses, while informative, slightly detracts from pure conciseness, though it remains well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (numerical comparison with tolerances), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on behavior, parameter meanings, and return values, making it insufficient for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It names 'absolute and relative tolerances' but does not explain parameters 'a', 'b', 'rel_tol', or 'abs_tol' beyond what the schema provides (types and defaults). This adds minimal semantic value, resulting in a baseline score due to inadequate compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool performs 'Relative tolerance comparison using both absolute and relative tolerances', which specifies the verb (comparison) and resource (tolerances). However, it does not clearly differentiate from siblings like 'approximately_equal' or 'close_to_zero', making it vague about its unique scope. The domain/category tags add context but don't refine the purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives like 'approximately_equal' or 'close_to_zero'. The description implies a comparison context but offers no criteria for selection among sibling tools, leaving the agent without practical usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does without any information on output format, error handling, computational limits, or side effects. This is inadequate for a tool with no structured behavioral hints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category note is efficiently appended without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not cover behavioral aspects, parameter details, or output expectations, making it insufficient for effective tool invocation in this context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not add any parameter semantics. It mentions 'digits' but does not explain valid ranges (e.g., positive integers, typical limits like 2-4 digits), constraints, or examples. With low schema coverage, the description fails to compensate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the Kaprekar constant for a given number of digits.' It specifies a verb ('Get') and resource ('Kaprekar constant'), and the domain/category context helps. However, it does not explicitly differentiate from sibling tools like 'kaprekar_numbers' or 'kaprekar_sequence', which is a minor gap.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify prerequisites, constraints, or compare it to related tools (e.g., 'kaprekar_numbers' or 'kaprekar_sequence'), leaving the agent without usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the test is non-parametric and for multiple independent samples, but lacks details on output format (e.g., test statistic, p-value), assumptions, or limitations (e.g., handles ties). For a statistical test with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the tool's name, purpose, and domain in one sentence without unnecessary details. It efficiently conveys the core function, though it could be slightly more structured by explicitly separating purpose from context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test, no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on inputs, outputs, assumptions, and comparisons to siblings. While it states the purpose, it does not provide enough context for effective use without external statistical knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'groups' and 'alpha' undocumented in the schema. The description adds no semantic information about these parameters—it does not explain what 'groups' represents (e.g., array of sample data) or 'alpha' (significance level). With low schema coverage and no compensation in the description, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs a Kruskal-Wallis test, which is a non-parametric ANOVA, and specifies its purpose: to test whether multiple independent samples come from the same distribution. It includes domain and category context, making the purpose explicit. However, it does not differentiate from sibling tools like 'anova_one_way' or 'mann_whitney_u', which are also statistical inference tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the test's purpose but does not indicate when it is appropriate (e.g., for non-normal data or ordinal outcomes) or when other tests like one-way ANOVA or Mann-Whitney U might be better. Without such context, users must infer usage from statistical knowledge alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what the tool calculates, with no information about computational characteristics (e.g., handling of edge cases, performance, memory usage), error conditions, or output format. For a statistical calculation tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: a single sentence with no wasted words. It front-loads the core purpose ('Calculate moving average') and adds only essential domain/category context. Every element earns its place, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (statistical calculation with two parameters), no annotations, 0% schema coverage, and no output schema, the description is insufficient. It doesn't explain what the tool returns, how it handles invalid inputs, or any behavioral nuances. For a tool that performs calculations on data, more context about input expectations and output format is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning neither parameter ('numbers', 'window') has descriptions in the schema. The tool description adds no parameter information beyond what's implied by the tool name. It doesn't explain what 'numbers' represents (e.g., numeric array, data format) or 'window' (e.g., integer size, valid range). With two undocumented parameters, the description fails to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate moving average (rolling average) of a dataset' with domain/category context. It specifies the verb ('calculate') and resource ('moving average of a dataset'), making the function unambiguous. However, it doesn't differentiate from sibling tools like 'simple_moving_average' or 'exponential_moving_average' that appear in the list, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but offers no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools like 'simple_moving_average' or 'exponential_moving_average'. The agent must infer usage from the name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool converts numbers to a specified base, but doesn't describe error handling (e.g., invalid bases), output format (e.g., string representation), or constraints (e.g., base range limits). For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain and category context without unnecessary elaboration. There's no wasted text, and it's structured effectively for quick understanding, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (base conversion), lack of annotations, no output schema, and 0% schema description coverage for two parameters, the description is incomplete. It doesn't explain the return value, error conditions, or parameter details, leaving the agent with insufficient context to use the tool correctly. It should provide more operational details to compensate for the missing structured data.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters 'n' and 'base' are undocumented in the schema. The description adds no information about what these parameters mean (e.g., 'n' as the input number, 'base' as the target radix), their valid ranges, or examples. With two required parameters and zero coverage, the description fails to compensate, making it inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert a number to specified base representation.' It includes a specific verb ('Convert') and resource ('number'), and distinguishes it from siblings like 'base_to_decimal' or 'decimal_to_base' by focusing on general base conversion. However, it doesn't explicitly differentiate from 'base_conversion' or 'add_in_base', which might have overlapping functionality, so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools like 'base_conversion', 'decimal_to_base', and 'binary_to_decimal', there's no indication of when this tool is preferred, what its limitations are, or any prerequisites. It only states the domain and category, which is insufficient for usage decisions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates parametric solutions but does not disclose behavioral traits like output format, error handling, computational limits, or whether it requires specific input constraints (e.g., integer ranges). This is inadequate for a tool with 5 parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain and category annotations are efficiently appended. There is no wasted text, though it could be more informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (5 parameters, no annotations, no output schema), the description is incomplete. It does not explain the tool's behavior, parameter meanings, or output structure. While it states the purpose, it lacks necessary details for effective use, especially compared to richer sibling tools.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description adds no information about parameters. It does not explain what 'a', 'b', 'c', 't_min', or 't_max' represent, their roles in the Diophantine equation, or any constraints. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate parametric solutions to linear Diophantine equation.' It specifies the verb ('Generate'), resource ('parametric solutions'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'solve_linear_diophantine' or 'count_solutions_diophantine', which limits the score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or comparisons with sibling tools such as 'solve_linear_diophantine' or 'diophantine_analysis'. This leaves usage context unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what the tool does ('solve'), without explaining how it behaves—e.g., whether it returns a solution, all solutions, or an error if unsolvable; computational complexity; or any side effects. This is inadequate for a tool with no annotation support.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage or redundancy, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a diophantine equation solver with no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks essential details: behavioral traits (e.g., solution format, error handling), parameter meanings, and output expectations. This leaves significant gaps for the agent to infer correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. The description mentions 'exact postage with given denominations,' which hints at the parameters ('amount' and 'denominations'), but does not clarify their semantics—e.g., that 'amount' is the target postage value, 'denominations' are available stamp values, or constraints like positive integers. This adds minimal value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve the postage stamp problem (exact postage with given denominations).' It specifies the verb ('solve'), resource ('postage stamp problem'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., other diophantine equation solvers like 'solve_linear_diophantine'), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('diophantine_equations'), but does not specify use cases, prerequisites, or comparisons to sibling tools like 'solve_linear_diophantine' or 'diophantine_analysis'. This leaves the agent with minimal contextual direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does ('analyze prime gaps') without explaining what 'analyze' entails—such as whether it returns statistical summaries, lists gaps, or performs computations. It fails to disclose critical behavioral traits like output format, computational complexity, or any constraints, leaving the agent with insufficient information to predict the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise, consisting of a single sentence that directly states the tool's purpose, followed by domain and category annotations. There is no wasted verbiage, and the information is front-loaded, making it easy to parse. This efficiency earns a top score for conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of prime gap analysis, the absence of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what the analysis entails, what results to expect, or any prerequisites or limitations. For a tool with two parameters and no structured output information, the description fails to provide sufficient context for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two required integer parameters ('start' and 'end') undocumented in the schema. The description mentions 'a given range' but does not elaborate on parameter meanings, valid ranges, or units. This adds minimal semantic value beyond the schema, failing to compensate for the coverage gap, especially since the schema itself lacks descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze prime gaps in a given range.' It specifies the verb ('analyze'), resource ('prime gaps'), and scope ('in a given range'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'prime_gap' or 'largest_prime_gap_in_range', which is why it scores a 4 instead of a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('prime_distribution'), but offers no explicit instructions on when to choose this tool over siblings like 'prime_gap' or 'prime_gap_records'. This lack of comparative context limits its utility for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does without describing how it behaves: no information on edge cases (e.g., window size larger than data length), performance characteristics, error handling, or output format. This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded in a single sentence: 'Compute rolling standard deviation over a window (Domain: timeseries, Category: analysis)'. Every word serves a purpose, with no wasted text, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical computation with parameters), lack of annotations, and no output schema, the description is incomplete. It fails to explain behavioral aspects, parameter details, or return values, leaving significant gaps for an AI agent to understand and invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, so the description must compensate. It mentions 'window' but does not explain its semantics (e.g., integer representing the rolling window size) or the 'data' parameter (e.g., array of numbers for time-series). The description adds minimal value beyond the schema's structural information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute rolling standard deviation over a window' with the domain 'timeseries' and category 'analysis'. It specifies the verb ('compute'), resource ('rolling standard deviation'), and scope ('over a window'), but does not explicitly differentiate from sibling tools like 'rolling_variance' or 'standard_deviation'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance with the domain 'timeseries' and category 'analysis', implying it's for time-series data analysis. However, it offers no explicit guidance on when to use this tool versus alternatives like 'rolling_variance', 'standard_deviation', or other statistical tools in the sibling list, nor does it mention prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the bisection method is 'robust and guaranteed', hinting at reliability and convergence, but fails to disclose key behavioral traits: it does not specify output format, error handling (e.g., if signs at endpoints are not opposite), iteration limits (though max_iter is in schema), or that it requires a continuous function with a root in [a,b]. For a numerical method tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first part clearly states the purpose, and the parenthetical additions ('robust and guaranteed') and domain/category tags are brief. However, the domain/category information ('Domain: calculus, Category: general') is somewhat redundant and could be integrated more smoothly, slightly reducing efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a numerical root-finding algorithm with 5 parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It misses critical context: parameter meanings, behavioral details (e.g., convergence criteria), output format, and error conditions. The domain/category tag adds minimal value, leaving the tool inadequately described for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the 5 parameters (func, a, b, tol, max_iter) are documented in the schema. The description adds no parameter semantics—it does not explain what 'func' should be (e.g., a string expression), that 'a' and 'b' are interval endpoints with opposite signs, or the roles of 'tol' (tolerance) and 'max_iter' (maximum iterations). This leaves all parameters undocumented, failing to compensate for the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find root of a function using the bisection method (robust and guaranteed)'. It specifies the verb ('Find root'), resource ('a function'), and method ('bisection'), distinguishing it from other root-finding tools like 'root_find_newton' and 'root_find_secant' in the sibling list. However, it does not explicitly differentiate from those siblings in the description text itself, keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the method is 'robust and guaranteed' and includes a domain/category tag ('Domain: calculus, Category: general'), which implies usage in mathematical contexts. However, it lacks explicit when-to-use instructions, prerequisites (e.g., function must be continuous with opposite signs at endpoints), or comparisons to alternatives like Newton's method. No exclusions or clear context are stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the method ('secant method') and a comparison to Newton's method, but does not disclose behavioral traits such as convergence properties, error handling, output format, or performance characteristics. For a numerical root-finding tool with 5 parameters, this lack of detail is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first. The parenthetical notes add context without unnecessary verbosity. However, the inclusion of 'Domain: calculus, Category: general' is somewhat redundant and could be omitted for better focus, slightly reducing efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a numerical root-finding tool with 5 parameters, no annotations, and no output schema, the description is incomplete. It lacks details on parameter usage, behavioral expectations, and output format. The description does not adequately compensate for the missing structured data, making it insufficient for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the 5 parameters have descriptions in the schema. The tool description does not mention any parameters, their meanings, or how they should be used (e.g., 'func' as a string representation of the function, 'x0' and 'x1' as initial guesses, 'tol' as tolerance, 'max_iter' as iteration limit). This leaves all parameters undocumented, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find root of a function using the secant method'. It specifies the verb ('find root'), resource ('function'), and method ('secant method'), and distinguishes it from Newton's method ('like Newton but without derivative'). However, it does not explicitly differentiate from sibling tools like 'root_find_bisection' or 'root_find_newton' in the sibling list, which would be needed for a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the secant method is 'like Newton but without derivative', which implies usage when derivatives are unavailable. However, it does not specify when to use this tool versus alternatives like bisection or Newton's method, nor does it mention prerequisites or exclusions. No explicit alternatives or context for selection are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the calculation but does not disclose behavioral traits like input format expectations (e.g., numeric arrays vs. strings), error handling, or output specifics. This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's purpose with no wasted words. It is appropriately sized and front-loaded, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It fails to explain parameter meanings, behavioral details, or output format, which are essential for correct tool invocation in this context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter details. The description does not compensate by explaining what 'vector_a' and 'vector_b' represent, their expected formats (e.g., numeric arrays), or any constraints (e.g., same dimension). This leaves parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool calculates scalar projection of one vector onto another, which is a clear purpose. However, it does not differentiate from sibling tools like 'vector_projection' or 'dot_product', which are closely related operations in linear algebra. The domain and category tags add context but do not specify uniqueness.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives such as 'vector_projection' or 'dot_product'. The description lacks any context about prerequisites, typical use cases, or comparisons to sibling tools, leaving the agent without usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool solves a triangulation problem but doesn't describe how it behaves: e.g., what coordinate system is used, whether it returns a single position or multiple solutions, error handling, or assumptions (e.g., 2D vs. 3D). The description is too vague for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a clear main sentence followed by domain/category context. It avoids unnecessary words, though it could be more structured (e.g., separating purpose from domain). The single sentence efficiently conveys the core function without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (trigonometry application with 4 parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on parameter usage, behavioral traits, return values, and error conditions. For a tool that computes positions from distances, this leaves significant gaps for an AI agent to invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the 4 parameters (point1, point2, distance1, distance2) are documented in the schema. The description adds no parameter information beyond the tool's general purpose. It doesn't explain what format 'point1' and 'point2' should be in (e.g., coordinates as strings), what units 'distance1' and 'distance2' use, or how they relate to the reference points.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve triangulation problem to find position from known distances to reference points.' It specifies the verb ('solve'), resource ('triangulation problem'), and outcome ('find position'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools (mostly mathematical functions), though triangulation is distinct in purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry, Category: applications') but doesn't specify prerequisites, typical scenarios, or comparisons to other positioning methods. Without usage context, an agent might struggle to apply it appropriately.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the calculation behavior but lacks critical details: input domain constraints (e.g., value must be between -1 and 1), error handling, output range (typically 0 to 180 degrees), or precision. For a mathematical tool with no annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. The additional domain/category context is brief and relevant. No wasted words, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits essential details: parameter semantics, input constraints, output format, and error conditions. For a mathematical function, this leaves significant gaps for an AI agent to use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no parameter information beyond the schema. It does not explain what 'value' represents (e.g., cosine value), its valid range, or units. With one undocumented parameter, the description fails to compensate for the schema's lack of descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arccosine with result in degrees.' It specifies the mathematical function (arccosine), the output unit (degrees), and provides domain/category context. However, it does not explicitly differentiate from its sibling 'acos' (which likely returns radians), missing full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (trigonometry) and category (inverse_functions), but offers no explicit when/when-not instructions or references to sibling tools like 'acos' or 'asin_degrees' for comparison.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates arccotangent but does not disclose behavioral traits such as input validation (e.g., handling of invalid values like zero), output range (e.g., radians or degrees), error handling, or performance characteristics. This is a significant gap for a mathematical function tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no unnecessary information, making it efficient. However, it could be slightly improved by structuring it to include key details like parameter guidance.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical function with no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks essential context such as output format, error conditions, and mathematical properties (e.g., branch cuts or range of results). This makes it inadequate for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The description does not add any meaning beyond the schema—it does not explain what 'value' represents (e.g., a real number, expected units, or domain restrictions like avoiding zero for cotangent). With low schema coverage, the description fails to compensate, leaving the parameter semantics unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arccotangent (inverse cotangent).' It specifies the mathematical function and its domain (trigonometry) and category (inverse_functions). However, it does not explicitly differentiate from sibling tools like 'acoth' (inverse hyperbolic cotangent) or 'atan' (inverse tangent), which could be relevant alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify use cases, prerequisites, or comparisons to sibling tools like 'acoth' or 'atan'. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a statistical test but does not describe what the tool returns (e.g., F-statistic, p-value), assumptions (e.g., normality, homogeneity of variance), or side effects (e.g., computational cost, error handling). For a statistical inference tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. It avoids redundancy and waste, though it could be more structured (e.g., separating purpose from domain/category). The brevity is appropriate, but the lack of elaboration on usage or parameters slightly limits its effectiveness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of statistical testing, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain what the tool returns, key assumptions, or how to interpret results. For a tool with 2 parameters and no structured support, the description should provide more context to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not explain the parameters: 'groups' (array of strings representing data groups) and 'alpha' (significance level, default 0.05). It mentions 'multiple groups' but does not clarify parameter roles, formats, or constraints. With low schema coverage, the description fails to compensate, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform one-way ANOVA (Analysis of Variance) to test whether means of multiple groups differ significantly.' It specifies the verb ('perform'), resource ('one-way ANOVA'), and statistical goal. However, it does not explicitly differentiate from sibling tools (e.g., kruskal_wallis, t_test_two_sample) that also compare group means, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('statistics') and category ('inference'), implying usage for statistical hypothesis testing. However, it lacks explicit when-to-use criteria (e.g., for normally distributed data, comparing ≥3 groups), when-not-to-use alternatives (e.g., non-parametric tests like kruskal_wallis), or prerequisites. This leaves the agent with insufficient context for optimal tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks critical details: it doesn't specify what 'approximation error' means (e.g., absolute vs. relative error), how the error is calculated, what the output format is, or any limitations (e.g., supported algorithms, term limits). For a tool with two parameters and no output schema, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain and category tags are appended efficiently. There's no wasted text, though it could benefit from additional context without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (two parameters, no annotations, no output schema), the description is incomplete. It doesn't explain how to interpret the results, what algorithms are available, or any error-handling behavior. For a tool that likely outputs numerical error values, the lack of output schema means the description should at least hint at the return type, which it doesn't.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'various pi algorithms' and 'approximation error', which hints at the 'method' parameter (algorithm type) and 'terms' parameter (possibly number of terms in a series). However, it doesn't explain what values 'method' accepts, what 'terms' represents (e.g., iterations, precision), or their relationships. This leaves parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate approximation error for various pi algorithms.' It specifies the verb ('calculate'), resource ('approximation error'), and domain context ('pi algorithms'). However, it doesn't explicitly distinguish this tool from sibling tools that might also involve pi calculations or error analysis, such as 'compute_pi_chudnovsky' or 'compute_pi_leibniz', which could be used for similar purposes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'various pi algorithms' but doesn't specify which algorithms are supported, when this tool is appropriate compared to direct pi computation tools, or any prerequisites. The domain and category tags ('arithmetic', 'mathematical_constants') are too generic to offer meaningful usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the computation action but does not describe output format, error handling, performance characteristics, or limitations (e.g., numerical precision, input constraints). For a mathematical tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted verbiage, and it efficiently communicates the core purpose. However, the inclusion of domain and category in parentheses, while informative, slightly disrupts flow but does not significantly detract from clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical computation tool with 3 undocumented parameters, no annotations, and no output schema, the description is incomplete. It lacks details on parameter meanings, formula used, output format, and error conditions. The description does not provide enough context for reliable tool invocation without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters (a, d, n) with 0% description coverage, meaning no parameter details are documented in the schema. The description does not explain what these parameters represent (e.g., first term, common difference, number of terms), their units, or valid ranges. It fails to compensate for the schema's lack of documentation, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute arithmetic series sum of terms in arithmetic progression.' It specifies the verb ('compute'), resource ('arithmetic series sum'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'arithmetic_sum' or 'arithmetic_sequence', which appear related, leaving room for ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('numerical') and category ('series'), but does not specify prerequisites, exclusions, or compare it to sibling tools such as 'arithmetic_sum' or 'geometric_series'. This lack of contextual usage information limits its effectiveness for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation and output format but does not mention input constraints (e.g., domain of arcsine: -1 ≤ value ≤ 1), error handling, precision, or performance characteristics. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core functionality in the first phrase. The additional domain/category context is brief and relevant. There is no wasted verbiage, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on input constraints, output format, error conditions, and sibling differentiation. While the purpose is clear, the overall context for reliable use is insufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, documenting only that 'value' is a required number. The description adds no parameter semantics—it does not explain what 'value' represents (e.g., sine ratio), valid ranges, or units. With low schema coverage, the description fails to compensate, leaving the parameter poorly defined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arcsine with result in degrees.' It specifies the mathematical operation (arcsine), the output unit (degrees), and the domain/category (trigonometry, inverse_functions). However, it does not explicitly differentiate from its sibling 'asin' (which likely returns radians), though the '_degrees' suffix implies this.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify use cases, prerequisites, or comparisons to siblings like 'asin' (radians output) or other inverse trigonometric functions. The agent must infer usage from the name and context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool computes but does not describe output format, error conditions, performance characteristics, or any side effects. For a computational tool with no annotations, this is a significant gap in transparency about how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted verbiage, and it efficiently communicates the core purpose. However, it could be slightly improved by structuring into multiple sentences for clarity, but it's still highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It does not explain parameter semantics, output format, or behavioral details. For a computational tool in a domain like timeseries analysis, more context is needed to ensure the agent can use it effectively without guesswork.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the input schema provides no descriptions for parameters 'data' and 'lag'. The description does not compensate by explaining what 'data' should contain (e.g., a time series array) or the meaning of 'lag' (e.g., integer shift). Without this, the agent lacks semantic understanding of the parameters, making it hard to use correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute autocorrelation at a given lag - measures correlation between series and itself shifted by lag periods'. It specifies the verb ('compute'), resource ('autocorrelation'), and provides a concise mathematical definition. However, it does not explicitly differentiate from sibling tools like 'correlation' or 'partial_autocorrelation', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('timeseries') and category ('analysis'), which implies a context, but does not specify scenarios, prerequisites, or comparisons to similar tools like 'correlation' or 'partial_autocorrelation' in the sibling list. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the algorithm used but does not describe key behaviors: computational complexity, typical use cases (e.g., for large numbers), limitations (e.g., memory usage), or output format. This is inadequate for a tool that performs a non-trivial mathematical computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it directly states the tool's purpose in one sentence, with no wasted words. The parenthetical domain/category adds minimal but relevant context without redundancy. Every sentence earns its place, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of the algorithm, lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain the tool's behavior, parameter meanings, or result format, which are essential for an AI agent to use it correctly. The conciseness comes at the cost of necessary detail.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters (g, h, n) with 0% description coverage in the schema. The description does not explain what these parameters represent (e.g., g as generator, h as target, n as modulus), their constraints, or how they relate to the discrete logarithm problem. This leaves the parameters entirely undocumented, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve discrete logarithm using Baby-step Giant-step algorithm.' It specifies the verb ('solve'), resource ('discrete logarithm'), and method ('Baby-step Giant-step algorithm'), which is more specific than just the tool name. However, it does not explicitly differentiate from sibling tools like 'discrete_log_naive', though the algorithm name implies a distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the algorithm and domain/category ('arithmetic, modular_arithmetic'), but does not specify scenarios, prerequisites, or comparisons with sibling tools such as 'discrete_log_naive'. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the base range (2-36) but does not describe error handling (e.g., invalid bases or number formats), output format, performance characteristics, or side effects. For a tool with three parameters and no annotations, this is a significant gap in transparency about how the tool behaves in practice.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's function. It avoids unnecessary words and efficiently communicates the core purpose. However, the inclusion of domain and category in parentheses, while potentially useful, slightly detracts from pure conciseness without adding operational value.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (three required parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameter formats, error conditions, output structure, and differentiation from sibling tools. For a base conversion operation that could involve validation and formatting nuances, this minimal description does not provide enough context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters ('number', 'from_base', 'to_base') are documented in the schema. The description only implies that 'number' is a string and bases are integers 2-36, but it does not explain format expectations (e.g., alphanumeric characters for bases >10), validation rules, or examples. This leaves the semantics of all three parameters inadequately defined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting a number between bases 2-36. It specifies the verb ('convert'), resource ('number'), and scope ('any base to any other base (2-36)'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'base_to_decimal' or 'decimal_to_base', which are more specific base conversion tools in the same domain.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance, only mentioning the domain ('arithmetic') and category ('number_systems'). It does not specify when to use this tool versus alternatives like 'base_to_decimal' or 'decimal_to_base', nor does it outline prerequisites, constraints, or typical use cases. This lack of contextual guidance leaves the agent with insufficient information to choose appropriately among similar tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates bearing, implying a read-only operation, but does not detail output format (e.g., degrees, radians), error handling (e.g., for invalid coordinates), or computational traits (e.g., precision, range). For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first: 'Calculate bearing (compass direction) from one point to another.' The additional domain and category tags are brief and relevant. There is no wasted verbiage, making it efficient, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (4 parameters, no annotations, no output schema), the description is incomplete. It lacks details on output (e.g., bearing in degrees), error conditions, and usage context relative to siblings. While concise, it does not provide enough information for an agent to confidently invoke the tool without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters (lat1, lon1, lat2, lon2) are undocumented in the schema. The description mentions 'from one point to another,' hinting at coordinate inputs, but does not explain parameter roles, units (e.g., degrees), or constraints (e.g., valid ranges). It adds minimal semantic value beyond the schema, failing to compensate for the low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate bearing (compass direction) from one point to another.' It specifies the verb ('calculate'), resource ('bearing'), and context ('from one point to another'), making the function unambiguous. However, it does not explicitly differentiate from siblings like 'geom_great_circle_distance' or 'angle_difference', which might handle related calculations, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance on when to use this tool. It includes domain and category tags ('Domain: trigonometry, Category: applications'), which imply context but do not specify when to choose this over alternatives like 'geom_great_circle_distance' for distance or 'angle_difference' for angular computations. No explicit when-to-use or when-not-to-use instructions are given, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the method ('resampling') and statistics ('mean or median'), but lacks critical behavioral details: computational intensity (e.g., 'n_bootstrap' default 1000 may be heavy), assumptions (e.g., data independence), output format, or error handling. For a statistical tool with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. It avoids redundancy and wastes no words, though it could be more structured (e.g., separating purpose from context). The domain/category note is concise but could be integrated better.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits parameter explanations, behavioral traits (e.g., performance, assumptions), and output details. For a 4-parameter statistical tool with resampling complexity, this leaves the agent under-informed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It only vaguely references 'statistic (mean or median)' and 'resampling', but does not explain the four parameters (data, statistic_func, n_bootstrap, confidence_level) or their semantics (e.g., what 'statistic_func' accepts beyond defaults). The description adds minimal value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate bootstrap confidence interval for a statistic (mean or median) using resampling.' It specifies the verb ('calculate'), resource ('bootstrap confidence interval'), and method ('resampling'), and distinguishes it from siblings like 'confidence_interval_mean' by mentioning bootstrap resampling. However, it doesn't explicitly differentiate from other statistical inference tools beyond naming the domain/category.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('inference'), but does not specify scenarios, prerequisites, or compare it to sibling tools like 'confidence_interval_mean' or 'permutation_test'. Without explicit usage context, the agent must infer applicability.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool tests for Carmichael numbers but doesn't disclose behavioral traits such as performance characteristics (e.g., computational complexity for large inputs), error handling (e.g., for non-integer or negative inputs), or output format. The description is minimal and lacks operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: a single sentence that directly states the tool's purpose. There's no wasted verbiage, and it efficiently communicates the core functionality. However, it could be more structured by including usage hints or parameter details without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (testing for Carmichael numbers involves advanced primality concepts), lack of annotations, no output schema, and minimal parameter semantics, the description is incomplete. It doesn't explain what a Carmichael number is beyond 'pseudoprime to all bases', nor does it cover return values, error cases, or performance considerations, leaving significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter 'n' with 0% description coverage (no schema descriptions). The tool description adds no parameter semantics—it doesn't explain what 'n' represents (e.g., a positive integer), valid ranges, or constraints. With low schema coverage, the description fails to compensate, leaving the parameter meaning unclear beyond the type 'integer'.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Test if a number is a Carmichael number (pseudoprime to all bases).' It specifies the verb ('Test'), resource ('a number'), and domain context ('advanced_primality'). However, it doesn't explicitly differentiate from sibling tools like 'is_carmichael_number' (which appears in the list), though the distinction might be in implementation details not described.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic, Category: advanced_primality') but doesn't specify prerequisites, when to prefer it over other primality tests (e.g., 'aks_primality_test', 'miller_rabin_test'), or any limitations. Usage is implied by the purpose statement alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates parameters and properties but does not describe what specific parameters or properties are returned, whether the calculation is deterministic, any error handling, or performance characteristics. For a mathematical tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain/category information is included parenthetically, adding context without unnecessary elaboration. There is no wasted verbiage, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical calculation tool with 2 undocumented parameters, no annotations, and no output schema, the description is insufficient. It does not explain what the tool returns (e.g., curve length, sag, tension), how results are formatted, or any mathematical assumptions. This leaves the agent without enough information to use the tool effectively in context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has two parameters ('a' and 'x') with 0% description coverage, meaning the schema provides no semantic information. The description does not explain what 'a' and 'x' represent (e.g., 'a' might be the scaling parameter, 'x' the independent variable), their units, or valid ranges. This fails to compensate for the lack of schema documentation, leaving parameters largely undefined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate catenary curve parameters and properties.' It specifies a verb ('calculate') and resource ('catenary curve parameters and properties'), and includes domain/category context ('trigonometry, hyperbolic'). However, it does not explicitly distinguish this tool from sibling tools like 'hyperbolic_functions' or 'verify_hyperbolic_identity', which might also involve hyperbolic functions or curves.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools (e.g., 'hyperbolic_functions' or other curve-related tools). The domain/category tags ('trigonometry, hyperbolic') imply a context but do not offer explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates without mentioning any behavioral traits such as input validation (e.g., handling negative integers), performance characteristics, error handling, or output format. For a tool with no annotation coverage, this leaves significant gaps in understanding how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. It avoids unnecessary details and wastes no words, making it efficient for quick understanding. However, the inclusion of domain and category in parentheses, while helpful, slightly detracts from absolute minimalism.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a mathematical calculation with one parameter), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what a centered square number is, provide examples, describe the output, or address potential edge cases. For a tool with no structured support, more contextual information is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description does not add any semantic meaning beyond the schema—it doesn't explain what 'n' represents (e.g., the index of the centered square number), valid ranges, or examples. With low schema coverage, the description fails to compensate, leaving the parameter's purpose unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth centered square number.' It specifies the verb ('calculate') and resource ('centered square number'), and distinguishes it from siblings by mentioning the domain 'arithmetic' and category 'figurate_numbers', which helps differentiate it from other mathematical tools. However, it doesn't explicitly contrast with similar tools like 'centered_hexagonal_number' or 'centered_polygonal_number', preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't specify scenarios where centered square numbers are applicable, nor does it refer to sibling tools like 'centered_hexagonal_number' or 'polygonal_number' for comparison. Without any usage context or exclusions, the agent lacks direction on appropriate application.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a value, implying it is a read-only operation, but does not specify computational complexity, error handling (e.g., for negative inputs), or output format. The description lacks details on whether it handles large integers, returns a specific data type, or has any side effects, which are gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information is brief and relevant. There is no wasted verbiage, making it efficient for quick understanding, though it could benefit from more detailed usage or parameter guidance.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain the formula or behavior, provide examples, or clarify the output. For a tool that performs a specific calculation, more context on the mathematical definition and expected result is needed to be fully helpful to an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, and the tool description does not add any semantic information about 'n'. It does not explain what 'n' represents (e.g., integer index starting from 1), valid ranges, or examples. With low schema coverage, the description fails to compensate, leaving the parameter's meaning unclear beyond its type.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth centered triangular number.' It specifies the verb ('calculate') and the resource ('centered triangular number'), and distinguishes it from other triangular number tools (e.g., 'triangular_number', 'triangular_numbers') by specifying the 'centered' variant. However, it does not explicitly differentiate from 'centered_polygonal_number' or 'centered_square_number' among siblings, which are similar figurate numbers.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It includes a domain ('arithmetic') and category ('figurate_numbers'), which implies context but does not specify when to use this tool versus alternatives like 'triangular_number' or 'centered_polygonal_number'. There is no explicit mention of when-not-to-use or prerequisites, leaving the agent to infer based on the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool solves Pell's equation using continued fractions, which implies a computational process, but doesn't describe what the tool actually returns (e.g., fundamental solution, all solutions, specific format), performance characteristics, error handling, or any constraints on the input 'n' (e.g., must be non-square). This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information in parentheses is brief and relevant. There's no wasted verbiage, making it efficient, though it could benefit from more detail given the complexity of the tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of solving Pell's equation, the lack of annotations, no output schema, and minimal parameter semantics, the description is incomplete. It doesn't explain what the tool returns (e.g., a solution pair, a list of solutions), how solutions are represented, or any algorithmic details. For a mathematical tool with potential nuances, this leaves too much unspecified for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage in the schema. The description doesn't add any semantic information about 'n'—it doesn't explain what 'n' represents in Pell's equation (e.g., a non-square integer), valid ranges, or constraints. This is inadequate given the low schema coverage, failing to compensate for the lack of parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve Pell's equation x² - ny² = 1 using continued fractions.' It specifies both the mathematical equation and the method (continued fractions), which is specific and informative. However, it doesn't explicitly differentiate from sibling tools like 'solve_pell_equation' or 'pell_solutions_generator' that might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain (arithmetic) and category (continued_fractions), which gives some context, but offers no explicit guidance on when to use this tool versus alternatives like 'solve_pell_equation' or other Pell-related tools in the sibling list. There's no mention of prerequisites, limitations, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'Find[s] characteristic polynomial' but does not describe what the tool returns (e.g., a polynomial expression, coefficients), error conditions, computational limits, or side effects. For a mathematical tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and it efficiently communicates the core functionality. However, the lack of additional context slightly limits its effectiveness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical operation with 1 parameter), no annotations, no output schema, and low schema description coverage, the description is incomplete. It fails to explain the tool's behavior, output format, or parameter semantics, leaving the agent with insufficient information to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('coeffs') with 0% description coverage. The description does not add any meaning beyond the schema—it does not explain what 'coeffs' represents (e.g., coefficients of the recurrence relation, their order, or constraints). With low schema coverage and no compensatory details in the description, parameter understanding is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find characteristic polynomial of linear recurrence relation.' It specifies a verb ('Find') and resource ('characteristic polynomial'), and distinguishes the domain ('arithmetic') and category ('recursive_sequences'). However, it does not explicitly differentiate from sibling tools, as none appear to be direct alternatives for this specific mathematical operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify prerequisites, typical use cases, or comparisons with other tools (e.g., 'solve_linear_recurrence' might be a sibling for related tasks). Without such context, the agent lacks clear usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a norm, implying a read-only operation, but does not specify output format, error handling, or performance characteristics (e.g., computational complexity). For a tool with no annotations, this is a significant gap, as the agent lacks insight into what to expect beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no unnecessary verbosity or redundant information. However, it could be more structured by separating usage context or parameter details, but given its brevity, it efficiently conveys the core function without waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical norm calculation, the description is incomplete. There are no annotations, no output schema, and low parameter coverage. The description does not explain the return value (e.g., a numeric result), error cases, or mathematical assumptions. For a tool with rich sibling context (e.g., other norm tools), more detail is needed to ensure the agent can use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'vector' of type array of strings. The description does not add any semantic details about this parameter, such as what the strings represent (e.g., numeric values), expected format, or constraints (e.g., non-empty array). With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Chebyshev norm (L∞ norm) of a vector'. It specifies the verb ('calculate'), the mathematical operation ('Chebyshev norm'), and the input ('vector'), which is specific and unambiguous. However, it does not explicitly differentiate from sibling tools like 'euclidean_norm' or 'manhattan_norm', which are also vector norms, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.vectors') and category ('general'), but this is too vague to inform usage decisions. There is no mention of when Chebyshev norm is preferred over other norms (e.g., Euclidean or Manhattan), nor any prerequisites or exclusions, leaving the agent without practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but does not describe how it behaves: e.g., whether it handles empty arrays, invalid inputs, large datasets, performance characteristics, or error conditions. For a tool with no annotations, this lack of behavioral context is a significant gap, though it doesn't contradict any annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in one sentence followed by domain/category metadata. There is no wasted text, and it efficiently communicates the main function. However, the domain/category tags add minimal value and could be considered slightly extraneous.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical calculations with multiple outputs), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain what 'and more' includes, the return format, or any behavioral aspects. For a tool that likely produces structured results, this lack of detail makes it inadequate for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('numbers') with 0% description coverage, and the description provides no parameter information. It does not explain what 'numbers' should contain (e.g., numeric values as strings), any constraints, or examples. With low schema coverage, the description fails to compensate, leaving parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate comprehensive statistics for a dataset including mean, median, mode, variance, and more.' It specifies the verb ('calculate'), resource ('statistics for a dataset'), and scope ('comprehensive... including mean, median, mode, variance, and more'). However, it does not explicitly differentiate from sibling tools like 'mean', 'median', 'variance', etc., which are separate tools on the server, so it misses full sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but this is too vague to help an agent choose between this and sibling tools like 'mean', 'median', or 'variance'. There are no explicit when/when-not instructions or named alternatives, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. While it explains what mathematical operation is performed, it lacks crucial behavioral details: it doesn't specify precision/accuracy characteristics, computational complexity, error handling for large/small n values, or what happens when n approaches infinity (practical implementation details). For a numerical computation tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence that states the purpose and mathematical formula, followed by domain/category metadata. There's no wasted verbiage, and the core information is front-loaded. The parentheses for domain/category could be better integrated, but overall it's appropriately concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a numerical computation tool with 1 parameter, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It explains the mathematical basis but misses implementation details, parameter guidance, accuracy information, and comparison to sibling tools. For proper agent usage, more context about practical computation considerations is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. The description mentions 'n' in the mathematical formula but provides no semantic explanation of what n represents (approximation parameter), appropriate ranges, or how choice of n affects accuracy. With one undocumented parameter and no additional guidance in the description, this leaves significant ambiguity for proper tool invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes the mathematical constant e using the limit definition, specifying the exact formula e = lim(n→∞) (1 + 1/n)^n. It distinguishes this from sibling tools like 'compute_e_series' by indicating a different computational approach (limit vs series). However, it doesn't explicitly differentiate from other mathematical constant tools beyond the formula mention.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance on when to use this tool. It mentions the domain (arithmetic) and category (mathematical_constants), but gives no explicit comparison to alternatives like 'compute_e_series' or 'e' (which appears to be a different tool). There's no guidance on appropriate n values, convergence considerations, or when to choose this method over other e-computation approaches.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what mathematical constant is computed and the method used, but doesn't disclose important behavioral aspects: what precision/accuracy to expect, computational complexity, whether it's an approximation or exact calculation, error handling for invalid inputs, or what the output format will be. For a computational tool with no annotations, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. The single sentence efficiently communicates what constant is computed and the method used. The parenthetical classification could be considered extraneous but doesn't significantly detract from conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a computational tool with 1 parameter, no annotations, and no output schema, the description is incomplete. It explains what is computed but not how (parameter usage), what to expect as output, accuracy considerations, or limitations. The presence of a sibling tool 'euler_gamma' without differentiation further reduces completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter 'terms' with 0% description coverage. The tool description doesn't mention this parameter at all, leaving it completely undocumented. Given the mathematical context, 'terms' likely refers to the number of terms in the harmonic series approximation, but this is not stated. With 0% schema coverage and no parameter information in the description, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes the Euler-Mascheroni constant γ using the harmonic series method, specifying the mathematical formula γ = lim(n→∞) (H_n - ln(n)). It distinguishes itself from the sibling tool 'euler_gamma' by explicitly mentioning the harmonic series approach. However, it doesn't explain how this differs from other possible methods for computing γ.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There's a sibling tool named 'euler_gamma' with no description provided, so it's unclear whether that tool uses a different method or serves a different purpose. The description mentions 'Domain: arithmetic, Category: mathematical_constants' but this is classification rather than usage guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. It states what the tool computes but doesn't describe important behavioral aspects: it doesn't mention whether this is a pure computation (no side effects), what happens with different depth values (convergence behavior, overflow risks), what format the result returns, or any precision/accuracy characteristics. The description is mathematically correct but operationally incomplete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise - a single sentence with the mathematical formula and domain/category tags. It's front-loaded with the core purpose. The domain/category information adds context without being verbose. However, the mathematical notation could be clarified for non-expert users.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a mathematical computation tool with 1 parameter (0% schema coverage), no annotations, and no output schema, the description is insufficient. It doesn't explain the parameter's meaning, the computation's behavior with different inputs, what the output represents (approximation accuracy, format), or how this method compares to alternatives. For a tool that computes a mathematical constant with configurable precision, more operational context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'depth' only implicitly through the continued fraction notation '...' but doesn't explain what the depth parameter means, what valid ranges are, or how it affects the computation. For a single parameter tool with no schema documentation, this represents a significant gap in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute golden ratio using continued fraction' with a specific mathematical formula provided. It distinguishes this method from alternatives like 'compute_golden_ratio_fibonacci' (a sibling tool) by specifying the continued fraction approach. However, it doesn't explicitly contrast with other golden ratio computation methods beyond the formula.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the continued fraction method, it doesn't explain when this approach is preferable to other golden ratio computation methods (like the Fibonacci-based approach available as a sibling tool) or what trade-offs exist. There's no mention of accuracy considerations, computational complexity, or appropriate depth values.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool computes the golden ratio but does not explain how it handles the 'terms' parameter (e.g., whether it approximates the limit or computes up to a given term), potential precision issues, or error handling for invalid inputs. For a computational tool with zero annotation coverage, this is a significant gap, warranting a score of 2.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the purpose and formula in a single sentence. The additional domain and category tags are minimal and do not detract from clarity. However, the lack of parameter details or usage guidelines means it could be more informative without sacrificing brevity, so it scores a 4.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical computation tool with no annotations, no output schema, and low parameter coverage, the description is incomplete. It fails to explain the computation method, parameter semantics, or expected output format, leaving critical gaps for the agent. This inadequacy results in a score of 2.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'terms' with 0% description coverage, and the tool description does not mention it at all. This leaves the parameter's meaning, valid range, and impact on the computation undocumented. With low schema coverage and no compensation in the description, the score is 2, as the agent lacks essential information to use the tool correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes the golden ratio using the Fibonacci sequence, specifying the mathematical formula φ = lim(n→∞) F(n+1)/F(n). It distinguishes itself from sibling tools like 'golden_ratio' or 'golden_ratio_cf' by explicitly mentioning the Fibonacci method. However, it does not fully differentiate from 'compute_golden_ratio_continued_fraction' in terms of when to choose one over the other, keeping it at a 4.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'compute_golden_ratio_continued_fraction' or 'golden_ratio'. It lacks context on prerequisites, such as the range or constraints for the 'terms' parameter, and does not mention any performance considerations or limitations. This absence of usage instructions results in a score of 2.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the formula but doesn't disclose behavioral traits like computational complexity, precision limits, error handling, or output format. For a mathematical computation tool, this leaves significant gaps in understanding its operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose and formula. The domain/category note is slightly redundant but not wasteful. It efficiently communicates the essential information in a single sentence.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the parameter's role, the tool's behavior, or what the output looks like (e.g., numeric value, precision). For a computational tool, this leaves too much undefined.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'terms' indirectly via the formula but doesn't explain what the 'terms' parameter means (e.g., number of iterations, precision level). The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes pi using Machin's formula, providing the specific mathematical formula and categorizing it as arithmetic/mathematical_constants. It distinguishes itself from sibling tools like compute_pi_chudnovsky, compute_pi_leibniz, and compute_pi_nilakantha by specifying the algorithm, though it doesn't explicitly contrast them.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like other pi-computation tools (e.g., compute_pi_chudnovsky). The description mentions the domain and category but offers no explicit when/when-not instructions or prerequisites for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the computation method but lacks behavioral details such as precision limits, performance characteristics, error handling, or output format. The description is minimal and does not disclose important operational traits.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. It efficiently states the method and formula in one sentence, with a brief domain/category note. There is no wasted verbiage, though it could be more informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits parameter details, behavioral context, and output information. For a computational tool with one parameter, this leaves significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description does not mention the 'terms' parameter at all. It fails to explain what 'terms' represents (e.g., number of series terms), its effect on accuracy, or valid ranges. The description adds no parameter semantics beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes pi using the Nilakantha series, specifying the mathematical method and providing the series formula. It distinguishes itself from sibling tools like compute_pi_chudnovsky and compute_pi_leibniz by naming the specific algorithm. However, it does not explicitly contrast with these siblings in the description text.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like compute_pi_chudnovsky or compute_pi_leibniz. It mentions the domain and category, but offers no explicit usage context, prerequisites, or performance considerations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a confidence interval but does not explain how it behaves—e.g., what statistical method is used (e.g., t-distribution for small samples), assumptions (e.g., normal distribution), output format, or error handling. This lack of detail is significant for a statistical tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first clause. The domain and category tags are efficiently appended. There is no wasted text, though it could be slightly more informative without losing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical inference with 2 parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not cover behavioral traits, parameter details, or output expectations, making it inadequate for effective use without additional context or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'sample data' and 'confidence level' implicitly but does not explain parameter semantics—e.g., that 'data' is a numeric array of sample values or typical ranges for 'confidence_level'. Without this, users might not understand how to provide inputs correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate confidence interval for population mean from sample data.' It specifies the verb ('calculate'), resource ('confidence interval'), and domain context ('population mean from sample data'). However, it does not explicitly differentiate from its sibling 'confidence_interval_proportion' or other statistical inference tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category tags ('Domain: statistics, Category: inference'), which imply usage context but do not provide explicit guidance on when to use this tool versus alternatives like 'confidence_interval_proportion' or other statistical methods. No when-not-to-use instructions or prerequisites are mentioned, leaving gaps in practical application advice.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe how it behaves: no information on output format (e.g., list of integers), error handling (e.g., for irrational numbers), computational limits, or whether it's deterministic. The description is purely functional without behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with a parenthetical domain/category note. It's front-loaded with the core purpose and wastes no words. However, it's arguably too brief given the tool's complexity and lack of parameter documentation, bordering on under-specification rather than optimal conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical complexity, three parameters, no annotations, and no output schema, the description is incomplete. It doesn't explain what the tool returns, how parameters affect the computation, or any behavioral traits. For a tool that computes continued fractions—a non-trivial algorithm—more context is needed to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The tool description doesn't mention any parameters, leaving all three (x, max_terms, tolerance) undocumented. It doesn't explain what 'x' represents, what 'max_terms' limits, or what 'tolerance' controls, failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute continued fraction expansion of a real number.' It specifies the verb ('compute'), resource ('continued fraction expansion'), and domain ('real number'), making it unambiguous. However, it doesn't differentiate from sibling tools like 'continued_fraction_e', 'continued_fraction_golden_ratio', or 'continued_fraction_pi', which compute expansions for specific constants rather than arbitrary real numbers.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('continued_fractions'), but doesn't explain when to choose this over sibling tools like 'cf_to_rational' (converts continued fractions to rationals) or 'rational_to_cf' (converts rationals to continued fractions). There's no mention of prerequisites, limitations, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool generates a continued fraction representation, implying a read-only operation, but doesn't disclose behavioral traits like whether it's deterministic, if there are rate limits, error handling for invalid depths, or performance characteristics. The example suggests it outputs a sequence, but no details on format or truncation behavior are given.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first phrase. The example and domain/category add context without unnecessary verbosity. However, the parentheses could be integrated more smoothly, and it lacks structural elements like bullet points for clarity, but overall it's efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical constant representation), lack of annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain the output format (e.g., list structure), error conditions, or practical usage notes. For a tool with one undocumented parameter and no structured output, more detail is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('depth') with 0% description coverage. The tool description adds no information about this parameter—it doesn't explain what 'depth' means (e.g., number of terms in the continued fraction), valid ranges, default behavior, or units. This is inadequate given the low schema coverage, failing to compensate for the lack of structured documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate continued fraction representation of pi' with a specific example. It distinguishes itself from siblings like 'pi_digits' or 'compute_pi_chudnovsky' by focusing on continued fraction representation rather than decimal digits or computation methods. However, it doesn't explicitly contrast with 'continued_fraction_e' or 'continued_fraction_golden_ratio' beyond the domain/category mention.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain (arithmetic) and category (mathematical_constants), which implies context, but gives no explicit when-to-use rules, prerequisites, or alternatives. For example, it doesn't specify when to choose this over 'pi_digits' or other pi-related tools, nor does it mention any constraints like depth limitations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool compares convergence rates but does not explain what that entails—e.g., whether it outputs a table, graph, or summary; if it runs simulations or uses predefined methods; or any performance or limitation details. For a tool with no annotations and unknown behavior, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first sentence. The additional domain and category information is brief and relevant. There is no wasted verbiage, making it efficient, though it could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of comparing convergence rates, the description is incomplete. There are no annotations, no output schema, and the input parameter is undocumented. The description does not cover what the tool returns, how the comparison is performed, or any prerequisites. For a tool that likely involves multiple methods and outputs, this lack of detail makes it inadequate for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('max_terms') with 0% description coverage, meaning the schema provides no semantic information. The description does not mention this parameter at all, failing to compensate for the lack of schema details. It should explain what 'max_terms' represents (e.g., maximum number of terms to evaluate in each method) but does not, leaving the parameter's meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compare convergence rates of different pi approximation methods.' It specifies the verb ('compare'), resource ('convergence rates'), and domain context ('pi approximation methods'), making it understandable. However, it does not explicitly differentiate from sibling tools like 'compute_pi_chudnovsky' or 'compute_pi_leibniz', which compute pi values rather than comparing convergence rates, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: arithmetic, Category: mathematical_constants'), but this is generic and does not help an agent decide between this tool and sibling tools like various pi computation methods or convergence analysis tools. There are no explicit when-to-use, when-not-to-use, or alternative recommendations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs conversions but does not describe how it handles invalid units, rounding, precision, errors, or the format of results. For a tool with no annotations and no output schema, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, using a single sentence to convey the core functionality. The domain/category note is slightly redundant but not wasteful. It is front-loaded with the main purpose, though it could be more structured with usage hints.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (3 parameters, no annotations, no output schema), the description is insufficient. It lacks details on parameter usage, error handling, result format, and differentiation from siblings. For a conversion tool, users need to know valid units and output expectations, which are not addressed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the schema only defines parameter types without meaning. The description mentions units like meters and feet but does not specify valid unit strings, formats, or examples for the 'from_unit' and 'to_unit' parameters. It adds minimal semantic context beyond the schema, failing to compensate for the low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting length between units like meters, feet, inches, etc. It specifies the verb ('convert') and resource ('length'), making the intent unambiguous. However, it does not explicitly differentiate from sibling conversion tools (e.g., convert_area, convert_volume), though the domain/category hints at its scope.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lists sibling tools like convert_area and convert_volume but does not explain how to choose between them (e.g., for length vs. area conversions). There is no mention of prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'validation and formulas,' which hints at input validation and mathematical operations, but doesn't disclose critical behavioral traits like error handling, precision, rounding, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The domain/category tags add context without verbosity. However, it could be more structured by separating usage notes from the main purpose, but it's efficient overall.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on behavior, parameters, return values, and error handling. For a tool with 3 required parameters and mathematical operations, more context is needed to ensure proper usage by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, and the tool description doesn't add any parameter-specific information. It doesn't explain what 'value', 'from_scale', or 'to_scale' mean, their expected formats (e.g., string values like 'Celsius'), or constraints. With low schema coverage, the description fails to compensate, leaving parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting temperature between Celsius, Fahrenheit, and Kelvin scales. It specifies the action ('convert') and resource ('temperature'), and mentions validation and formulas. However, it doesn't explicitly differentiate from sibling tools like convert_angle or convert_length, though the domain/category tags help.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but doesn't specify prerequisites, constraints, or compare it to other conversion tools in the sibling list (e.g., convert_angle, convert_area). Usage is implied by the name and description alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs conversions but does not describe any behavioral traits such as error handling (e.g., invalid units), precision, rounding, or output format. For a tool with no annotations, this is a significant gap in transparency about how the tool behaves in practice.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. It avoids unnecessary details and wastes no words, making it easy to parse. However, the inclusion of domain and category in parentheses, while informative, slightly detracts from absolute minimalism.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (3 parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameter constraints, behavioral traits, and output format, which are crucial for correct tool invocation. Without annotations or an output schema, the description does not provide enough context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It lists example units (seconds, minutes, hours, etc.) which partially clarifies the 'from_unit' and 'to_unit' parameters, but does not specify allowed unit strings, case sensitivity, or constraints on the 'value' parameter. With 3 undocumented parameters, the description adds some meaning but is insufficient to fully explain parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting time between different units like seconds, minutes, hours, etc. It specifies the verb ('Convert') and resource ('time'), and includes a domain/category for context. However, it does not explicitly differentiate from sibling tools like convert_angle or convert_length, which serve similar conversion purposes but for different quantities.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify any prerequisites, constraints, or scenarios where this tool is preferred over other conversion tools (e.g., convert_speed, convert_temperature). This lack of explicit usage context leaves the agent without clear direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool performs conversions but does not disclose behavioral traits such as error handling (e.g., invalid units), precision, supported unit list, or output format. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The additional domain and category information is brief but could be considered slightly extraneous. Overall, it is efficient with little waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (3 parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameter semantics, behavioral transparency, and usage guidelines, making it inadequate for reliable agent invocation without further context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, with three parameters (value, from_unit, to_unit) undocumented in the schema. The description lists example units but does not explain parameter meanings, valid unit strings, or constraints. It adds minimal value beyond the schema, failing to compensate for the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting volume between units like liters, gallons, cubic meters, and cubic feet. It specifies the action ('convert') and resource ('volume'), but does not differentiate from sibling tools like convert_area or convert_length, which are similar unit conversion tools for different quantities.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify use cases, prerequisites, or compare it to sibling conversion tools (e.g., convert_area, convert_length), leaving the agent to infer usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the conversion action but lacks details on error handling (e.g., invalid units), precision, rounding, or output format. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core function in a single sentence. The domain/category note adds minimal but relevant context without redundancy. It avoids unnecessary elaboration, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (3 parameters, no output schema, no annotations), the description is incomplete. It lacks details on parameter usage, behavioral traits, and output expectations. For a conversion tool with multiple inputs, more context is needed to ensure correct invocation and result interpretation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description does not explain the parameters. It mentions units like kilograms and pounds but does not clarify the expected format for 'from_unit' and 'to_unit' (e.g., abbreviations, case sensitivity) or the meaning of 'value'. With low schema coverage, the description fails to compensate, leaving parameters poorly defined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting weight/mass between units like kilograms, pounds, ounces, and grams. It specifies the verb ('convert') and resource ('weight/mass'), making the function evident. However, it does not explicitly differentiate from sibling tools like convert_length or convert_temperature, though the domain/category hints at specialization within conversions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or exclusions. Without explicit usage context, the agent must infer applicability from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the optimization method but fails to describe key behavioral traits: it does not specify what the tool returns (e.g., optimal values, convergence status), whether it handles constraints, error conditions, or performance characteristics like iteration limits. For a numerical optimization tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and includes domain/category context. There is no wasted verbiage, and every word contributes to understanding the tool's function. This is an example of efficient communication.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a numerical optimization tool with 5 parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It lacks essential details: parameter explanations, return values, error handling, and usage distinctions from siblings. While concise, it does not provide enough context for an agent to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the 5 parameters (f, x0, step_size, max_iterations, tolerance) are documented in the schema. The description does not mention any parameters or their meanings, failing to compensate for the lack of schema documentation. This leaves the agent with no semantic understanding of what inputs are required.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform coordinate descent optimization by optimizing one variable at a time'. It specifies the verb ('Perform coordinate descent optimization') and the method ('optimizing one variable at a time'), and includes domain/category context. However, it does not explicitly distinguish this from sibling optimization tools like 'gradient_descent' or 'nelder_mead', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('numerical') and category ('optimization'), which implies context, but does not specify when to use this tool versus alternatives (e.g., 'gradient_descent' or 'nelder_mead'), nor does it outline prerequisites or typical scenarios. This lack of explicit guidance limits its helpfulness for an agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it mentions the output range (-1 to 1), it doesn't describe error handling (e.g., what happens with invalid inputs like arrays of different lengths), computational characteristics, or any side effects. For a statistical calculation tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core functionality. The single sentence efficiently communicates the calculation, output range, and domain/category. No unnecessary words or redundant information are present.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It doesn't explain parameter semantics, error conditions, or return format. For a tool performing a mathematical calculation with two required parameters, more contextual information is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning neither parameter (xs, ys) has descriptions in the schema. The description mentions 'two datasets' but doesn't explain what xs and ys represent, their expected format (numeric strings?), or any constraints (e.g., equal length required). This leaves parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Pearson correlation coefficient between two datasets (ranges from -1 to 1)'. It specifies the statistical method (Pearson correlation), the input (two datasets), and the output range. However, it doesn't explicitly differentiate from sibling tools like 'covariance' or 'autocorrelation', which are related statistical measures.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain (statistics) and category (general), but gives no explicit instructions on when to use this tool versus alternatives like 'covariance' (a sibling tool) or other correlation methods. There's no mention of prerequisites, data requirements, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method (Taylor series) but doesn't describe key behaviors: what 'n' represents (number of terms?), accuracy implications, computational complexity, error handling, or output format. For a computational tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise (one sentence with parenthetical note) and front-loaded with the core purpose. There's no wasted text, though it could benefit from more detail. The structure is efficient but under-specified rather than overly verbose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and a computational tool with two parameters, the description is incomplete. It doesn't explain parameter meanings, behavioral traits, or output expectations. The agent lacks sufficient context to use this tool correctly compared to siblings like 'cos'.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description adds no information about what 'x' and 'n' mean (e.g., 'x' is the angle in radians? 'n' is the number of series terms?). It must compensate for the schema gap but fails to do so, leaving both parameters semantically undefined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute cosine function using Taylor series expansion'. It specifies the verb ('compute'), resource ('cosine function'), and method ('Taylor series expansion'). However, it doesn't differentiate from sibling tools like 'cos' or 'cos_degrees', which likely compute cosine directly rather than via series expansion.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance with 'Domain: numerical, Category: series', but this is vague and doesn't explain when to use this tool versus alternatives like 'cos' or 'cos_degrees'. No explicit when/when-not instructions or named alternatives are provided, leaving the agent with little practical guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('calculate covariance') without detailing behavioral traits such as input validation (e.g., handling non-numeric strings in arrays), error handling, computational complexity, or output format. For a statistical calculation tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first phrase. The additional context in parentheses ('measures how variables change together') and domain/category tags add value without unnecessary verbosity. However, the domain/category tags might be slightly redundant if the server context already implies statistical tools, but they do not detract significantly from clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical calculation with 3 parameters (2 required), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks essential details such as parameter explanations, behavioral context, and output expectations. For a tool that performs a non-trivial mathematical operation, this description does not provide enough information for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description does not explain the parameters at all. It mentions 'two datasets' but does not clarify the meaning of 'xs', 'ys', or 'population'. Without any parameter semantics in the description, the agent must rely solely on the schema's property names, which is insufficient for understanding how to use the tool correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the covariance between two datasets' with a brief explanation ('measures how variables change together'). It specifies the verb ('calculate') and resource ('covariance between two datasets'), making the function unambiguous. However, it does not differentiate from sibling tools like 'correlation', which is a related statistical measure, leaving room for improvement in sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but this is too vague to help an agent decide between this and sibling tools like 'correlation' or 'variance'. There are no explicit when/when-not instructions or named alternatives, limiting its utility in tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the mathematical method ('Chinese Remainder Theorem') but doesn't disclose behavioral traits like input constraints (e.g., moduli must be coprime), error handling, output format, or computational limits. This leaves significant gaps for a tool performing mathematical computations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The domain/category tags add context without verbosity. However, the lack of elaboration on parameters or usage slightly undermines efficiency, as key details are omitted.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (solving congruences), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't cover input constraints, output format, error cases, or mathematical assumptions, making it inadequate for reliable use without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It doesn't explain the parameters 'remainders' and 'moduli' beyond what the schema provides (arrays of integers). No details on array lengths, constraints (e.g., equal lengths, coprime moduli), or examples are given, leaving parameter meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve system of congruences using Chinese Remainder Theorem.' It specifies the verb ('solve'), resource ('system of congruences'), and method ('Chinese Remainder Theorem'). However, it doesn't explicitly differentiate from sibling tools like 'generalized_crt' or other modular arithmetic tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It includes domain and category tags ('Domain: arithmetic, Category: modular_arithmetic'), which imply context, but offers no explicit advice on when to use this tool versus alternatives (e.g., 'generalized_crt' or other solving methods). No prerequisites, limitations, or comparisons are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool computes coefficients for 'smooth interpolation', hinting at output behavior, but lacks details on what the coefficients represent (e.g., polynomial segments), computational constraints (e.g., input array length requirements, error handling), or output format. For a mathematical tool with no annotations, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. It consists of a single sentence that directly states the tool's function, with no wasted words. However, the parenthetical 'Domain: numerical, Category: interpolation' could be integrated more smoothly, but overall it is efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain what the coefficients are used for, how they relate to interpolation, or what the output looks like. For a computational tool with two parameters, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It does not mention the parameters 'x_points' and 'y_points' at all, leaving their roles (e.g., arrays of x and y coordinates) and requirements (e.g., equal length, sorted) undocumented. The description adds no parameter semantics beyond the schema, failing to address the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute cubic spline coefficients for smooth interpolation'. It specifies the verb ('compute'), resource ('cubic spline coefficients'), and domain/category context. However, it does not explicitly differentiate from its sibling 'cubic_spline_interpolate', which likely uses these coefficients, leaving some ambiguity about when to compute versus apply coefficients.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions 'Domain: numerical, Category: interpolation', which implies a context but does not specify when to use this tool versus alternatives like 'cubic_spline_interpolate' or other interpolation methods (e.g., 'linear_interpolate', 'lagrange_interpolate'). No explicit when-to-use or when-not-to-use instructions are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'smooth curve fitting' which implies continuity and differentiability, but doesn't disclose critical behavioral traits like error handling, performance characteristics, mathematical assumptions (e.g., sorted x_points), or what happens with invalid inputs. For a numerical tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with domain/category in parentheses. Every word earns its place: 'Perform' (action), 'cubic spline interpolation' (method), 'for smooth curve fitting' (purpose), and context in parentheses. There's no fluff or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of cubic spline interpolation (a mathematical operation with multiple parameters), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain what the tool returns, error conditions, or mathematical details. The conciseness comes at the cost of leaving too much undefined for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds zero information about parameters beyond what's in the schema. With 0% schema description coverage and three required parameters (x_points, y_points, x), the description doesn't explain what these arrays represent, their relationships, constraints (e.g., equal lengths, monotonic x), or the interpretation of the output. This leaves parameters completely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform cubic spline interpolation for smooth curve fitting' with domain and category context. It specifies the verb ('perform'), resource ('cubic spline interpolation'), and objective ('smooth curve fitting'), though it doesn't explicitly differentiate from sibling interpolation tools like 'linear_interpolate' or 'lagrange_interpolate'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category hints at numerical interpolation contexts, there are no explicit instructions about when cubic spline interpolation is preferred over other methods (e.g., linear or Lagrange interpolation), nor any prerequisites or limitations mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the conversion action but lacks behavioral details: it doesn't specify output format (e.g., string representation), error handling for invalid inputs, or performance characteristics. The base range (2-36) is noted, but other critical behaviors like input validation or edge cases are omitted.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: a single sentence directly states the tool's function, followed by domain/category metadata. Every word earns its place with no redundancy or fluff, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (conversion with range constraints), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It lacks details on output format, error conditions, and parameter semantics, leaving significant gaps for an AI agent to invoke it correctly without additional context or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters 'number' and 'base' are undocumented in the schema. The description adds minimal semantics: it implies 'number' is a decimal integer and 'base' is an integer between 2 and 36, but doesn't clarify parameter roles, units, or constraints beyond the base range. This is inadequate for two required parameters with no schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert a decimal number to its representation in another base (2-36).' It specifies the verb ('convert'), resource ('decimal number'), and target ('another base'), with explicit base range constraints. However, it doesn't distinguish from sibling tools like 'base_to_decimal' or 'number_to_base', which handle related but inverse operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('general'), but offers no explicit when/when-not instructions or references to sibling tools like 'base_to_decimal' for reverse conversions. Usage is implied by the function name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but does not disclose behavioral traits such as input constraints (e.g., handling of negative numbers, large integers), output format (e.g., string representation with '0x' prefix), error handling, or performance considerations. The description is minimal and lacks necessary operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted verbiage, and it efficiently communicates the core purpose. However, the brevity contributes to gaps in other dimensions like guidelines and transparency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (1 parameter, no output schema, no annotations), the description is incomplete. It lacks details on output (e.g., format of hexadecimal result), input constraints, and usage context. For a conversion tool, users need to know what to expect in return and any limitations, which are not addressed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It mentions 'decimal' but does not add meaning beyond the schema's type (integer). No details are provided about valid ranges, examples, or semantics (e.g., whether it accepts only non-negative integers). The description fails to enhance parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting decimal numbers to hexadecimal (base-16). It specifies the domain (arithmetic) and category (number_systems), making the verb+resource explicit. However, it does not distinguish this tool from its sibling 'decimal_to_binary' or 'decimal_to_octal', which perform similar base conversions, so it lacks sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention when to choose hexadecimal conversion over other base conversions (e.g., binary or octal) or other related tools like 'base_conversion'. There is no context for usage, prerequisites, or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the calculation method but doesn't disclose important behavioral traits: what precision to expect, error characteristics of backward difference, whether it handles symbolic functions or only numeric evaluation, what happens with invalid inputs, or what the output format is. For a mathematical computation tool with zero annotation coverage, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with a single sentence that states the core purpose. The domain/category information ('Domain: calculus, Category: general') is somewhat redundant but not wasteful. However, it could be more front-loaded by immediately explaining key parameters or usage context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical complexity, zero annotation coverage, 0% schema description coverage, and no output schema, the description is insufficient. It doesn't explain the mathematical method in detail, parameter requirements, output format, error handling, or precision considerations. For a derivative calculation tool that likely produces numeric results, more context is needed to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate but doesn't. It mentions no parameters at all, while the schema shows three parameters (func, x, h). The description doesn't explain what 'func' should contain (e.g., mathematical expression syntax), what 'x' represents (evaluation point), or what 'h' is (step size, with default shown in schema but not described). With 0% schema coverage and no parameter information in the description, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate numeric derivative using backward difference method'. It specifies the verb ('calculate'), resource ('numeric derivative'), and method ('backward difference'), with domain/category context. However, it doesn't differentiate from sibling tools like 'derivative_central' or 'derivative_forward', which are presumably alternative differentiation methods.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the method ('backward difference'), it doesn't explain when this method is appropriate compared to forward or central difference methods (which appear as sibling tools). There are no usage prerequisites, exclusions, or comparisons to help the agent choose correctly.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the methods (z-score, IQR) but does not describe what the tool returns (e.g., list of outliers, indices, scores), error handling, performance characteristics, or any constraints. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and methods. There is no wasted text, and it efficiently conveys the core functionality without unnecessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (statistical outlier detection with 3 parameters), lack of annotations, and no output schema, the description is incomplete. It does not explain the return values, error cases, or practical usage details. The description fails to provide sufficient context for effective tool invocation by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'z-score or IQR method' which relates to the 'method' parameter, but does not explain the 'numbers' parameter (an array of strings representing the dataset) or the 'threshold' parameter (default 3, likely for z-score). The description adds minimal semantic value beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Detect outliers in a dataset using z-score or IQR method.' It specifies the action (detect outliers), resource (dataset), and methods (z-score, IQR). However, it does not explicitly differentiate from sibling tools, which are primarily mathematical functions rather than statistical detection tools, so it lacks explicit sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the methods (z-score, IQR) but does not specify contexts, prerequisites, or exclusions. There is no mention of when to choose one method over the other or how it compares to other statistical tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool detects seasonal patterns, implying a read-only analysis function, but lacks details on computational behavior, output format, error handling, or limitations (e.g., data length requirements). This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. It avoids unnecessary words, though it could be more informative without sacrificing brevity. The parenthetical domain and category add minor context without clutter.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (time series analysis with parameters), lack of annotations, 0% schema coverage, and no output schema, the description is insufficient. It does not explain what 'seasonal patterns' means, how results are returned, or any assumptions about the input data, leaving critical gaps for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It does not mention the 'data' parameter (required array of numbers) or 'max_period' (optional integer with default 12). No additional meaning, constraints, or examples are provided, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Detect seasonal patterns in time series data.' It specifies the verb ('detect'), resource ('seasonal patterns'), and domain context ('time series data'), making the intent unambiguous. However, it does not differentiate from sibling tools like 'seasonal_decompose' or 'seasonal_strength', which are related but not explicitly contrasted.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('timeseries') and category ('analysis'), but does not specify scenarios, prerequisites, or exclusions. For example, it does not indicate whether it's for preliminary analysis or when other seasonal tools might be more appropriate.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states the test is 'deterministic' and uses 'known witnesses for specific ranges,' which hints at reliability constraints, but doesn't explain what happens outside those ranges, error conditions, computational complexity, or output format. For a primality testing tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. It efficiently conveys the core functionality, though it could benefit from additional context without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of primality testing, no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on ranges, witnesses, result interpretation, and error handling, making it inadequate for reliable tool invocation in a mathematical context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% description coverage. The description adds that 'n' is tested for primality, but doesn't specify valid ranges, integer constraints, or handling of edge cases (e.g., negative numbers, small values). Given the low schema coverage, the description provides minimal compensation, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs a 'Deterministic Miller-Rabin test' with 'known witnesses for specific ranges,' which is a specific verb+resource combination. It distinguishes from sibling tools like 'miller_rabin_test' by specifying it's deterministic rather than probabilistic, though it doesn't explicitly contrast with other primality tests like 'aks_primality_test' or 'fermat_primality_test'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions 'specific ranges' but doesn't clarify what those ranges are or when to use this deterministic version versus probabilistic alternatives like 'miller_rabin_test.' No explicit when-to-use or when-not-to-use criteria are given, leaving the agent with little practical direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool removes trends to achieve stationarity, implying a transformation, but does not describe how the trend is removed (e.g., linear regression, differencing), what happens to the input data (e.g., modified or returned as residuals), or any limitations (e.g., assumes specific trend types). This leaves significant gaps for a mutation-like operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The domain and category annotations are efficiently appended. There is no wasted text, though it could benefit from more detail given the tool's complexity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (transformation of time series data), lack of annotations, no output schema, and low schema description coverage, the description is insufficient. It does not explain the method of trend removal, output format (e.g., residuals array), or behavioral implications, leaving the agent with inadequate information to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, with one parameter ('data') documented only as an array of numbers in the schema. The description adds no information about this parameter, such as what 'data' represents (e.g., time series values), expected format (e.g., ordered sequence), or constraints (e.g., minimum length). It fails to compensate for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Remove trend from time series to obtain stationary residuals.' It specifies the verb ('Remove'), resource ('trend from time series'), and outcome ('stationary residuals'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'detect_trend' or 'deseasonalize', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('timeseries') and category ('analysis'), but does not specify prerequisites (e.g., requires a time series with a trend), when-not-to-use scenarios (e.g., for non-time-series data), or refer to related tools like 'detect_trend' or 'deseasonalize' for context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'apply differencing' which implies a transformation operation, but doesn't describe what the transformation entails (e.g., whether it modifies data in-place, returns a new series, handles edge cases like missing values, or has specific requirements like data length). For a tool with no annotations and two parameters, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. It efficiently states the purpose and includes domain/category context. However, the brevity comes at the cost of completeness, as noted in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has no annotations, 0% schema description coverage, no output schema, and two parameters, the description is incomplete. It lacks details on parameter semantics, behavioral traits (e.g., how differencing is applied, error handling), and output expectations. For a transformation tool in a domain like time series analysis, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning neither parameter ('data' and 'lag') has descriptions in the schema. The tool description adds no information about parameters—it doesn't explain what 'data' should contain (e.g., a time series array), what 'lag' means (e.g., the order of differencing), or any constraints (e.g., lag must be positive, data must be numeric). With two undocumented parameters, the description fails to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Apply differencing to make time series stationary' with domain and category context. It specifies the action ('apply differencing') and the goal ('make time series stationary'), which is more specific than just restating the name. However, it doesn't explicitly differentiate from potential sibling tools that might also handle time series stationarity (like 'detrend' or 'stationarity_test'), though those are distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('timeseries') and category ('analysis'), but offers no explicit when-to-use, when-not-to-use, or comparison to sibling tools (e.g., 'detrend' for removing trends or 'stationarity_test' for checking stationarity). Usage is implied by the purpose statement alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the iterative process and termination condition, but does not cover critical aspects like error handling (e.g., for negative inputs), performance characteristics (e.g., iteration limits), or output format. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core functionality in one sentence. The domain and category in parentheses are additional but not wasteful. It avoids redundancy and is efficiently structured, though it could be slightly more informative without losing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for the single parameter, the description is incomplete. It explains the high-level process but omits details on input validation, output format, error conditions, and performance limits. For a tool with iterative behavior, this lack of context makes it insufficient for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter 'n' with 0% description coverage, and the tool description adds no information about 'n' (e.g., its meaning, valid range, or constraints). With low schema coverage, the description fails to compensate, leaving the parameter undocumented. This is inadequate for a tool with a required parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate sequence by repeatedly applying digital product until single digit or zero.' It specifies the verb ('generate sequence'), resource ('digital product'), and termination condition ('until single digit or zero'). However, it does not explicitly differentiate from sibling tools like 'digital_persistence' or 'digital_root', which may involve similar concepts, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context on prerequisites, typical use cases, or comparisons to sibling tools such as 'digital_persistence' or 'digital_root'. The domain and category hints ('arithmetic, iterative_sequences') are too vague to serve as practical usage guidelines.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It describes the iterative process but does not specify output format (e.g., list of integers), handling of edge cases (e.g., negative or zero input), or performance characteristics (e.g., iteration limits). This leaves gaps for a tool with one parameter and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first in a single sentence. The additional domain and category information is brief and relevant. There is no unnecessary verbosity, making it efficient, though slightly more detail could improve completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It explains the process but misses key details: parameter meaning, output format, error handling, and differentiation from siblings. For a tool with one parameter and iterative behavior, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description does not explain what 'n' represents (e.g., starting number), its valid range, or constraints (e.g., must be positive). This fails to compensate for the lack of schema documentation, leaving the parameter's meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate sequence by repeatedly applying digital sum until single digit.' It specifies the verb ('generate sequence'), the method ('repeatedly applying digital sum'), and the termination condition ('until single digit'). However, it does not explicitly differentiate from sibling tools like 'digital_root' or 'digital_persistence', which are related but distinct concepts, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('iterative_sequences'), which gives some context, but does not specify when to use this tool versus alternatives like 'digital_root' (which computes a single value) or 'digital_persistence' (which counts iterations). No explicit when/when-not instructions or prerequisites are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool counts digits, but does not mention any behavioral traits such as error handling (e.g., for negative bases or invalid inputs), performance characteristics, or output format. This leaves significant gaps for a tool with parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted verbiage, and the core function is front-loaded. However, the domain/category tags add little value and could be considered slightly redundant if the sibling list already implies this context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not address key contextual aspects such as parameter details, behavioral constraints, or return values. For a tool with two parameters and mathematical operations, more information is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters 'n' and 'base' are undocumented in the schema. The description only mentions 'a number' and 'given base', which adds minimal semantic context. It does not explain what 'n' represents (e.g., integer input), the valid range for 'base', or the default value of 10 for 'base', failing to compensate for the low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Count the number of digits in a number for given base.' It specifies the verb ('Count'), resource ('digits in a number'), and scope ('for given base'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'digit_frequency' or 'digit_sum', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('digital_operations'), but this is too vague to help an agent choose between similar tools like 'digit_frequency' or 'digit_sum'. No explicit when/when-not instructions or named alternatives are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does, without explaining how it behaves—e.g., whether it handles negative numbers, large inputs, or invalid bases, what the output format is, or if there are any error conditions. This leaves significant gaps in understanding the tool's operational characteristics.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no wasted verbiage or redundancy, making it efficient and easy to parse, though this brevity contributes to gaps in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to provide necessary context such as parameter details, behavioral traits, or output expectations. For a tool with two parameters and mathematical operations, more information is needed to ensure the agent can use it correctly without confusion.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, meaning parameters 'n' and 'base' are undocumented in the schema. The description does not compensate by explaining what these parameters represent, their valid ranges, or examples of usage. For instance, it does not clarify that 'n' is the integer whose digits are summed or that 'base' defaults to 10, leaving the agent to guess parameter meanings.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sum of digits of a number in given base.' It specifies the verb ('calculate'), resource ('sum of digits'), and context ('number in given base'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'digital_sum_sequence' or 'digit_product', which are related but distinct operations, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: arithmetic, Category: digital_operations'), but this is too vague to inform usage decisions. There is no mention of prerequisites, typical use cases, or comparisons to siblings like 'digital_root' or 'digit_product', leaving the agent without practical usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior1/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the basic operation ('Divide the first number by the second number') without mentioning critical behaviors such as error handling (e.g., division by zero), input constraints (e.g., numeric types), or output format (e.g., floating-point result). This is inadequate for a mutation tool with zero annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single, direct sentence that states the core functionality, followed by brief domain/category tags. There is no wasted verbiage or redundancy, making it efficient and easy to parse for an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (2 parameters, no output schema, no annotations), the description is incomplete. It fails to address key contextual elements like error conditions (division by zero), numerical precision, or return value details. While the operation is straightforward, the lack of behavioral and output information leaves significant gaps for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds minimal semantic context by specifying 'first number' and 'second number' for parameters 'a' and 'b'. This clarifies the order of operands, which is essential for division. However, it doesn't detail data types, ranges, or special cases (e.g., 'b' cannot be zero), so it only partially compensates for the schema's lack of descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Divide') and identifies the resources ('first number by the second number'), making the operation unambiguous. It also includes domain/category context ('Domain: arithmetic, Category: core'), which helps situate it. However, it doesn't explicitly differentiate from sibling tools like 'element_wise_divide' or 'quotient', which perform similar division operations, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, constraints (e.g., division by zero), or comparisons to sibling tools like 'element_wise_divide' or 'quotient', leaving the agent without explicit usage context. The domain/category hint is minimal and doesn't substitute for practical guidelines.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool calculates, without mentioning behavioral aspects such as input validation (e.g., vectors must be of equal length), error handling, performance characteristics, or output format. This leaves significant gaps for a tool that performs a mathematical operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain/category tag is appended efficiently. There is no wasted verbiage, making it easy to parse, though it could benefit from more detail given the lack of annotations and schema descriptions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical operation with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to address key contextual elements such as parameter details, behavioral traits, error conditions, or output expectations. This makes it insufficient for an AI agent to reliably invoke the tool without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not add any parameter semantics. It does not explain what 'vector_a' and 'vector_b' represent (e.g., arrays of numbers), their expected format (e.g., numeric strings), constraints (e.g., equal length), or examples. This is inadequate given the low schema coverage and the tool's reliance on correct parameter interpretation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the dot product of two vectors (inner product)'. It specifies the verb ('calculate'), resource ('dot product'), and provides the synonym 'inner product' for clarity. However, it does not explicitly differentiate from sibling tools like 'cross_product' or 'scalar_projection', which are related vector operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It includes a domain/category tag ('Domain: linear_algebra.vectors, Category: general'), which implies context but does not specify when to use this tool versus alternatives like 'cross_product' or 'scalar_projection'. No explicit when-to-use, when-not-to-use, or prerequisite information is given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the mathematical operation but doesn't disclose important behavioral aspects: what happens with negative or non-integer inputs (though schema says integer), whether there are computational limits, error handling, or performance characteristics. The formula implies the operation but lacks implementation details an agent would need.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences: one defining the operation and one providing domain/category tags. It's front-loaded with the core purpose. The mathematical formula is efficiently expressed. However, the domain/category tags add little value and could be considered extraneous.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It explains what the tool does mathematically but doesn't cover parameter semantics, return values, error conditions, or practical usage context. For a mathematical function with potential edge cases (like negative inputs), this leaves significant gaps for an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It only mentions 'n' indirectly in the formula without explaining what values are valid (e.g., non-negative integers typically for double factorial). No information about parameter constraints, defaults, or examples is provided beyond what's inferable from the mathematical notation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool calculates the double factorial of a number and provides the mathematical formula (n!! = n × (n-2) × ...). It distinguishes itself from the sibling 'factorial' tool by specifying the double factorial operation. However, it doesn't explicitly contrast with other mathematical operations in the sibling list beyond the formula.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools for mathematical calculations (like factorial, power, etc.), there's no indication of appropriate contexts, edge cases, or comparisons to similar tools. The domain/category tags are generic and don't offer practical usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates an expansion but does not specify output format (e.g., list of integers), handling of invalid inputs, computational limits, or error conditions. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in one sentence. The additional domain and category information is brief and does not add unnecessary length. However, the lack of detail on parameters or usage slightly reduces efficiency, as key information is missing.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what the expansion output looks like, how 'terms' affects results, or any limitations. For effective use, more context on behavior and parameters is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('terms') with 0% description coverage, and the tool description provides no information about this parameter. It does not explain what 'terms' represents (e.g., number of expansion terms), valid ranges, or default behavior. With low schema coverage, the description fails to compensate, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate continued fraction expansion of e (Euler's number).' It specifies the verb ('Generate'), resource ('continued fraction expansion'), and target ('e'), making the function unambiguous. However, it does not differentiate from sibling tools like 'continued_fraction_e' or 'continued_fraction_expansion', which could cause confusion in selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('continued_fractions'), but this is too generic given siblings like 'continued_fraction_e' and 'continued_fraction_expansion'. There are no explicit instructions on prerequisites, constraints, or comparisons to other tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but lacks behavioral details such as formula used, assumptions (e.g., for t-tests), error handling, or output format. The description is minimal and does not disclose important traits beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core function in a single sentence. The domain/category information is appended efficiently. There is no wasted text, though it could benefit from more detail without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on the conversion method, parameter meanings, output interpretation, and statistical context. For a tool with two required parameters and no structured documentation, the description does not provide sufficient context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 't-statistic' and implies 'df' (degrees of freedom) via context, but does not explain what these parameters represent, their units, valid ranges, or how they relate to the conversion. The description adds minimal semantic value beyond the parameter names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert t-statistic to effect size r (correlation coefficient)'. It specifies the verb ('convert'), the input ('t-statistic'), and the output ('effect size r'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools, though the domain/category hint helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('inference'), which implies context, but offers no explicit when-to-use rules, prerequisites, or comparisons with sibling tools like 'cohens_d' or other statistical functions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. It mentions that EMA 'gives more weight to recent observations', which is useful context about the algorithm's behavior. However, it doesn't address important aspects like numerical stability, handling of edge cases (e.g., small datasets), performance characteristics, or what the output represents. For a computational tool with no annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise - a single sentence followed by domain/category tags. It's front-loaded with the core purpose. The domain/category tags could be considered slightly extraneous but don't significantly impact conciseness. Every element serves a purpose, though more parameter guidance would improve completeness without harming conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a 3-parameter computational tool with 0% schema description coverage and no output schema, the description is incomplete. It identifies the tool as an EMA calculator but doesn't explain parameter meanings, algorithm details, or expected output format. The domain/category tags provide some context but don't compensate for the lack of operational guidance needed to use this tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. The description mentions 'EMA' but doesn't explain what the three parameters (data, alpha, initial) represent or how they interact. While 'EMA' implies a timeseries input, no guidance is given about alpha's role as the smoothing factor or initial's purpose as the starting value. The description adds minimal value beyond the parameter names visible in the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute Exponential Moving Average (EMA) - gives more weight to recent observations'. It specifies the verb ('Compute'), resource ('Exponential Moving Average'), and a key behavioral characteristic (weighting). However, it doesn't differentiate from sibling tools like 'simple_moving_average' or 'weighted_moving_average' beyond mentioning 'EMA' specifically.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance through domain/category tags ('Domain: timeseries, Category: analysis'), which implies context but doesn't explicitly state when to use this tool versus alternatives. No specific when/when-not instructions or named alternatives are provided, leaving the agent to infer appropriate usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a PDF but doesn't describe output format, error handling, computational limits, or assumptions (e.g., rate > 0). For a statistical tool with zero annotation coverage, this is a significant gap in transparency about how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded in a single sentence: 'Calculate the probability density function (PDF) of the exponential distribution (Domain: probability, Category: general).' Every word contributes essential information without waste, making it efficient and well-structured for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical tool with no annotations, no output schema, and low parameter coverage, the description is incomplete. It states the purpose but lacks details on behavior, parameters, output, or usage context. For a tool that performs calculations with mathematical assumptions, more information is needed to ensure correct invocation and interpretation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds no information about parameters beyond what the input schema provides. With 0% schema description coverage and two parameters (x, rate), the schema only defines types and defaults. The description doesn't explain what x represents (e.g., input value) or rate (e.g., λ parameter), leaving semantics undocumented. This fails to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the probability density function (PDF) of the exponential distribution.' It specifies the verb ('calculate'), resource ('PDF'), and domain ('probability, Category: general'), making it unambiguous. However, it doesn't differentiate from sibling tools like 'exponential_cdf' or 'exponential_sample', which are related but distinct operations, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('probability') but doesn't specify scenarios, prerequisites, or comparisons to sibling tools like 'exponential_cdf' (cumulative distribution) or 'normal_pdf' (other distribution). This lack of context leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool performs a 'forecast,' implying a read-only operation that generates predictions, but does not disclose behavioral traits such as output format, error handling, computational limits, or assumptions (e.g., stationarity). The description is too vague to inform the agent about how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: a single sentence with no wasted words. It is front-loaded with the core purpose and includes domain/category context efficiently. Every part of the description adds value, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a forecasting tool with 3 parameters), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It states what the tool does but lacks essential details: parameter explanations, behavioral context, output information, and usage guidelines. For a tool with undocumented inputs and no structured output, more descriptive content is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not mention any parameters or their semantics (e.g., what 'alpha' or 'forecast_periods' represent). It fails to compensate for the lack of schema documentation, leaving the agent with no guidance on input meaning beyond the raw schema structure.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Simple exponential smoothing forecast for time series' specifies the verb ('forecast'), resource ('time series'), and method ('simple exponential smoothing'). It distinguishes from siblings by mentioning the domain ('timeseries') and category ('analysis'), but does not explicitly differentiate from similar forecasting tools like 'holt_winters_forecast' or 'moving_average_forecast'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('timeseries') and category ('analysis'), implying usage for time series forecasting. However, it lacks explicit when-to-use instructions, prerequisites, or alternatives (e.g., when to choose this over other forecasting methods like Holt-Winters). No exclusions or comparisons to sibling tools are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('Taylor series') and domain ('numerical'), but fails to describe key behaviors such as convergence properties, error handling for large inputs, computational complexity, or output format. For a tool with two parameters and no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence with additional context in parentheses. There is no wasted verbiage, and it efficiently communicates the essential information. However, it could be slightly improved by integrating the parameter semantics or usage guidelines more seamlessly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a Taylor series computation with two parameters, no annotations, and no output schema, the description is incomplete. It lacks details on parameter meanings, behavioral traits like accuracy or limitations, and expected output. For a mathematical tool with potential precision issues, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description does not add any semantic information about the parameters 'x' (the exponent) and 'n' (likely the number of terms in the Taylor series). It fails to explain what these parameters represent, their expected ranges, or how they affect the computation, leaving them undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute exponential function e^x using Taylor series'. It specifies the verb ('compute'), resource ('exponential function e^x'), and method ('Taylor series'), making the action unambiguous. However, it does not explicitly differentiate from sibling tools like 'exp' or 'compute_e_series', which might offer alternative methods for computing exponential functions, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance with 'Domain: numerical, Category: series', which implies it's for numerical inputs and series computations, but it lacks explicit instructions on when to use this tool versus alternatives. For example, it doesn't compare to 'exp' (which might be a direct exponential function) or 'compute_e_series' (which might compute e via series), leaving the agent without clear context for selection among siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a length, implying a read-only operation, but does not disclose behavioral traits such as computational complexity, input constraints (e.g., n must be non-negative), error handling, or output format. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the purpose, followed by domain/category in parentheses. There is no wasted verbiage, and the structure is efficient, though it could benefit from more detail given the lack of other documentation.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of mathematical tools, no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what a Farey sequence is, how the length is computed, or what the output looks like (e.g., integer result). This leaves significant gaps for an AI agent to understand and use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description does not add any semantic meaning beyond the schema—it does not explain what 'n' represents (e.g., order of the Farey sequence), valid ranges, or units. This fails to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the length of Farey sequence F_n.' It specifies the verb ('calculate') and resource ('length of Farey sequence'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'farey_sequence' or 'farey_sequence_properties', which could provide overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but gives no explicit when/when-not instructions, prerequisites, or references to sibling tools like 'farey_sequence' (which might generate the sequence itself) or 'farey_sequence_properties' (which might offer other calculations).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details: it doesn't specify output format (e.g., list of integers), handling of edge cases (e.g., n=0 or negative n), performance characteristics, or error conditions. The description is minimal and doesn't compensate for the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence plus domain/category tags—with no wasted words. It's front-loaded with the core purpose. However, the brevity comes at the cost of completeness, as it omits necessary details for effective tool use.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't cover parameter semantics, behavioral traits, or output details. For a tool with one parameter and no structured documentation, this description leaves significant gaps in understanding how to invoke and interpret results.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description adds minimal semantics. It mentions 'n' implicitly ('first n Fibonacci numbers') but doesn't explain its meaning, valid range, or constraints (e.g., must be positive integer). This is insufficient given the low schema coverage, failing to compensate for the undocumented parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n Fibonacci numbers.' It specifies the verb ('Generate') and resource ('Fibonacci numbers') with a parameter scope ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'fibonacci' or 'fibonacci_greedy_egyptian', which might have different behaviors or outputs.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags ('arithmetic', 'basic_sequences') give some context, there's no explicit mention of when to choose this over similar tools like 'fibonacci' or 'fibonacci_greedy_egyptian', nor any prerequisites or constraints for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds sociable numbers but gives no information about computational limits, performance characteristics, error handling, or output format. For a tool with two parameters and no output schema, this lack of behavioral context is a significant gap, leaving the agent with insufficient information to predict the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence followed by domain/category tags. It avoids unnecessary words and gets straight to the point. However, the domain/category tags might be considered slightly redundant if the server context already implies arithmetic/special numbers, but they don't significantly detract from conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (finding mathematical sequences with two parameters), the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to explain parameters, behavioral traits, or output expectations. For a tool in a server with many mathematical functions, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning the input schema provides no descriptions for the parameters 'limit' and 'max_chain_length'. The tool description does not mention these parameters at all, failing to compensate for the schema's lack of documentation. This leaves the agent guessing about what 'limit' and 'max_chain_length' mean in the context of finding sociable numbers.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find sociable numbers (amicable chains of length > 2).' It specifies the mathematical concept (sociable numbers) and distinguishes them from amicable pairs by noting chains of length > 2. However, it does not explicitly differentiate from sibling tools like 'find_amicable_pairs' beyond the domain/category tags, which is why it doesn't reach a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It includes domain and category tags ('Domain: arithmetic, Category: special_numbers'), but these are generic and don't help an agent choose between this and similar sibling tools (e.g., 'find_amicable_pairs', 'amicable_numbers', 'aliquot_sequence_analysis'). There's no mention of prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool generates but doesn't disclose behavioral traits like computational complexity, output format, whether it's deterministic, error handling, or any constraints (e.g., parameter limits). The description is minimal and lacks operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that efficiently states the tool's purpose and domain. It's front-loaded with the core functionality and wastes no words, though this brevity comes at the cost of completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical sequence generation with two parameters), no annotations, 0% schema coverage, and no output schema, the description is inadequate. It doesn't explain what the tool returns, how parameters interact, or any implementation details. For a tool with undocumented parameters and no structured context, more descriptive content is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description provides no information about the parameters 'limit' and 'size'. It doesn't explain what these parameters mean, their units, valid ranges, or how they affect the generated Sidon set. The description fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate a Sidon set (B_h sequence) - no two distinct sums are equal.' It specifies the verb ('Generate'), resource ('Sidon set'), and provides a mathematical property definition. However, it doesn't explicitly differentiate from sibling tools, though the domain/category context helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('additive_number_theory'), it offers no explicit usage context, prerequisites, or comparison with sibling tools that might handle similar mathematical sequences.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation purpose but does not describe output format, error handling, precision, or computational characteristics. For a mathematical tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. It avoids unnecessary words, though the parenthetical domain/category annotation could be considered slightly extraneous. Overall, it is appropriately sized with zero waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and two parameters, the description is incomplete. It lacks details on parameter formats, return values, error conditions, and behavioral traits. For a tool performing a mathematical operation, this leaves critical context gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter details. The description does not explain what 'p1' and 'p2' represent (e.g., coordinate formats like 'x,y,z'), their expected data types beyond 'string', or any constraints. It adds no meaningful semantics beyond the tool's purpose.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Calculate') and resource ('Euclidean distance between two 3D points'), making the purpose specific and understandable. However, it does not explicitly differentiate from sibling tools like 'geom_distance' (2D distance) or 'geom_great_circle_distance', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('geometry') and category ('general'), but offers no explicit when/when-not instructions or references to sibling tools for comparison, leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates a sequence but does not describe output format (e.g., list of numbers), error handling (e.g., for invalid inputs like negative num_terms), or computational constraints (e.g., limits on term size). This leaves significant gaps for a tool with three parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. The parenthetical note about domain and category is brief and does not detract from clarity. However, it could be slightly more structured by separating usage notes from the core purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (three parameters, no annotations, no output schema), the description is incomplete. It lacks details on output format, error conditions, and example usage, which are crucial for an agent to invoke it correctly. The domain/category hint is insufficient to compensate for these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description only lists parameter names ('first term, common ratio, and number of terms') without explaining their semantics, units, or valid ranges. For example, it doesn't clarify if 'num_terms' must be positive or if 'common_ratio' can be zero. This adds minimal value beyond the schema's property names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate a geometric sequence with given first term, common ratio, and number of terms.' It specifies the verb ('generate'), resource ('geometric sequence'), and required inputs. However, it does not explicitly differentiate from sibling tools like 'geometric_series' or 'geometric_sum', which are related but distinct operations, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but this is too vague to help an agent choose between similar tools like 'geometric_series' or 'arithmetic_sequence'. There are no explicit instructions on use cases, prerequisites, or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a distance, implying a read-only operation, but does not address potential behaviors like error handling (e.g., invalid point formats), computational limits, or output format. The description is too sparse to fully inform the agent about how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. There is no wasted verbiage, and the domain/category tags are efficiently appended. However, the brevity comes at the cost of completeness, as it omits necessary details for full understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a mathematical calculation with 2 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not explain parameter formats, expected output, or any behavioral nuances. For a tool that requires precise input formatting to avoid errors, this leaves significant gaps in contextual understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (p1, p2) with 0% description coverage, meaning the schema provides no details on their format or meaning. The description only mentions 'two 2D points' without specifying how points should be represented (e.g., as strings like 'x,y'). It adds minimal semantic value, failing to compensate for the lack of schema documentation, which is critical for proper tool invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Manhattan (taxicab) distance between two 2D points.' It specifies the verb ('calculate'), resource ('Manhattan distance'), and domain/context ('geometry'). However, it does not explicitly differentiate from sibling tools like 'geom_distance' or 'geom_distance_3d', which likely compute Euclidean distances, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance: it mentions the domain ('geometry') and category ('general'), but offers no explicit advice on when to use this tool versus alternatives (e.g., 'geom_distance' for Euclidean distance). There is no mention of prerequisites, constraints, or typical scenarios, leaving the agent with little contextual direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the domain and category but fails to describe key behavioral traits: what happens if segments don't intersect (e.g., returns null, error, or specific value), whether the tool handles degenerate cases (e.g., overlapping or parallel segments), or the format of the output (e.g., coordinates, boolean). This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The additional context ('Domain: geometry, Category: general') is brief and relevant, though it could be more informative. There is no wasted verbiage, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (2 parameters with nested objects, 0% schema coverage, no output schema, and no annotations), the description is insufficient. It lacks details on parameter formats, behavioral outcomes (e.g., intersection logic), and return values. For a geometry tool with undefined input structures, more context is needed to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two required parameters ('seg1' and 'seg2') of type 'object' but no details on their structure (e.g., expected properties like endpoints). The description does not add any parameter semantics beyond what the schema provides—it doesn't explain what 'seg1' and 'seg2' represent or how they should be formatted. This is inadequate given the low schema coverage and nested object complexity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find intersection point of two line segments in 2D space.' It specifies the verb ('Find'), resource ('intersection point'), and domain ('2D space'), making it easy to understand what the tool does. However, it does not explicitly differentiate from sibling tools like 'geom_line_intersection' or 'geom_circle_intersection', which is why it doesn't achieve a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance by mentioning the domain ('geometry') and category ('general'), but it does not specify when to use this tool versus alternatives (e.g., 'geom_line_intersection' for lines instead of segments, or 'geom_circle_intersection' for circles). There is no explicit 'when' or 'when not' context, leaving the agent to infer usage based on tool names alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs gradient descent to find a minimum, implying iterative optimization, but doesn't describe key behaviors like convergence criteria (e.g., based on tolerance or max_iterations), error handling (e.g., for non-convex functions), output format, or performance characteristics (e.g., computational cost). This is inadequate for a tool with 6 parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. Every word earns its place with no redundancy or fluff, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (numerical optimization with 6 parameters), lack of annotations, and no output schema, the description is incomplete. It doesn't cover parameter meanings, behavioral details (e.g., iteration limits, convergence), or return values. While conciseness is high, it sacrifices necessary context for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 6 parameters with 0% description coverage, meaning none are documented in the schema. The description adds no parameter semantics—it doesn't explain what 'f', 'grad_f', 'x0', 'learning_rate', 'max_iterations', or 'tolerance' represent, their expected formats (e.g., 'f' as a string expression), or typical values. This leaves parameters completely undocumented, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform gradient descent optimization to find minimum of a function.' It specifies the verb ('Perform gradient descent optimization'), resource ('function'), and scope ('find minimum'), and distinguishes it from sibling tools like 'coordinate_descent' and 'gradient_descent_momentum' by not mentioning momentum or coordinate-specific methods. However, it doesn't explicitly differentiate from 'nelder_mead' (another optimization tool), so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('numerical') and category ('optimization'), which implies when to use it, but doesn't specify when to choose this over alternatives like 'gradient_descent_momentum', 'coordinate_descent', or 'nelder_mead'. No exclusions or prerequisites are stated, leaving the agent with little practical direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the action ('Apply Gram-Schmidt orthogonalization') but does not describe what the tool returns (e.g., orthogonal vectors, orthogonal basis), error conditions, performance characteristics, or side effects. For a mathematical transformation tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and it efficiently communicates the core functionality. However, the inclusion of domain and category in parentheses, while informative, slightly disrupts the flow but does not significantly detract from clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a linear algebra transformation tool with 2 parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It lacks details on input format, output format, error handling, and mathematical assumptions (e.g., linear independence). For a tool that performs a non-trivial operation, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the schema provides no descriptions for the parameters. The description does not compensate by explaining what 'vectors' should contain (e.g., format, representation) or what 'normalize' does (e.g., whether it normalizes to unit vectors). This leaves the parameters largely undocumented, failing to add meaningful semantics beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Apply Gram-Schmidt orthogonalization to a set of vectors.' It specifies the verb ('Apply Gram-Schmidt orthogonalization') and resource ('a set of vectors'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'orthogonalize' or 'normalize_vector', which could perform similar or related operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify prerequisites, typical use cases, or when to choose this over sibling tools like 'orthogonalize' or 'normalize_vector'. Without such context, the agent must infer usage from the tool name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates trigonometric functions but does not describe output format, error handling, computational limits, or whether it requires specific input units (e.g., radians vs. degrees). For a calculation tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The additional domain/category context is brief and relevant. There is no wasted text, making it efficient, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (trigonometric calculations), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not cover behavioral aspects, parameter details, or output expectations, making it insufficient for an AI agent to fully understand how to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It does not explain the 'angle' parameter (e.g., expected units, range) or the 'function' parameter beyond what the enum in the schema provides. The description adds no semantic details about parameters, leaving them inadequately documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate trigonometric functions using half angle formulas.' It specifies the verb ('calculate'), resource ('trigonometric functions'), and method ('half angle formulas'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'double_angle_formulas' or other trigonometric tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('identities'), which implies context, but does not specify use cases, prerequisites, or comparisons to sibling tools like 'double_angle_formulas' or basic trigonometric functions (e.g., 'sin', 'cos'). This lack of explicit guidance limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a partial sum, implying a read-only operation, but does not cover important aspects like computational complexity, error handling, or output format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. It avoids unnecessary details, though it could be more informative. The structure is efficient, with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical calculation with two parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not address parameter meanings, behavioral traits, or result format, making it inadequate for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'start' and 'end' undocumented. The description mentions 'given terms' but does not explain what these parameters represent (e.g., integer indices, inclusive/exclusive ranges) or provide examples. This fails to compensate for the lack of schema documentation, leaving parameters ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate partial sum of harmonic series with given terms.' It specifies the verb ('calculate'), resource ('partial sum of harmonic series'), and scope ('with given terms'). However, it does not explicitly differentiate from sibling tools like 'harmonic_series' or 'harmonic_number', which might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('harmonic_series'), but does not specify use cases, prerequisites, or comparisons to sibling tools such as 'harmonic_series' or 'harmonic_number'. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the domain ('arithmetic') and category ('digital_operations'), but fails to describe key behaviors: whether the tool is read-only or mutative, what the output format is (e.g., list of integers), performance considerations, or error handling. This leaves significant gaps for a tool with parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a single sentence stating the core functionality followed by domain/category tags. There is no wasted text, and it efficiently communicates the essential purpose without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (2 parameters, no annotations, no output schema), the description is inadequate. It lacks details on parameter meanings, output format, behavioral traits, and usage context. For a tool that generates a list of numbers, more completeness is needed to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters 'limit' and 'base' are undocumented in the schema. The description only mentions 'limit' indirectly ('up to a limit') and omits 'base' entirely, failing to explain their purposes (e.g., 'limit' as the upper bound, 'base' as the numeral system defaulting to 10). It adds minimal value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all Harshad numbers up to a limit.' It specifies the verb ('find'), resource ('Harshad numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_harshad_number' or 'harshad_numbers' (if duplicates exist), keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it implies usage for finding Harshad numbers within a limit, but offers no explicit advice on when to use this tool versus alternatives (e.g., 'is_harshad_number' for checking individual numbers) or any prerequisites. Without such context, the agent lacks clear direction for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a value, implying a read-only operation, but doesn't disclose behavioral traits like computational complexity, error handling (e.g., for invalid 'n'), output format, or any side effects. For a tool with no annotation coverage, this is inadequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence states the core purpose, followed by domain/category tags. There's no wasted text, and it's appropriately sized for a simple calculation tool. However, the parentheses and tags could be slightly streamlined for better readability.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what a hexagram number is mathematically, how it's computed, what the output looks like, or any constraints. For a tool with such sparse structured data, the description should provide more context to be useful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one required parameter 'n' of type integer. The description adds minimal semantics by implying 'n' is an index ('nth hexagram number'), but doesn't specify valid ranges (e.g., n ≥ 1?), meaning, or examples. This doesn't compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth hexagram number (Star of David).' It specifies the verb ('calculate'), the resource ('hexagram number'), and provides clarifying context ('Star of David') and domain/category tags. However, it doesn't explicitly differentiate from sibling tools (like 'star_number' or other figurate number calculators), preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), which implies context but doesn't specify use cases, prerequisites, or comparisons to sibling tools (e.g., 'star_number', 'centered_hexagonal_number'). This leaves the agent with minimal direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'efficient computation', which hints at performance characteristics, but fails to describe critical behavioral traits: what the tool returns (e.g., a single numeric result), error handling (e.g., for invalid inputs), computational complexity, or any side effects. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. The single sentence 'Evaluate polynomial using Horner's method (efficient computation)' efficiently states the main function, and the parenthetical domain/category adds minimal but relevant context without redundancy. However, the lack of parameter explanations or usage guidelines means it may be overly terse for full understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (polynomial evaluation with a specific algorithm), no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to explain parameters, return values, error conditions, or algorithmic details. While it names the method and hints at efficiency, it doesn't provide enough context for reliable use without external knowledge of Horner's method.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It does not explain the parameters at all—no mention of what 'coefficients' represents (e.g., polynomial coefficients in descending order) or what 'x' is (e.g., the evaluation point). The description adds no semantic information beyond the bare schema, leaving parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Evaluate polynomial using Horner's method (efficient computation)'. It specifies the verb ('evaluate'), resource ('polynomial'), and method ('Horner's method'), and distinguishes it from generic polynomial evaluation tools by mentioning efficiency. However, it doesn't explicitly differentiate from potential sibling polynomial evaluation tools (though none are listed among siblings).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('numerical') and category ('series'), which gives some context, but offers no explicit guidance on when to use this tool versus alternatives (e.g., direct polynomial evaluation methods). There's no mention of prerequisites, performance trade-offs, or specific scenarios where Horner's method is preferred.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but does not disclose behavioral traits such as error handling (e.g., for invalid inputs like zero denominator), computational constraints, or output format details. The description is basic and lacks critical operational context for a tool with parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. It efficiently conveys the core purpose and domain/category. However, the brevity comes at the cost of completeness, as noted in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a conversion tool with 2 parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not explain parameter meanings, output format, or error conditions, making it inadequate for reliable tool invocation by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (numerator, denominator) with 0% description coverage, meaning no schema documentation. The description does not add any parameter semantics—it does not explain what these parameters represent, their constraints (e.g., integers, non-zero denominator), or how they relate to the conversion. This fails to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert improper fraction to mixed number and Egyptian fraction for fractional part.' It specifies the verb (convert) and the resource (improper fraction), and distinguishes the output types (mixed number and Egyptian fraction). However, it does not explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'binary_remainder_egyptian', which might handle similar conversions, so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain (arithmetic) and category (egyptian_fractions), which implies context but does not specify when to use this tool versus alternatives like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction'. There is no explicit when/when-not or named alternatives, leaving usage vague.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the types of integers generated (positive, negative, and zero), which adds some behavioral context, but lacks details on output format (e.g., list, sequence), ordering, inclusivity of endpoints, or error handling for invalid ranges. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context, which is somewhat redundant but not wasteful. Overall, it's efficiently structured with minimal fluff.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It fails to explain parameter usage, output format, or behavioral constraints like range validation. For a simple 2-parameter tool, this leaves significant gaps that could hinder correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It implies parameters for defining a range ('in a given range'), but doesn't name or explain 'start' and 'end' parameters from the schema, their semantics (e.g., inclusive/exclusive), or valid values. This leaves key parameter details undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate integers (positive, negative, and zero) in a given range.' It specifies the action (generate), resource (integers), and scope (range), though it doesn't explicitly differentiate from siblings like 'range_value' or 'in_range' that might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description includes a domain and category ('Domain: arithmetic, Category: number_systems'), but this is generic and doesn't help the agent choose between this and sibling tools like 'range_value' or 'natural_numbers'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a definite integral but does not describe key behaviors such as error handling, performance characteristics, or what the output looks like (e.g., numeric result, error estimate). For a computational tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. It avoids unnecessary words, but the inclusion of 'Domain: calculus, Category: general' adds minimal value and could be considered slightly redundant. Overall, it is efficiently structured with no wasted sentences.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a numerical integration tool with 4 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It fails to explain parameter meanings, expected output format, error behavior, or usage context. This leaves the agent with insufficient information to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters (func, a, b, n_steps) are documented in the schema. The description does not add any semantic information about these parameters—it does not explain what 'func' should contain (e.g., a mathematical expression), what 'a' and 'b' represent (integration limits), or the role of 'n_steps' (number of subdivisions). This leaves all parameters unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate definite integral using the midpoint rule'. It specifies the verb ('calculate'), resource ('definite integral'), and method ('midpoint rule'), which is specific and unambiguous. However, it does not explicitly differentiate from sibling tools like 'integrate_simpson' or 'integrate_trapezoid', which are also numerical integration methods, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('calculus') and category ('general'), but this is too vague to inform usage decisions. There is no mention of when this method is preferred over other integration tools or any prerequisites, leaving the agent without practical usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool 'checks' something, implying a read-only operation, but does not disclose behavioral traits such as computational complexity, error handling (e.g., for invalid inputs), or output format. The description is minimal and lacks details on what the tool actually does beyond the high-level check.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that states the purpose, followed by domain/category in parentheses. There is no wasted text, and it efficiently conveys the core functionality without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (3 parameters, 0% schema coverage, no annotations, no output schema), the description is incomplete. It lacks details on parameter semantics, behavioral traits, and expected output. For a tool that performs a mathematical check with multiple inputs, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'a set' and 'limit', which loosely map to 'basis' and 'limit', but does not explain parameter meanings (e.g., what 'basis' represents, the role of 'max_terms' with its default). No semantic details are added beyond the schema's property names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a set forms an additive basis for integers up to limit.' It specifies the verb ('Check'), resource ('a set'), and scope ('for integers up to limit'), with domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., other 'is_*' tools like 'is_perfect_square'), though the mathematical context is distinct.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('additive_number_theory'), which implies context, but offers no explicit when/when-not instructions or references to sibling tools for related tasks (e.g., 'sum_of_two_squares' or 'waring_representation').
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool 'checks' a number, implying a read-only operation, but doesn't disclose behavioral traits like error handling for invalid inputs (e.g., negative numbers), performance characteristics, or what the output looks like (e.g., boolean or detailed result). For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a single sentence that directly states the purpose. The domain/category addition is brief and relevant. There's no wasted text, making it efficient, though it could benefit from slightly more detail given the lack of other documentation.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (checking amicable numbers involves mathematical logic), no annotations, no output schema, and low parameter coverage, the description is incomplete. It doesn't explain what amicable numbers are, provide examples, describe the return value, or address edge cases. For a tool with no structured support, this leaves too much undefined for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description doesn't add any semantic information about 'n', such as valid ranges (e.g., positive integers only), examples, or what 'amicable' means in context. With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is amicable (part of an amicable pair).' It specifies the verb ('Check') and resource ('number'), and the domain/category context helps clarify it's about arithmetic special numbers. However, it doesn't explicitly differentiate from sibling tools like 'find_amicable_pairs', which might cause confusion about when to use each.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With sibling tools like 'find_amicable_pairs' available, there's no indication whether this tool is for single-number checks or part of broader analyses. The domain/category hint is minimal and doesn't address usage context or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool checks for a constant difference but does not specify behavioral traits like error handling (e.g., for invalid inputs), performance characteristics, or output format (e.g., boolean result). This leaves significant gaps in understanding how the tool behaves in practice.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence. The additional domain and category information is brief and does not add unnecessary length. However, the lack of detail on parameters and usage slightly reduces efficiency, as more information could improve clarity without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a tool with two parameters, no annotations, and no output schema), the description is incomplete. It fails to explain parameter semantics, behavioral traits, or output expectations. For a tool that performs a mathematical check, more context on input format, tolerance usage, and result interpretation is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It does not explain the parameters 'sequence' (an array of strings) or 'tolerance' (a number with default 1e-9), such as what the sequence represents (e.g., numeric values as strings) or how tolerance affects the arithmetic check. This lack of semantic detail makes parameter usage unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a sequence is arithmetic (constant difference between consecutive terms).' It specifies the verb ('Check'), resource ('sequence'), and condition ('constant difference between consecutive terms'). However, it does not explicitly differentiate from sibling tools like 'arithmetic_sequence' or 'arithmetic_series', which may have overlapping or related functionality, preventing a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context such as prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'is_geometric' or other sequence analysis tools. The domain and category tags ('Domain: arithmetic, Category: general') are too vague to serve as meaningful usage guidelines.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but does not describe how it behaves: e.g., what tolerance means in practice, whether it handles edge cases like empty sequences or non-numeric inputs, or what the output looks like (e.g., boolean or detailed result). This leaves significant gaps for a tool with parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is zero waste, and every part earns its place by providing essential information efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (checking geometric sequences with tolerance), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not cover parameter meanings, behavioral details, or output format, making it inadequate for an agent to use the tool correctly without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds no meaning beyond the input schema. Schema description coverage is 0%, and the description does not explain the 'sequence' parameter (e.g., that it should be numeric) or the 'tolerance' parameter (e.g., its role in checking the constant ratio). With two parameters and no schema descriptions, the description fails to compensate, leaving parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a sequence is geometric (constant ratio between consecutive terms).' It specifies the verb ('Check'), resource ('sequence'), and defines the geometric property. However, it does not explicitly differentiate from sibling tools like 'is_arithmetic' or 'geometric_sequence', which are related but serve different purposes, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but this is vague and does not help an agent decide between this tool and siblings like 'is_arithmetic' or 'geometric_sequence'. There are no explicit when-to-use or when-not-to-use instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool's function but doesn't describe what a 'happy number' is, how the check is performed (e.g., iterative process), what inputs are valid (e.g., positive integers only?), or what the output looks like (e.g., boolean). For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence plus domain/category annotations. It's front-loaded with the core purpose and avoids unnecessary words. However, the brevity comes at the cost of completeness, as noted in other dimensions, but as pure conciseness, it's efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (involves a mathematical concept), no annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't define 'happy number', explain the algorithm, specify input/output formats, or provide examples. For a tool that requires understanding a specific mathematical property, this is inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage (no schema description). The tool description doesn't mention parameters at all, failing to compensate for the lack of schema documentation. It doesn't explain what 'n' represents (e.g., integer to test) or any constraints (e.g., must be positive). With low schema coverage, the description adds no parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a happy number.' It includes a specific verb ('Check') and resource ('a number'), and the domain/category annotation ('Domain: arithmetic, Category: iterative_sequences') provides additional context. However, it doesn't explicitly differentiate from its sibling tool 'happy_numbers' (which likely lists happy numbers rather than testing a single number), so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like 'happy_numbers' or other number-checking tools (e.g., 'is_prime', 'is_perfect_square'), nor does it specify prerequisites or typical use cases. The domain/category hints at context but doesn't constitute explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool checks and shows the split, implying a read-only operation that returns a boolean and split details, but it doesn't disclose behavioral traits like error handling (e.g., for invalid inputs), performance characteristics, or output format specifics. The description is minimal and lacks necessary context for safe invocation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core functionality in the first clause. The additional domain/category information is brief but could be considered slightly extraneous. Overall, it's efficient with minimal waste, though it lacks structural elements like examples or bullet points.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical check with a split output), no annotations, no output schema, and low parameter coverage, the description is incomplete. It doesn't explain what a Kaprekar number is, how the split is shown, or what the return values look like. The agent would struggle to use this tool effectively without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter 'n' with 0% description coverage, and the tool description adds no parameter semantics. It doesn't explain what 'n' represents (e.g., a positive integer, any integer), valid ranges, or constraints. With low schema coverage, the description fails to compensate, leaving the parameter meaning unclear beyond its type.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a Kaprekar number and show the split.' It specifies both the verification function and the additional output of the split, which is more informative than just the name. However, it doesn't explicitly differentiate from sibling tools like 'kaprekar_numbers' or 'kaprekar_sequence', which likely serve different purposes (listing numbers vs checking a single number).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: arithmetic, Category: special_numbers'), but this is generic and doesn't help an agent choose between this and sibling tools like 'kaprekar_numbers' (which might list Kaprekar numbers) or 'kaprekar_sequence' (which might generate sequences). No explicit when/when-not instructions or prerequisites are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the domain ('arithmetic') and category ('digital_operations'), but does not explain critical behaviors like what constitutes a palindromic number, how base conversion affects the check, error handling for invalid inputs, or the return format (e.g., boolean). This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core functionality in the first sentence. The domain and category annotations are brief and relevant. There is no wasted text, making it efficient for quick understanding, though it could benefit from more detail given the lack of other documentation.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a palindromic check with base conversion, no annotations, no output schema, and low schema coverage, the description is incomplete. It does not cover behavioral aspects, parameter details, or return values, leaving the agent with insufficient information to use the tool effectively beyond basic inference.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions parameters 'n' and 'base' implicitly ('number' and 'given base'), but does not explain their semantics, constraints (e.g., base range, integer requirements), or default behavior (base defaults to 10 per schema). This adds minimal value beyond the schema's structural information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is palindromic in given base.' It specifies the verb ('Check'), resource ('number'), and scope ('in given base'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'palindromic_numbers' or 'next_palindrome', which reduces it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context on prerequisites, typical use cases, or comparisons to sibling tools such as 'palindromic_numbers' (which might list palindromic numbers) or 'next_palindrome' (which finds the next palindrome). Without such information, the agent must infer usage from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool's function but does not describe output format (e.g., boolean or detailed result), error handling (e.g., for invalid inputs like n ≤ 0), or performance characteristics. For a tool with no annotations, this leaves significant gaps in understanding how it behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence clearly states the tool's purpose, and the second adds domain/category context. There is no wasted text, and it efficiently conveys the essential information in two brief sentences, making it easy to scan and understand.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical check with two parameters), no annotations, no output schema, and low schema coverage (0%), the description is incomplete. It lacks details on output format, error conditions, and mathematical nuances (e.g., handling of composite n). While it states the purpose, it does not provide enough context for reliable use without additional assumptions or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, providing only types (integers) without explanations. The description mentions 'a' and 'n' in context ('Check if a is a quadratic residue modulo n'), which adds some meaning (e.g., 'a' is the number to check, 'n' is the modulus). However, it does not detail constraints (e.g., n must be positive), default values, or examples, failing to fully compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a is a quadratic residue modulo n.' It specifies the verb ('Check'), the mathematical operation ('quadratic residue'), and the parameters involved ('a' and 'n'). However, it does not explicitly differentiate from sibling tools like 'quadratic_residues' or 'legendre_symbol', which might offer related functionality, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it includes a domain ('arithmetic') and category ('modular_arithmetic'), which gives some context. However, it does not specify when to use this tool versus alternatives (e.g., 'legendre_symbol' or 'quadratic_residues' among siblings), nor does it mention prerequisites or constraints. This lack of explicit usage instructions limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states it's a calculation function, implying it's read-only and non-destructive, but doesn't explicitly confirm this or mention any constraints like input validation, error handling, computational complexity, or output format. For a mathematical function tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the core purpose in the first clause, adds clarifying context in parentheses. There's zero wasted language, and every word earns its place. The structure is optimal for a simple mathematical function tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical function with 2 parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the function computes mathematically, parameter semantics, return values, or error conditions. While conciseness is good, it sacrifices necessary completeness for this context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (n and k) with 0% description coverage in the schema. The tool description provides no information about what these parameters represent, their mathematical meaning, valid ranges (e.g., n > 0, k integer), or units. This leaves both parameters completely undocumented beyond their types, which is inadequate for a mathematical function.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Jordan's totient function J_k(n) - generalization of Euler's totient.' It specifies the verb ('calculate'), the mathematical function, and provides context about its relationship to Euler's totient. However, it doesn't explicitly differentiate from sibling tools like 'euler_totient' beyond mentioning it's a generalization.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('arithmetic_functions'), which gives some context, but offers no explicit guidance on when to use this tool versus alternatives like 'euler_totient' or other arithmetic functions. There's no mention of prerequisites, typical use cases, or comparison to siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool creates lagged versions by shifting values, which implies a read-only transformation, but doesn't clarify if it modifies input data, handles edge cases (e.g., missing values at boundaries), or describes output format. For a tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence, followed by domain/category context. There's no wasted verbiage, and every part contributes to understanding. However, the domain/category annotation could be considered slightly redundant if already inferred from context, but it's still efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (time series transformation), lack of annotations, no output schema, and low schema coverage (0%), the description is incomplete. It doesn't explain the output (e.g., format, handling of shifted values), error conditions, or practical usage examples. For a 2-parameter tool with no structured support, this leaves the agent under-informed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'shift values by specified number of periods', which hints at the 'lags' parameter's purpose, but doesn't explain 'data' (e.g., expected format, time series requirements) or provide details on 'lags' (e.g., valid ranges, multiple lag support). This adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Create lagged version of time series - shift values by specified number of periods'. It includes a specific verb ('Create'), resource ('lagged version of time series'), and operation details. However, it doesn't explicitly differentiate from sibling tools like 'differencing' or 'autocorrelation' that might also manipulate time series data, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('timeseries') and category ('analysis'), but offers no explicit when/when-not instructions or references to sibling tools like 'differencing' or 'moving_average' that might serve similar purposes in time series analysis.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a statistical test but does not describe output format, error handling, computational limits, or assumptions (e.g., data distribution requirements). While it implies a read-only operation (testing), it lacks details on behavioral traits like whether it returns a p-value, test statistic, or interpretation, which is insufficient for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence with additional domain/category context. There is no wasted verbiage, and it efficiently communicates the essential function. However, it could be slightly improved by integrating parameter hints or usage notes without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test, no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on input data format, output structure, statistical assumptions, and error conditions. For a tool performing inference with multiple parameters, this minimal description does not provide enough context for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, and the tool description does not explain them. It mentions 'groups' and 'alpha' implicitly in the purpose but provides no semantics on what 'groups' represents (e.g., array of data arrays or group labels) or how 'alpha' is used (significance level). With low schema coverage, the description fails to compensate, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Levene's test for equality of variances to test whether groups have equal variances.' It specifies the verb ('perform'), resource ('Levene's test'), and objective ('test whether groups have equal variances'), with domain/category context. However, it does not differentiate from sibling tools like 'variance' or 'fishers_exact_test' that also involve statistical testing, which prevents a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('inference'), but does not specify scenarios, prerequisites, or comparisons to other statistical tests (e.g., 'variance' for single-group analysis or 'fishers_exact_test' for categorical data). This lack of explicit usage context limits its helpfulness for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the operation but doesn't disclose behavioral traits: it doesn't explain the interpolation formula (y = y0 + (x - x0)*(y1 - y0)/(x1 - x0)), error handling (e.g., division by zero if x0 = x1), output format, or numerical precision. For a mathematical tool with 5 parameters, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's function. It's appropriately sized for a simple mathematical operation, with no wasted words. However, it could be more front-loaded by immediately specifying it's for 1D interpolation, but overall it's concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical interpolation with 5 parameters), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the interpolation formula, parameter roles, constraints, or return value. For a tool in a server with many mathematical functions, more context is needed to use it correctly without trial and error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description adds minimal semantics: it implies parameters are numerical points for interpolation but doesn't explain what x, x0, y0, x1, y1 represent (e.g., x is the input value, (x0,y0) and (x1,y1) are the two points). It doesn't clarify constraints like x0 ≠ x1 or ordering. The description fails to compensate for the lack of schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform linear interpolation between two points'. It specifies the domain (numerical) and category (interpolation), making the verb+resource explicit. However, it doesn't distinguish from sibling tools like 'bilinear_interpolate' or 'linear_interpolate_sequence', which would require mentioning it's for 1D interpolation between exactly two points.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like 'bilinear_interpolate' (for 2D) or 'linear_interpolate_sequence' (for multiple points), nor does it specify prerequisites or typical use cases. The agent must infer usage from the name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does (linear regression) and returns (slope, intercept, R²), but lacks critical details such as input format expectations (e.g., numeric arrays vs. strings), error handling, computational limits, or assumptions (e.g., linearity). This is insufficient for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, efficiently conveying the core functionality in a single sentence. It avoids unnecessary details and is structured to immediately inform the user about the tool's purpose and outputs. However, it could be slightly improved by integrating parameter hints, but it remains highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical tool with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It covers the basic operation and outputs but misses essential context such as parameter explanations, error conditions, and behavioral traits. This makes it inadequate for reliable tool invocation by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two required parameters ('xs' and 'ys') of type array of strings. The description does not explain what these parameters represent (e.g., independent and dependent variables), their expected format (e.g., numeric strings), or any constraints (e.g., equal length arrays). This leaves the semantics unclear, failing to compensate for the schema's lack of documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform linear regression to fit y = mx + b and return slope, intercept, and R²'. It specifies the statistical operation (linear regression), the model (y = mx + b), and the outputs (slope, intercept, R²). However, it does not explicitly differentiate from sibling tools (e.g., 'correlation' or other regression-related tools), which prevents a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (statistics) and category (general), but offers no explicit context, prerequisites, or comparisons to sibling tools like 'correlation' or other statistical methods. This lack of usage direction limits its effectiveness for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the algorithm's core behavior ('each composite marked exactly once') but lacks critical information: what the tool returns (list of primes? count? something else?), time/space complexity details, input constraints (e.g., valid limit range), error handling, or any side effects. For a computational tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence plus domain/category tags) with zero wasted words. Every element serves a purpose: algorithm name, key characteristic, and classification. However, the lack of essential information makes this conciseness borderline under-specification rather than optimal efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for a computational algorithm tool, the description is incomplete. It identifies the algorithm but fails to explain what it returns, how to interpret results, input constraints, or performance characteristics. The domain/category tags add some context but don't compensate for these fundamental gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'linear time sieve' which implies a 'limit' parameter, but doesn't explain what 'limit' represents (upper bound for prime generation? something else?), its valid range, units, or constraints. The single parameter remains semantically unclear beyond its name.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool implements a 'linear time sieve (Sieve of Euler)' algorithm with the specific behavior that 'each composite marked exactly once.' It also provides domain/category context ('Domain: arithmetic, Category: sieve_algorithms'). However, it doesn't explicitly distinguish this from sibling sieve tools like 'sieve_of_eratosthenes', 'sieve_of_atkin', or 'segmented_sieve', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this specific sieve algorithm versus alternatives. There are multiple sieve-related sibling tools (sieve_of_eratosthenes, sieve_of_atkin, segmented_sieve, incremental_sieve, prime_counting_sieve, etc.), but the description offers no comparison, prerequisites, or context about performance characteristics or use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions using Taylor series but doesn't disclose important behavioral aspects: convergence properties (e.g., works best for |x| < 1), accuracy dependence on parameter 'n', computational complexity, error handling for invalid inputs, or what happens when the series diverges. For a numerical approximation tool with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise - a single sentence with parenthetical domain/category information. It's front-loaded with the core purpose. However, the extreme brevity comes at the cost of completeness, making it more under-specified than optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a mathematical approximation tool with 2 required parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain the mathematical context (Taylor series approximation), parameter roles, convergence conditions, accuracy trade-offs, or return format. The 'Domain: numerical, Category: series' hint is insufficient for proper tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description doesn't explain what 'x' and 'n' represent beyond implying they're numerical. It doesn't clarify that 'x' is the argument to ln(1+x) or that 'n' is the number of Taylor series terms. For a tool with two required parameters and zero schema coverage, the description adds minimal semantic value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute natural logarithm ln(1+x) using Taylor series.' It specifies the mathematical function (natural logarithm with argument 1+x) and the computational method (Taylor series). However, it doesn't explicitly differentiate from sibling tools like 'ln' or 'ln_series' alternatives that might exist, though the method specification helps somewhat.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions 'Domain: numerical, Category: series' which gives some context about input type and mathematical category, but offers no explicit guidance on when to use this tool versus alternatives like the standard 'ln' tool or other approximation methods. No prerequisites, limitations, or comparison to siblings are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates a sequence but doesn't disclose behavioral traits like output format (e.g., list of strings/numbers), handling of invalid inputs (e.g., non-numeric 'start'), performance characteristics, or error conditions. The description is functional but lacks operational details needed for safe invocation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The domain/category tags are efficiently appended. There's no wasted text, though it could benefit from slightly more detail given the lack of annotations and schema descriptions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't compensate for missing structured data: parameters are unexplained, behavioral traits are omitted, and return values are unspecified. For a tool with two required parameters and no annotations, this leaves significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description doesn't explain the parameters 'start' (e.g., expected format, valid ranges) or 'terms' (e.g., meaning, constraints). It mentions 'starting from a number' but doesn't clarify if 'start' is a string or numeric input, or what 'terms' represents (e.g., number of sequence terms to generate). The description adds minimal value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the look-and-say sequence starting from a number.' It specifies the verb ('generate'), resource ('look-and-say sequence'), and starting condition. However, it doesn't explicitly differentiate from sibling tools like 'collatz_sequence' or 'fibonacci_sequence' beyond the domain/category tags, which are helpful but not explicit differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with only domain/category tags ('Domain: arithmetic, Category: iterative_sequences'). It doesn't specify when to use this tool versus alternatives (e.g., other sequence generators), mention prerequisites, or outline exclusions. The tags imply context but lack explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates sequences but does not describe output format, error handling, computational limits, or side effects. For a mathematical computation tool with zero annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no unnecessary information, and it efficiently communicates the core functionality. However, the inclusion of domain and category in parentheses, while brief, could be considered slightly extraneous but does not significantly detract.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical sequence calculation with 3 parameters, no annotations, and no output schema, the description is incomplete. It lacks details on parameter meanings, output format, and behavioral traits. The tool's purpose is clear, but without additional context, an agent would struggle to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters (n, P, Q) with 0% description coverage, meaning no parameter details are provided in the schema. The description only mentions 'parameters P, Q' without explaining what n, P, or Q represent, their valid ranges, or their roles in the calculation. This fails to compensate for the schema's lack of documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Lucas U_n and V_n sequences with parameters P, Q.' It specifies the verb ('calculate'), the mathematical objects ('Lucas U_n and V_n sequences'), and the required parameters ('P, Q'). However, it does not explicitly differentiate from sibling tools like 'lucas_number' or 'lucas_sequence', which might be related, so it misses the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), but this is too vague to inform usage decisions. There is no mention of prerequisites, typical use cases, or how it differs from similar tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'element-wise' which clarifies the addition behavior, but fails to disclose critical behavioral traits: it doesn't specify that matrices must have the same dimensions, doesn't mention error handling for mismatched sizes, doesn't describe the return format (e.g., a matrix array), and doesn't address numerical precision or overflow concerns.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with a single sentence that front-loads the core purpose ('Add two matrices element-wise'). The domain/category annotation is efficiently appended. There's no wasted verbiage, though it could benefit from slightly more detail given the lack of annotations and schema descriptions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of matrix operations, no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks essential context: matrix format expectations, dimension matching requirements, error conditions, return value structure, and numerical considerations. The domain/category hint helps but doesn't compensate for these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'two matrices' which aligns with the two parameters (matrix_a, matrix_b), but adds no semantic details beyond what the parameter names imply: no explanation of matrix format (2D arrays of strings representing numbers), no dimension requirements, no examples, and no constraints on element values.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Add two matrices element-wise' specifies the verb (add) and resource (matrices) with the operation type (element-wise). It distinguishes from siblings like 'matrix_multiply' and 'matrix_subtract' by specifying element-wise addition, but doesn't explicitly differentiate from 'add' (which appears to be scalar addition) or 'vector_add'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with the domain/category annotation ('Domain: linear_algebra.matrices, Category: general'), but offers no explicit when-to-use instructions, no mention of prerequisites (e.g., matrix dimensions must match), and no alternatives for when this tool is inappropriate versus other matrix operations like 'matrix_multiply' or 'matrix_subtract'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but doesn't describe what happens with invalid inputs (e.g., non-numeric strings, wrong matrix dimensions), error handling, performance characteristics, or output format. For a computational tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. The domain/category information is concise and adds context without verbosity. However, it could be slightly more structured by separating the calculation statement from the metadata for clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't address input validation, error cases, output format (e.g., numeric result), or mathematical assumptions. For a tool with one parameter but poor schema documentation, more detail is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema only indicates a 'matrix' parameter as an array of strings without explaining format. The description adds no parameter semantics—it doesn't specify that the matrix should be 3x3, how elements are represented (e.g., as numbers in strings), or ordering (row-major). With low schema coverage and no compensation in the description, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Calculate') and resource ('determinant of a 3x3 matrix'), making the tool's purpose unambiguous. It also includes domain/category context ('Domain: linear_algebra.matrices, Category: general'), which adds specificity. However, it doesn't explicitly differentiate from sibling tools like 'matrix_det_2x2' or 'matrix_solve_3x3', which would require a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention when to prefer this over 'matrix_det_2x2' for 2x2 matrices or 'matrix_solve_3x3' for solving systems, nor does it specify prerequisites like matrix format requirements. The domain/category hints at context but lacks explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('Multiply two matrices') without any information about constraints (e.g., matrix dimensions must be compatible for multiplication), error handling, performance characteristics, or output format. For a mathematical operation with potential complexity, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with the core purpose and domain/category context. It's front-loaded with the main action ('Multiply two matrices') and avoids unnecessary words. However, the parenthetical domain/category might be slightly redundant if the context is already clear from the toolset.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of matrix multiplication (involving dimension compatibility rules), no annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address key contextual aspects like input format details, error conditions, or what the output looks like (e.g., a resulting matrix). For a tool with mathematical precision requirements, this is inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, and the description doesn't add any semantic information about them. It doesn't explain what 'matrix_a' and 'matrix_b' represent, their expected formats (e.g., 2D arrays of numbers), or constraints (e.g., number of columns in matrix_a must equal rows in matrix_b). The description fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Multiply two matrices (matrix-matrix multiplication)'. It specifies the verb ('Multiply') and resource ('two matrices'), and the domain/category context helps clarify it's a linear algebra operation. However, it doesn't explicitly distinguish it from sibling tools like 'matrix_add' or 'matrix_scalar_multiply', which would require a more specific differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category context ('linear_algebra.matrices') implies the general area, there's no mention of when matrix multiplication is appropriate compared to other matrix operations available in the sibling list (like 'matrix_add', 'matrix_scalar_multiply', 'dot_product', or 'cross_product').
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the operation is 'element-wise', which clarifies the subtraction method, but it does not cover other critical aspects: it does not mention input validation (e.g., matrix dimensions must match), error handling, performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it directly states the tool's purpose in a single, clear sentence. The additional domain and category information is minimal and does not detract from clarity. There is no wasted verbiage, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the context: no annotations, no output schema, and 0% schema description coverage for two parameters, the description is incomplete. It adequately explains the core operation but lacks necessary details about parameter semantics, behavioral traits (e.g., error conditions), and output expectations. For a tool performing matrix subtraction, which involves non-trivial constraints like dimension matching, this leaves the agent under-informed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning the input schema provides no descriptions for parameters. The tool description does not add any information about the parameters 'matrix_a' and 'matrix_b', such as their expected formats (e.g., 2D arrays of numbers), constraints (e.g., must be same shape), or examples. With two required parameters and no semantic details provided, the description fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Subtract one matrix from another element-wise'. It specifies the verb ('subtract'), resource ('matrices'), and operation type ('element-wise'), which is specific and unambiguous. However, it does not explicitly differentiate from sibling tools like 'matrix_add' or 'vector_subtract', which are similar operations on different data structures, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.matrices') and category ('general'), but this does not help an agent choose between this tool and other matrix or subtraction-related tools in the sibling list, such as 'matrix_add' or 'subtract'. There is no explicit when-to-use or when-not-to-use information.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It explains what the median is ('middle value... separates higher half from lower half'), but lacks critical behavioral details: how it handles empty lists, even vs. odd list lengths, non-numeric inputs, or error conditions. For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise and front-loaded: the first sentence directly states the purpose, and the second adds clarifying definition. The parenthetical domain/category note is brief and relevant. There is no wasted verbiage, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is incomplete. It lacks details on parameter handling, edge cases (e.g., empty arrays, even-length lists), and expected output format. While the purpose is clear, the absence of behavioral and parametric context makes it insufficient for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'numbers' of type array of strings. The description does not compensate by explaining parameter semantics: it doesn't clarify that 'numbers' should be numeric strings, specify format (e.g., integers, floats), mention handling of invalid entries, or note that the array must be non-empty. This leaves the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the median (middle value) of a list of numbers.' It specifies the verb ('calculate') and resource ('median'), and distinguishes it from siblings by mentioning its statistical domain. However, it doesn't explicitly differentiate from similar statistical tools like 'mean' or 'mode' in the sibling list, which would require a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (statistics) and category (general), but offers no explicit when/when-not instructions or references to sibling tools like 'mean' or 'quartiles' for comparison. This leaves the agent without practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states the test is 'probabilistic' and for 'cryptographic applications,' which hints at reliability and use cases, but doesn't explain error rates, performance characteristics, or what 'probabilistic' entails (e.g., confidence levels based on parameter 'k'). This leaves significant gaps for a tool with potential cryptographic implications.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first phrase. The additional context about industry standards and domain is brief and relevant. However, it could be more structured by explicitly separating purpose from usage notes.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a probabilistic primality test, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on parameters, behavioral traits (e.g., accuracy, speed), and output format, making it inadequate for informed tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'Miller-Rabin probabilistic primality test' but doesn't explain parameters 'n' (the number to test) or 'k' (the number of iterations/confidence parameter). Without this, users must infer parameter meanings from the tool name alone, which is insufficient for effective use.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs a 'Miller-Rabin probabilistic primality test' and mentions it's an 'industry standard for cryptographic applications.' It specifies the mathematical operation (primality test) and domain context, though it doesn't explicitly differentiate from sibling tools like 'aks_primality_test' or 'deterministic_miller_rabin' beyond the 'probabilistic' qualifier.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (cryptographic applications) but doesn't specify scenarios where probabilistic testing is preferred over deterministic methods or other primality tests available in the sibling list, such as 'aks_primality_test' or 'fermat_primality_test'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions efficiency but doesn't disclose behavioral traits like computational complexity, memory usage, error handling, or output format. For a mathematical function tool with no structured safety hints, this leaves the agent guessing about performance and reliability.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The domain/category in parentheses is slightly redundant but not wasteful. It avoids fluff and stays focused, though it could be more informative without losing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., list of values, dictionary mapping), error conditions, or performance characteristics. For a computational tool with one parameter, this leaves significant gaps in understanding how to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter 'n' with 0% description coverage (no schema descriptions). The tool description adds no parameter semantics—it doesn't explain what 'n' represents (e.g., upper bound of range, range size, or starting point), valid ranges, or units. This is inadequate given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Möbius function values for a range of numbers efficiently.' It specifies the verb ('calculate'), resource ('Möbius function values'), and scope ('range of numbers'), though it doesn't explicitly differentiate from its sibling 'mobius_function' (which likely calculates for a single number). The domain/category tags add context but aren't part of the core description.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention the sibling 'mobius_function' (for single values) or 'apply_mobius_inversion' (for applying the inversion formula), nor does it specify prerequisites like input constraints or typical use cases. The efficiency claim is vague and not actionable.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description mentions what the tool does but doesn't explain how it behaves: it doesn't describe the expected format of g_values, what happens when n is invalid, whether the operation is deterministic, or what kind of output to expect. For a tool with 2 parameters and no annotations, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first clause. The parenthetical domain/category information is efficiently appended. No unnecessary words or redundant information is present.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical transformation tool with 2 parameters, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain parameter meanings, expected behavior, output format, or error conditions. The domain/category hints are helpful but insufficient for proper tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning neither parameter has descriptions in the schema. The tool description doesn't explain what g_values or n represent, their expected formats, or their roles in the Möbius inversion. With 2 undocumented parameters, the description fails to compensate for the schema's lack of documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Apply Möbius inversion formula to recover function from its summatory function.' It specifies both the action (apply formula) and the mathematical context (arithmetic domain, Möbius functions category). However, it doesn't explicitly differentiate from its sibling 'apply_mobius_inversion' tool, which appears to serve a similar purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. While it mentions the domain (arithmetic) and category (mobius_functions), it doesn't explain when to use this tool versus alternatives like 'apply_mobius_inversion' or other mathematical tools. No explicit when/when-not instructions or prerequisite conditions are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. It states what the tool calculates but doesn't describe important behaviors: input constraints (e.g., non-negative integers?), output format, error handling, or computational limits. The description is purely declarative without operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence with a clarifying parenthetical. It wastes no words and gets directly to the point. However, the parenthetical 'Domain: arithmetic, Category: general' adds minimal value and could be more informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is inadequate for a mathematical computation tool. It doesn't explain the mathematical formula, input requirements, output format, or edge cases. For a tool with one parameter but zero schema documentation, this leaves too much undefined for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description provides no parameter information beyond the generic term 'numbers.' It doesn't explain what the array represents (e.g., group sizes for multinomial coefficient calculation), expected length, value constraints, or examples. The description fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the multinomial coefficient.' It specifies this is a generalization of the binomial coefficient for multiple groups, which helps distinguish it from simpler binomial tools. However, it doesn't explicitly differentiate from sibling tools like 'binomial_pmf' or 'binomial_cdf' beyond mentioning the generalization concept.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance: it mentions the domain (arithmetic) and category (general), but offers no explicit when-to-use instructions, prerequisites, or alternatives. There's no indication of when to choose this over binomial tools or other combinatorial functions in the extensive sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the operation ('Multiply') but does not describe key behaviors: whether it handles overflow, error conditions (e.g., invalid base or number formats), output format (e.g., string or number), or performance characteristics. For a tool with no annotations, this leaves significant gaps in understanding how it behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by a brief domain/category note. There is no wasted verbiage or redundancy, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (arithmetic operation in arbitrary bases), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not address parameter semantics, error handling, output format, or usage context. For a tool with three required parameters and no structured documentation, the description fails to provide sufficient context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters (num1, num2, base) are documented in the schema. The description does not compensate by explaining what these parameters represent (e.g., that num1 and num2 are strings representing numbers in the given base, and base is an integer like 2, 8, 10, 16). Without this, the parameters are effectively undocumented, making it difficult to use the tool correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Multiply two numbers in a specified base.' It includes a specific verb ('Multiply'), resource ('two numbers'), and context ('in a specified base'), making the action unambiguous. However, it does not explicitly distinguish this tool from its sibling 'multiply' (which likely operates in decimal/base-10 by default), so it misses full sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, constraints (e.g., valid base ranges), or comparisons to siblings like 'multiply' or 'add_in_base'. Without this, users must infer usage from the tool name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'FIXED' but does not clarify what this means (e.g., fixed output format, immutable algorithm). It fails to describe critical behaviors like error handling for invalid inputs, performance characteristics, or the format of the returned row. This leaves significant gaps for a tool with a single parameter.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose. It consists of a single sentence that directly states the tool's function, with no unnecessary words. The domain and category annotations are efficiently appended, though they could be integrated more smoothly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not compensate for these gaps by explaining the parameter, return format, or behavioral details. For a combinatorial tool that likely returns a sequence or array, this omission makes it difficult for an agent to use effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description does not explain the parameter 'n'. It does not specify what 'n' represents (e.g., row index starting from 0 or 1), valid ranges, or constraints. For a single-parameter tool with no schema documentation, this is a major deficiency that hinders correct usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate row n of Narayana triangle - FIXED.' It specifies the verb ('Generate'), resource ('row n of Narayana triangle'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'narayana_number' or 'narayana_cow_number', which are related but distinct combinatorial tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context about the Narayana triangle's applications, prerequisites, or comparisons to other combinatorial number tools (e.g., 'catalan_number', 'bell_triangle'). Without such information, users must infer usage from the tool name and category alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the algorithm type and optimization context but lacks critical behavioral details: it doesn't specify what the tool returns (e.g., optimal point, iterations), error handling, convergence behavior, or computational characteristics. For a complex optimization tool with 8 parameters, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded in a single sentence, with no wasted words. Every part ('Perform Nelder-Mead simplex algorithm for derivative-free optimization') contributes directly to the tool's purpose, and the domain/category annotations are efficiently appended.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of an optimization algorithm with 8 parameters, no annotations, and no output schema, the description is incomplete. It lacks essential context: what the tool returns, how to interpret results, parameter meanings, and usage examples. This makes it inadequate for effective agent invocation without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description provides no information about any parameters. It doesn't explain what 'f' (the objective function), 'x0' (initial guess), or the Greek-letter parameters (alpha, gamma, rho, sigma) represent, nor does it cover 'max_iterations' and 'tolerance'. With 8 parameters and no schema descriptions, the description fails to add any semantic value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Nelder-Mead simplex algorithm for derivative-free optimization' with domain and category context. It specifies the verb ('Perform'), resource ('Nelder-Mead simplex algorithm'), and optimization context, but does not explicitly differentiate from sibling optimization tools like 'gradient_descent' or 'golden_section_search'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description mentions 'derivative-free optimization' which implies usage when derivatives are unavailable, but it doesn't name specific sibling tools or scenarios for comparison, leaving the agent without clear selection criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description states what the tool does but does not disclose any behavioral traits such as error handling (e.g., what happens if input arrays are mismatched), performance characteristics, numerical stability, or output format. For a numerical interpolation tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence: 'Perform Newton polynomial interpolation using divided differences (Domain: numerical, Category: interpolation).' It efficiently conveys the core action and context without unnecessary elaboration. However, the parenthetical domain/category could be integrated more smoothly, and the brevity comes at the cost of completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a numerical interpolation tool with 3 parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It lacks essential details such as parameter meanings, constraints, error conditions, and what the tool returns (e.g., interpolated value, polynomial coefficients). The description does not adequately compensate for the missing structured information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters (x_points, y_points, x) with 0% schema description coverage, meaning no parameter descriptions are provided in the schema. The description does not add any parameter semantics—it does not explain what x_points and y_points represent (e.g., arrays of data points), what x is (e.g., the point to interpolate at), or any constraints (e.g., arrays must be equal length, x must be within range). This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Newton polynomial interpolation using divided differences.' It specifies the mathematical method (Newton polynomial interpolation with divided differences) and provides domain/category context (numerical, interpolation). However, it does not explicitly differentiate from sibling tools like 'lagrange_interpolate' or 'linear_interpolate', which are also interpolation tools on this server.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (numerical) and category (interpolation), but does not indicate specific scenarios, prerequisites, or comparisons to other interpolation methods available (e.g., 'lagrange_interpolate', 'linear_interpolate', 'cubic_spline_interpolate'). This leaves the agent without explicit usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the action ('normalize') but does not explain what normalization entails (e.g., scaling by magnitude), potential errors (e.g., handling zero vectors), or output format. For a tool with 3 parameters and no annotations, this leaves significant gaps in understanding its behavior and constraints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence—and front-loaded with the core purpose. Every word earns its place, and there is no redundancy or unnecessary elaboration. It efficiently communicates the essential action without waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (3 parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameters, behavioral traits (e.g., error handling), and output expectations. While conciseness is high, the description does not provide enough context for an agent to use the tool effectively without additional inference or trial.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not mention any parameters ('vector', 'norm_type', 'tolerance') or their roles, such as what 'norm_type' (default 2) or 'tolerance' (default 1e-10) mean. With 3 parameters and no compensation in the description, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Normalize a vector to unit length.' It specifies the verb ('normalize'), resource ('vector'), and outcome ('unit length'), which is precise. However, it does not distinguish this tool from its many siblings, such as 'vector_norm' or 'euclidean_norm', which might have overlapping or related functionality, so it lacks sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('linear_algebra.vectors') and category ('general'), but these are generic and do not specify use cases, prerequisites, or exclusions. Without explicit when/when-not instructions or named alternatives, the agent must infer usage from context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions 'better performance' but fails to describe critical behaviors: what the tool returns (e.g., boolean result, detailed output), error handling for invalid inputs, computational complexity, or any side effects. The performance claim is vague and unsupported by concrete details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with no wasted words. It front-loads the core purpose ('Optimized Wilson's theorem test') and adds a brief technical detail ('pairing technique for better performance'). However, the parenthetical domain/category note feels redundant given the tool name and could be omitted for better focus.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a primality testing tool with no annotations, no output schema, and 0% parameter documentation, the description is severely incomplete. It doesn't explain what the tool returns, how to interpret results, error conditions, or performance characteristics. The domain/category hint doesn't compensate for these fundamental gaps in a tool that likely has non-trivial behavior.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' undocumented in both schema and description. The description adds no semantic information about 'n' (e.g., that it should be a positive integer, its typical range, or its role in Wilson's theorem). This leaves the parameter meaning entirely ambiguous, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs 'Optimized Wilson's theorem test' with a 'pairing technique for better performance', specifying both the mathematical operation (Wilson's theorem test) and the optimization method. It distinguishes itself from siblings like 'wilson_theorem_check', 'wilson_theorem_test', and 'wilson_theorem_verify' by emphasizing performance optimization, though it doesn't explicitly contrast their functional differences.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus its sibling tools (wilson_theorem_check, wilson_theorem_test, wilson_theorem_verify). It mentions 'better performance' but doesn't specify scenarios where this optimization is beneficial or when alternative tools might be more appropriate, leaving usage context entirely implicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the domain and category ('Domain: arithmetic, Category: digital_operations'), but this is vague and does not clarify key behaviors like whether the tool returns a list, if it includes the limit itself, performance characteristics, or error handling. For a tool with two parameters and no annotations, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The additional domain and category information is brief and does not add unnecessary length. However, the lack of detail on parameters and usage slightly undermines its effectiveness, but it remains efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It does not explain what the tool returns (e.g., a list of numbers), how 'base' affects the search, or any behavioral nuances. For a tool that generates sequences, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the input schema provides no descriptions for the parameters 'limit' and 'base'. The description only mentions 'limit' implicitly ('up to a limit') and does not explain 'base' at all. It fails to compensate for the lack of schema documentation, leaving parameter meanings unclear, especially for 'base' which defaults to 10.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all palindromic numbers up to a limit.' It specifies the verb ('find'), resource ('palindromic numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_palindromic_number' or 'next_palindrome', which test or generate individual palindromic numbers, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, exclusions, or comparisons to sibling tools such as 'is_palindromic_number' (for checking a single number) or 'next_palindrome' (for finding the next palindrome). Without this, users must infer usage from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool computes but does not describe output format, error conditions, performance characteristics, or any side effects. For a statistical analysis tool with no annotations, this lack of behavioral details is a significant gap, leaving the agent with incomplete operational understanding.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core function in the first phrase. The additional context (domain and category) is brief and relevant. There is no wasted verbiage, making it efficient, though it could be slightly more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical analysis tool, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on output format, error handling, and practical usage, which are essential for an agent to use the tool effectively. The minimal information provided does not suffice for the tool's context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'data' and 'lag' implicitly but does not explain their semantics, constraints, or examples (e.g., data as a time series array, lag as a positive integer). Without this added meaning, the parameters remain poorly defined, hindering correct invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute partial autocorrelation at a given lag' with the clarifying phrase 'correlation after removing effects of intermediate lags'. It specifies the domain (timeseries) and category (analysis), making the intent unambiguous. However, it does not explicitly differentiate from its sibling 'autocorrelation', which is a closely related tool, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (timeseries) and category (analysis), but does not specify scenarios, prerequisites, or comparisons to sibling tools like 'autocorrelation'. Without explicit usage instructions, the agent must infer context, which is insufficient for effective tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates solutions but does not specify how (e.g., algorithm, output format, limitations like integer overflow or performance for large n). For a tool with mathematical complexity and no annotations, this lack of detail on behavior is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated in the first sentence. The additional domain and category information is brief and relevant. There is no wasted text, making it efficient to parse, though it could benefit from more detail to improve completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of Pell's equation, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on algorithm, output format, error handling, and performance considerations. For a tool that likely involves non-trivial computation, this minimal description does not provide enough context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'n' and implies 'num_solutions' but does not explain their roles (e.g., n is the coefficient in the equation, num_solutions is the count to generate) or constraints (e.g., n must be non-square, num_solutions positive). This leaves parameters largely undocumented, failing to add meaningful semantics beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate multiple solutions to Pell's equation x² - ny² = 1.' It specifies the verb ('generate'), resource ('solutions'), and mathematical domain ('Pell's equation'), making it easy to understand what the tool does. However, it does not explicitly differentiate from sibling tools like 'solve_pell_equation' or 'cf_solve_pell', which might offer different approaches or scopes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('diophantine_equations'), but this is too generic to help an agent choose between this and sibling tools like 'solve_pell_equation' or 'cf_solve_pell'. There are no explicit instructions on prerequisites, constraints, or comparative use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates and analyzes, implying a read-only computation, but doesn't mention output format, error handling, assumptions (e.g., small-angle approximation), or performance characteristics. For a tool with three parameters and no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence with a parenthetical note, making it easy to parse. It avoids redundancy and gets straight to the point, though the domain/category note could be more integrated. Every part serves a purpose, but it's slightly terse given the lack of parameter or usage details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (three parameters with physics implications), lack of annotations, and no output schema, the description is incomplete. It doesn't cover parameter semantics, behavioral traits, or return values, leaving critical gaps for an AI agent to use the tool correctly. The domain/category hint is helpful but insufficient for full contextual understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the three parameters (length, gravity, angle) are documented in the schema. The description adds no parameter-specific information—it doesn't explain units (e.g., meters for length, m/s² for gravity, radians/degrees for angle), default values (gravity has a default in schema but not mentioned), or constraints (e.g., angle range). With low coverage, the description fails to compensate, leaving parameters largely unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Calculate') and resource ('pendulum period'), and adds 'analyze pendulum motion' for broader context. It distinguishes itself from siblings by specifying the domain (trigonometry) and category (applications), though it doesn't explicitly differentiate from other physics or motion-related tools in the list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit context, prerequisites, or comparisons to sibling tools (e.g., angular_velocity_from_period_or_frequency, oscillation_analysis, spring_oscillation), leaving the agent to infer usage based on parameter names alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates a sequence but doesn't disclose behavioral traits like whether n has constraints (e.g., must be positive), what happens for invalid inputs, the output format (list of numbers? string?), performance characteristics, or error handling. The description is minimal and lacks essential operational details for a tool with parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence plus domain/category tags. It's front-loaded with the core purpose. However, the domain/category information ('Domain: arithmetic, Category: basic_sequences') might be redundant if already inferable from context, slightly reducing efficiency. Overall, it's brief but could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 1 parameter with no schema descriptions, no annotations, and no output schema, the description is incomplete. It doesn't explain what pentagonal numbers are (though inferable from name), parameter constraints, return format, or error conditions. For a basic sequence generator, more context is needed to ensure correct usage, especially without structured support.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% description coverage in the schema. The description mentions 'first n pentagonal numbers', which implies n determines the count, but doesn't add meaning beyond this basic interpretation. It doesn't specify constraints (e.g., n must be positive integer), units, or examples. With low schema coverage, the description fails to compensate adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n pentagonal numbers.' It specifies the verb ('generate') and resource ('pentagonal numbers') with a clear scope ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'pentagonal_number' (which likely generates a single pentagonal number) or 'polygonal_sequence' (which might handle general polygonal sequences), though the domain/category hint helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: basic_sequences' which gives general context, but doesn't specify when to choose this over similar tools like 'pentagonal_number', 'polygonal_sequence', or other sequence generators (e.g., 'triangular_sequence', 'square_numbers'). No explicit when/when-not instructions or prerequisites are included.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does (calculates percentiles) but does not describe how it behaves—e.g., how it handles edge cases (empty arrays, invalid percentiles), computational methods (linear interpolation), or output format. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of two clear sentences that directly state the tool's purpose. There is no unnecessary verbiage, and each sentence adds value by defining percentiles and providing domain context. It could be slightly improved by integrating usage hints, but it is efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical calculation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not address parameter details, behavioral traits, or output expectations, leaving the agent with insufficient information to use the tool effectively in context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It does not explain the parameters 'numbers' (e.g., that they are numeric strings representing the dataset) or 'percentile' (e.g., that it should be between 0 and 100). Without this semantic clarification, the agent may misuse the tool due to unclear parameter expectations.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate percentiles of a dataset. Find the value below which a certain percentage of data falls.' It specifies the verb ('calculate'), resource ('percentiles of a dataset'), and includes a domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., 'quartiles'), which are related but distinct statistical functions, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but offers no explicit context, prerequisites, or comparisons to sibling tools like 'quartiles' or 'comprehensive_stats'. Without such information, the agent lacks clear usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'non-parametric test using random permutations' which hints at computational/monte carlo behavior, but doesn't disclose critical behavioral traits: what the output looks like (p-value? test statistic? confidence interval?), whether it's deterministic or stochastic, computational requirements, or any limitations. For a statistical test with randomization, this is a significant transparency gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently packed into a single sentence with domain/category tags. Every element serves a purpose: the core function, methodology hint, and contextual classification. There's no wasted verbiage. However, the lack of structure (no separation of purpose, parameters, or usage) slightly reduces clarity despite the brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical hypothesis test with randomization, no annotations, no output schema, and 0% schema description coverage, the description is severely incomplete. It doesn't explain what the tool returns, how to interpret results, statistical assumptions, or implementation details. For a 4-parameter tool performing non-trivial computation, this leaves the agent with insufficient context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so parameters are undocumented in the schema. The description adds no parameter semantics whatsoever - it doesn't explain what data1/data2 represent (sample arrays), what n_permutations controls (number of random permutations), or what alpha means (significance level). The agent must infer parameter meanings from names alone, which is inadequate for proper tool invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs a permutation test for difference in means, specifying it's a non-parametric test using random permutations. It includes the domain (statistics) and category (inference), providing a specific verb+resource combination. However, it doesn't explicitly distinguish this tool from potential sibling alternatives for hypothesis testing (like t-tests or other non-parametric tests).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags imply statistical inference contexts, there's no explicit mention of when permutation testing is preferred (e.g., for small samples, non-normal data, or when parametric assumptions are violated) or what alternatives exist among the many sibling tools. The agent receives no usage boundaries or recommendations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool calculates but does not describe any behavioral traits such as error handling, performance characteristics, input validation, or output format. For a tool with two parameters and no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category tags are efficiently appended. However, it could be more structured by explicitly addressing parameters or usage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (two parameters, no annotations, no output schema), the description is incomplete. It lacks information on parameter meanings, behavioral traits, and output format. The domain/category tags add some context but do not compensate for the missing details needed for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters 'n' and 'base' are undocumented in the schema. The description does not mention these parameters at all, failing to add any semantic meaning beyond the bare schema. With two parameters and no coverage, the description should compensate but does not.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate persistent digital root (number of steps to reach single digit).' It specifies the verb ('calculate'), resource ('persistent digital root'), and scope ('number of steps to reach single digit'). However, it does not explicitly differentiate from sibling tools like 'digital_root' or 'digital_persistence', though the domain/category tags provide some context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There are sibling tools such as 'digital_root' and 'digital_persistence' that likely perform related operations, but the description does not mention them or specify any context, prerequisites, or exclusions for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates approximations, implying it's a read-only operation, but doesn't clarify if it's deterministic, what the output format is (e.g., list of fractions, accuracy metrics), or any performance considerations. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first sentence. The second sentence adds domain and category context, which is relevant but could be integrated more seamlessly. There's no wasted text, making it efficient, though it could be slightly more structured for clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical approximation tool), lack of annotations, no output schema, and incomplete parameter documentation, the description is insufficient. It doesn't explain what the approximations look like, how they're generated, or any error handling. For a tool that likely produces structured output, more detail is needed to guide an agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('terms') with 0% description coverage, and the tool description adds no information about it. The description doesn't explain what 'terms' means (e.g., number of terms in the continued fraction, precision level) or its valid range. With low schema coverage, the description fails to compensate, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate various continued fraction approximations to π.' It specifies the verb ('Generate'), resource ('continued fraction approximations'), and target ('π'), making the function unambiguous. However, it doesn't differentiate from sibling tools like 'continued_fraction_pi' or 'compute_pi_chudnovsky', which likely serve similar mathematical purposes, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('continued_fractions'), but this is too vague to help an agent choose between this and other π-related or continued fraction tools in the sibling list. There are no explicit instructions on prerequisites, limitations, or comparisons to similar tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a value but does not describe any behavioral traits such as error handling (e.g., for invalid inputs), performance characteristics, or output format. For a computational tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and every part earns its place by providing essential information efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, two required parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It lacks parameter explanations, behavioral context, and output details, making it insufficient for an agent to use the tool effectively without additional inference or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters 'n' and 's' are undocumented in the schema. The description does not add any meaning beyond the tool name—it does not explain what 'n' and 's' represent (e.g., 'n' as the index, 's' as the number of sides). With two required parameters and no schema or description coverage, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth s-gonal (polygonal) number.' It specifies the verb ('calculate') and resource ('polygonal number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'centered_polygonal_number' or 'polygonal_sequence', which are closely related, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit when-to-use, when-not-to-use, or alternative tool recommendations (e.g., compared to 'centered_polygonal_number' or 'polygonal_sequence' in the sibling list). This leaves the agent without contextual usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the calculation but doesn't disclose behavioral traits such as input validation (e.g., must p be prime?), error handling, performance characteristics, or output format. For a computational tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of one clear sentence followed by domain/category metadata. There's no wasted verbiage, and the core purpose is stated immediately. However, the domain/category tags, while informative, could be integrated more seamlessly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, 1 parameter, no annotations, and no output schema, the description is incomplete. It doesn't cover parameter meaning, output format, error conditions, or usage context. For a tool that performs a specific mathematical calculation, more detail is needed to ensure correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no information about the parameter 'p'. It doesn't explain what 'p' represents (presumably a prime number), its valid range, or any constraints. With 1 parameter and no schema descriptions, the description fails to compensate for the lack of parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the gap between a prime and the next prime.' It specifies the verb ('calculate'), resource ('gap'), and domain context ('prime gaps'). However, it doesn't explicitly differentiate from sibling tools like 'prime_gaps_analysis' or 'largest_prime_gap_in_range', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't indicate prerequisites, constraints (e.g., input range), or when to choose this over siblings like 'next_prime' or 'prime_gaps_analysis'. Usage is implied only by the tool name and description.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates and returns a product, implying a read-only operation, but does not disclose behavioral traits such as error handling (e.g., for empty lists or non-numeric strings), performance considerations, or output format details. This leaves significant gaps in understanding how the tool behaves beyond basic functionality.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with two sentences that directly state the tool's function and return value. The additional domain and category information is brief and non-redundant. However, the lack of detail reduces overall helpfulness, though it remains structurally efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is incomplete. It does not explain the return value format (e.g., numeric type), error conditions, or how the input strings are interpreted. For a tool with undocumented parameters and no annotations, more context is needed to ensure reliable use by an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'numbers' of type array of strings. The description adds minimal semantics by implying the list contains numbers, but does not clarify the expected format (e.g., numeric strings), constraints (e.g., minimum list length), or handling of non-numeric inputs. This fails to compensate for the low schema coverage, leaving parameter meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the product of all numbers in a list. Returns the multiplication of all elements.' It specifies the verb ('calculate'), resource ('product of all numbers in a list'), and outcome. However, it does not explicitly differentiate from sibling tools like 'multiply' or 'element_wise_multiply', which might handle similar operations differently.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but does not specify contexts, prerequisites, or comparisons to sibling tools like 'multiply' or 'element_wise_multiply', leaving the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a statistical test but does not describe key behaviors such as output format (e.g., p-value, test statistic), assumptions (e.g., large sample sizes), or error handling. This is a significant gap for a tool with no annotation coverage, limiting the agent's ability to predict its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and it efficiently communicates the core function. However, it could be slightly more structured by separating usage notes, but this is minor.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test with 5 parameters, no annotations, and no output schema, the description is incomplete. It does not explain the tool's behavior, output, or parameter meanings, leaving critical gaps for the agent. While conciseness is good, the lack of contextual details makes it inadequate for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the parameters (successes1, n1, successes2, n2, alpha) are documented in the schema. The description does not add any parameter semantics—it does not explain what these inputs represent (e.g., counts and sample sizes for two groups, significance level) or their constraints. With low coverage and no compensation in the description, the agent lacks necessary context for correct invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform two-proportion z-test to test whether two population proportions differ significantly.' It specifies the verb ('perform'), resource ('two-proportion z-test'), and domain/category. However, it does not explicitly differentiate from sibling tools like 'z_test' or 'fishers_exact_test', which might handle similar statistical tests, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('statistics') and category ('inference'), which implies context, but does not specify when to use this tool versus alternatives (e.g., 'z_test' for one-sample tests or 'fishers_exact_test' for small samples). No explicit when/when-not instructions or prerequisites are given, leaving the agent with insufficient guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. While it mentions 'verify and compute', it doesn't disclose what verification entails, what gets computed, whether there are precision limitations, or what the output format looks like. For a mathematical tool with no annotation coverage, this leaves significant behavioral questions unanswered.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with a single sentence that gets straight to the point. The domain/category information is efficiently appended in parentheses. There's no wasted verbiage, though the structure could be slightly improved by separating the core functionality from the metadata.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the mathematical nature of the tool, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain what Pythagorean identities are being verified/computed, what the expected output looks like, or how the parameters influence the operation. For a tool with two parameters and mathematical complexity, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage and two parameters (angle, tolerance), the description provides no information about parameter meanings. It doesn't explain what 'angle' represents (radians/degrees), what 'tolerance' controls, or how these parameters affect the verification/computation. The description fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('verify and compute') and resource ('Pythagorean trigonometric identities'), and provides domain/category context. However, it doesn't differentiate from sibling tools like 'verify_identity' or 'verify_hyperbolic_identity', which could cause confusion about when to choose this specific identity verification tool.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools for identity verification and trigonometric calculations, there's no indication of when this specific Pythagorean identity tool is appropriate versus general identity verification tools or other trigonometric functions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the mathematical operation but lacks behavioral details such as output format (e.g., list of triples, range constraints), performance characteristics (e.g., computational limits for 'limit'), or error handling. This is inadequate for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, stating the core purpose in one sentence with additional domain/category context. There is no wasted text, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical computation with parameters), lack of annotations, and no output schema, the description is incomplete. It fails to explain parameter meanings, output format, or behavioral traits, leaving significant gaps for the agent to operate effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description provides no information about the parameters 'limit' and 'primitive_only'. With 0% schema description coverage and no explanation in the description, the semantics of these parameters are completely undocumented, leaving the agent to guess their purpose and usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find Pythagorean triples (x, y, z) where x² + y² = z².' It specifies the mathematical operation and domain (arithmetic, diophantine_equations). However, it doesn't explicitly differentiate from sibling tools like 'solve_quadratic_diophantine' or 'diophantine_analysis', which could handle similar equations, so it doesn't reach the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools for mathematical computations (e.g., 'solve_quadratic_diophantine', 'diophantine_analysis'), there's no indication of specific contexts, prerequisites, or exclusions for using this tool over others.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it explains what quartiles are, it doesn't describe how the tool behaves: whether it sorts input data, handles non-numeric strings in the 'numbers' array, returns errors for empty arrays, provides output format, or has any computational constraints. For a statistical tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences that directly address the tool's function. It's front-loaded with the core purpose and avoids unnecessary elaboration. However, the parenthetical domain/category note adds minor redundancy without enhancing clarity for tool selection.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's statistical nature, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain input requirements, error conditions, output format, or behavioral details. For a tool that performs calculations on data arrays, more context is needed to ensure correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'numbers' of type array of strings. The description adds no information about this parameter—it doesn't explain what 'numbers' represents, expected format (e.g., numeric strings), handling of invalid entries, or example usage. With low schema coverage, the description fails to compensate, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate quartiles of a dataset (Q1, Q2/median, Q3). Divides data into four equal parts.' It specifies the verb ('calculate'), resource ('quartiles'), and output details. However, it doesn't explicitly differentiate from sibling tools like 'percentile' or 'comprehensive_stats', which could provide similar statistical calculations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but offers no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools like 'percentile' or 'median'. This leaves the agent without clear usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but lacks behavioral details: it doesn't specify the output format (e.g., list of integers), error handling (e.g., for q=0), computational limits, or whether the input rational must be in simplest form. For a tool with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and front-loaded with the core purpose in the first sentence. The domain/category tags are efficiently appended. However, the lack of essential details (like parameter meanings) means it's under-specified rather than optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for a 2-parameter tool, the description is incomplete. It doesn't explain what the tool returns, how to interpret the continued fraction output, or handle edge cases. For a conversion tool with mathematical nuances, this is inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema only indicates p and q are required integers. The description adds no parameter semantics—it doesn't explain that p is the numerator and q is the denominator, or that q must be non-zero. With low schema coverage, the description fails to compensate, leaving parameters poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Convert') and resource ('rational number to continued fraction'), making the purpose unambiguous. It distinguishes from sibling tools like 'cf_to_rational' by specifying the direction of conversion. However, it doesn't explicitly differentiate from 'continued_fraction_expansion' or other continued fraction tools, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with the domain/category tags ('arithmetic', 'continued_fractions'), which imply context but don't specify when to use this tool versus alternatives like 'cf_to_rational' or 'continued_fraction_expansion'. No explicit when/when-not instructions or prerequisites are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'Count[s]' something, implying a read-only operation, but does not clarify computational complexity, potential limitations (e.g., large n values), or output format. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context, which is somewhat useful but not essential. There is no wasted text, making it efficient, though it could be more structured with clearer separation of purpose and usage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical partition counting), lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what a 'restricted partition' is, how the counting is performed, or what the output looks like (e.g., integer count). This leaves too many unknowns for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, so the description must compensate. It mentions 'max_part' in the constraint ('largest part is at most max_part'), which adds some meaning, but does not explain 'n' or provide any details on parameter roles, valid ranges, or interactions. This is insufficient given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Count restricted partitions where largest part is at most max_part.' It specifies the verb ('Count'), resource ('restricted partitions'), and constraint ('largest part is at most max_part'). However, it does not explicitly differentiate from sibling tools like 'distinct_partitions' or 'partition_count', which is why it's not a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('partitions'), but this is too vague to help an agent choose between similar tools like 'distinct_partitions' or 'partition_count'. There are no explicit when/when-not statements or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a calculation (power analysis), implying it's a read-only operation, but doesn't clarify output format (e.g., returns an integer sample size), assumptions (e.g., normal distribution, equal variances), or limitations (e.g., large effect sizes may yield small samples). For a statistical tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category tags. There is zero wasted verbiage, and every element (calculation, sample size, means comparison, power analysis) earns its place by contributing essential context. The structure is clear and efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical power analysis with 4 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It identifies the tool's domain and high-level purpose but omits critical details: parameter meanings, behavioral assumptions, output format, and usage context. For a tool that requires precise statistical inputs, this leaves too much undefined.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the 4 parameters (effect_size, alpha, power, alternative) are documented in the schema. The description adds no parameter semantics—it doesn't explain what 'effect_size' represents (e.g., Cohen's d), the meaning of 'alpha' (significance level), 'power' (probability of detecting an effect), or valid values for 'alternative' (e.g., 'two-sided', 'greater', 'lesser'). This forces the agent to guess parameter meanings, which is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate required sample size per group for comparing means (power analysis)'. It specifies the verb ('calculate'), resource ('sample size per group'), and context ('comparing means', 'power analysis'), with domain/category tags adding precision. However, it doesn't explicitly differentiate from sibling tools like 'power_analysis' or 't_test_two_sample', which might handle related statistical tasks.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'power analysis' and 'comparing means', but doesn't specify prerequisites, scenarios (e.g., experimental design, hypothesis testing), or contrast with siblings like 'power_analysis' (general) or 't_test_two_sample' (which might compute test statistics). Without such context, an agent must infer usage from the tool name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states the decomposition action but lacks critical details: whether it's read-only or mutative (though 'decompose' suggests analysis), what algorithm or assumptions are used (e.g., additive/multiplicative model), output format, error handling, or performance considerations. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core action and output. The domain/category tag adds context without verbosity. Every part earns its place, though it could be more informative without sacrificing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (time series decomposition), lack of annotations, 0% schema coverage, and no output schema, the description is insufficient. It doesn't cover behavioral traits, parameter details, output structure, or usage context. For a statistical analysis tool with two required parameters, this leaves too many gaps for effective agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'time series' and 'components', which loosely relates to 'data' and 'period', but doesn't explain parameter meanings, units, constraints (e.g., period must be integer > 0), or data format expectations. The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('decompose') and resource ('time series'), specifying the output components (trend, seasonal, residual). It distinguishes the tool's purpose from many siblings (e.g., 'detect_seasonality', 'detrend', 'deseasonalize') by focusing on full decomposition rather than detection or removal. However, it doesn't explicitly differentiate from all potential analysis siblings in the extensive list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance, only implying usage for time series analysis via the domain/category tag. It doesn't specify when to use this tool versus alternatives like 'detect_seasonality', 'detrend', or 'deseasonalize', nor does it mention prerequisites (e.g., data must be periodic) or exclusions. No explicit when/when-not or alternative tool references are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states the computation method (Taylor series expansion) which implies approximation behavior rather than exact calculation, but doesn't specify accuracy characteristics, convergence conditions, error bounds, or computational complexity. For a numerical approximation tool with zero annotation coverage, this represents significant gaps in behavioral transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with a single sentence containing the core computation method and domain/category metadata. It's front-loaded with the main purpose ('Compute sine function using Taylor series expansion') and wastes no words. The parenthetical domain/category information could be integrated more smoothly but doesn't detract significantly from readability.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a 2-parameter numerical computation tool with no annotations and no output schema, the description is incomplete. It doesn't explain what the tool returns (approximated sine value), error characteristics, or practical usage considerations. For a Taylor series implementation, important context like convergence radius, typical 'n' values for reasonable accuracy, and comparison to direct sine computation is missing, making this inadequate for informed tool selection.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage, so the description must compensate but fails to do so adequately. It doesn't explain what parameters 'x' and 'n' represent (presumably angle and series terms count), their units (radians vs degrees), valid ranges, or the relationship between 'n' and accuracy. The description adds no parameter semantics beyond what's implied by 'Taylor series expansion' for those familiar with the method.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute sine function using Taylor series expansion' with domain and category context. It specifies the mathematical method (Taylor series) and function (sine), distinguishing it from simpler trigonometric tools like 'sin' or 'sin_degrees' in the sibling list. However, it doesn't explicitly differentiate from 'cos_series' or other series-based siblings beyond naming the sine function.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions 'Domain: numerical, Category: series' which gives some context about input types and mathematical category, but offers no explicit guidance on when to use this tool versus alternatives like 'sin', 'sin_degrees', or other approximation methods. There's no mention of trade-offs between accuracy and computational cost, or when Taylor series approximation is preferable to direct computation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe any behavioral traits: no information about computational complexity, error handling, input constraints (e.g., n must be non-square), output format, or performance characteristics. This is inadequate for a mathematical solver tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise - a single sentence plus domain/category tags. It's front-loaded with the core purpose and wastes no words. However, the extreme brevity comes at the cost of completeness, as noted in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical solver with no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what a 'fundamental solution' means, what format the output takes, any limitations or constraints, or how it relates to other Pell equation tools in the system. The context signals indicate this tool needs much more documentation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with only one parameter 'n' of type integer. The description mentions 'n' in the equation context but provides no additional semantic information: no constraints (e.g., n must be positive, non-square), no examples, no explanation of what 'n' represents mathematically. This leaves significant gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve Pell's equation x² - ny² = 1 for fundamental solution.' It specifies the mathematical equation, the type of solution (fundamental), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'cf_solve_pell' or 'solve_negative_pell_equation', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain (arithmetic) and category (diophantine_equations), it doesn't specify use cases, prerequisites, or compare it to related tools like 'cf_solve_pell' or 'solve_negative_pell_equation' that appear in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description mentions the equation form but doesn't explain key behavioral aspects: what the 'coeffs' and 'bounds' parameters mean, how solutions are returned (e.g., integer pairs, existence checks), computational complexity, or limitations (e.g., handling large coefficients). For a mathematical solver with two parameters, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the tool's purpose, and the parenthetical adds domain context without unnecessary elaboration. There's no wasted verbiage, making it efficient for quick understanding. However, the lack of detail on parameters and usage slightly limits its effectiveness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of solving quadratic Diophantine equations, the description is incomplete. With no annotations, no output schema, and 0% schema description coverage, it doesn't provide enough context for effective use. It misses crucial details like parameter meanings, solution format, error handling, and mathematical assumptions (e.g., integer constraints). For a specialized mathematical tool, this leaves too many unknowns.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the schema provides no parameter documentation. The description doesn't explain what 'coeffs' and 'bounds' represent (e.g., that 'coeffs' is likely [a, b, c, d, e, f] and 'bounds' might define search ranges). Without this semantic clarification, the parameters remain cryptic, and the description fails to compensate for the schema's lack of documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve general quadratic Diophantine equation ax² + bxy + cy² + dx + ey + f = 0.' It specifies the verb ('solve') and the mathematical resource (quadratic Diophantine equation), making the intent unambiguous. However, it doesn't differentiate from sibling tools like 'solve_linear_diophantine' or 'count_solutions_diophantine', which is why it doesn't achieve a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. The parenthetical '(Domain: arithmetic, Category: diophantine_equations)' offers some context about the tool's mathematical domain, but it doesn't explain when to use this tool versus alternatives (e.g., 'solve_linear_diophantine' for linear equations or 'count_solutions_diophantine' for counting solutions). There's no explicit guidance on prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does but lacks behavioral details: it doesn't mention input validation (e.g., handling non-numeric strings in the 'numbers' array), error conditions, performance characteristics, or output format. The description is minimal and does not compensate for the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence states the core purpose. The second sentence adds context (relationship to variance), and the parenthetical provides domain categorization. There is no wasted text, though it could be more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (statistical calculation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain parameter semantics, behavioral traits, or output format. For a tool with undocumented parameters and no structured guidance, the description should provide more context to be adequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'a list of numbers' which aligns with the 'numbers' parameter, but does not explain the 'population' parameter (whether to use population or sample standard deviation). The description adds minimal meaning beyond the schema, failing to clarify parameter purposes or usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the standard deviation of a list of numbers.' It specifies the verb ('calculate') and resource ('standard deviation'), and adds domain context ('Domain: statistics, Category: general'). However, it does not explicitly differentiate from sibling tools like 'variance' or 'comprehensive_stats', which is why it's not a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the relationship to variance ('The square root of variance'), but does not indicate when to choose standard deviation over variance or other statistical measures like 'z_scores' or 'comprehensive_stats'. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'FIXED IMPLEMENTATION', which hints at a stable or deterministic calculation, but does not elaborate on computational characteristics (e.g., performance, limitations for large inputs), error handling, or output format. For a mathematical computation tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, consisting of a single sentence that states the core function. The additional note 'FIXED IMPLEMENTATION' and domain/category are somewhat extraneous but not overly verbose. It is front-loaded with the main purpose, though could be more structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a combinatorial number calculation, the description is insufficient. There are no annotations, no output schema, and the input parameters are poorly documented. The description does not cover important aspects like the mathematical definition, typical use cases, or example outputs, leaving the agent with inadequate context to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'n' and 'k' documented only by type (integer). The description does not explain what these parameters represent (e.g., that 'n' and 'k' are non-negative integers with k ≤ n for Stirling numbers of the first kind), their constraints, or typical usage ranges. It fails to compensate for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Stirling number of the first kind s(n,k)'. It specifies both the verb ('Calculate') and the mathematical resource ('Stirling number of the first kind'), making the function unambiguous. However, it does not explicitly differentiate from its sibling tool 'stirling_second', though the naming implies a distinction between first and second kind Stirling numbers.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions 'FIXED IMPLEMENTATION' and a domain/category, these do not indicate specific contexts, prerequisites, or comparisons with sibling tools like 'stirling_second'. There is no explicit when-to-use or when-not-to-use information.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the calculation method but does not disclose behavioral traits such as input constraints (e.g., numeric ranges for angles), output format, error handling, or computational limits. For a tool with no annotations, this leaves significant gaps in understanding its operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the main purpose in the first sentence, followed by domain/category tags. There is no wasted text, and it efficiently communicates the core function without unnecessary details, though it could be slightly more informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a trigonometric calculation tool with 3 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral aspects, or output details, making it inadequate for an agent to use the tool effectively without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not explain the parameters (a, b, operation). It mentions 'sum and difference formulas' but does not clarify what a and b represent (e.g., angles in radians or degrees) or how the operation parameter affects the calculation. With low schema coverage, the description fails to compensate, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate trigonometric functions using sum and difference formulas.' It specifies the verb ('calculate'), resource ('trigonometric functions'), and method ('sum and difference formulas'). However, it does not differentiate from sibling tools like 'double_angle_formulas' or 'half_angle_formulas', which are also trigonometric identity tools, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with the domain and category tags ('Domain: trigonometry, Category: identities'), but this is too vague to indicate when to use this tool versus alternatives. It lacks explicit when-to-use instructions, prerequisites, or comparisons to sibling tools like 'verify_sum_difference_formulas', which might be for verification rather than calculation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states what the tool does (expresses a number as sum of four squares) but doesn't describe important behavioral aspects: what format the output takes (e.g., list of integers, string representation), whether there are multiple valid decompositions and how one is chosen, input constraints (e.g., non-negative integers only), or error handling. For a tool with no annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise - a single sentence that states the core purpose with mathematical context. It's front-loaded with the main functionality. The parenthetical domain/category information is potentially useful but could be considered slightly extraneous. Overall, it's efficient with minimal waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical decomposition algorithm), no annotations, no output schema, and poor parameter documentation, the description is incomplete. It doesn't explain what the tool returns, how results are formatted, input constraints, or algorithmic behavior. For a tool implementing Lagrange's theorem with one parameter, users need more context about the output and any limitations.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, providing only that parameter 'n' is an integer. The description adds no parameter semantics whatsoever - it doesn't explain what 'n' represents (presumably the number to decompose), its valid range, or any constraints. With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Express a number as sum of four squares (Lagrange's theorem).' It specifies both the action ('Express') and the mathematical resource ('sum of four squares'), and references Lagrange's theorem for context. However, it doesn't explicitly differentiate from sibling tools like 'sum_of_two_squares' or 'sum_of_two_squares_all', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('additive_number_theory'), which gives some context about when this mathematical tool might be relevant, but offers no explicit guidance on when to use this versus alternatives like 'sum_of_two_squares' or other decomposition tools. There are no when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states the tool expresses a number as a sum of two squares 'if possible,' implying it may return a result or indicate impossibility, but doesn't specify the output format, error handling, or performance characteristics. For a tool with mathematical computation, more behavioral context would be helpful.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that states the core purpose followed by domain context. There's no wasted verbiage, and the structure is clear. However, the parenthetical domain information could be integrated more smoothly, and the brevity comes at the cost of completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low parameter documentation, the description is incomplete. It doesn't explain what the output looks like (e.g., pair of integers, error message), mathematical constraints, or how it handles edge cases. The domain context helps but doesn't compensate for these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds minimal parameter semantics by implying 'n' is the number to be expressed, but doesn't specify constraints (e.g., positive integers, range limits) or provide examples. Given the low schema coverage, the description doesn't adequately compensate for the lack of parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Express a number as sum of two squares if possible.' It specifies the verb ('express'), resource ('a number'), and condition ('if possible'), and mentions the mathematical domain. However, it doesn't explicitly differentiate from sibling tools like 'sum_of_two_squares_all' or 'sum_of_four_squares', which would require more specific scope information.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('arithmetic, Category: additive_number_theory'), which gives some context, but offers no explicit instructions on when to use this tool versus alternatives like 'sum_of_two_squares_all' or other number decomposition tools. There's no mention of prerequisites, constraints, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the calculation but lacks behavioral details: it doesn't specify input format (e.g., how arrays are represented as strings), error handling (e.g., for mismatched array lengths), output format, or computational constraints. The description is minimal and doesn't compensate for the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context but is somewhat redundant. Overall, it's efficient with minimal waste, though it could be slightly more informative without losing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (multi-array operation), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't address input formatting, output structure, error cases, or usage examples. For a tool with one parameter but unclear semantics, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'multiple arrays' but doesn't explain the 'arrays' parameter's semantics: what the strings represent (e.g., comma-separated numbers), minimum number of arrays required, or how corresponding elements are aligned. The description adds little beyond the schema's structure, leaving key details undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sum of products of corresponding elements in multiple arrays.' It specifies the verb ('calculate') and resource ('sum of products'), and distinguishes it from sibling tools like 'dot_product' or 'element_wise_multiply' by focusing on a multi-array operation. However, it doesn't explicitly differentiate from potential similar siblings beyond the domain/category note.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but this is too vague to help an agent choose between this and siblings like 'dot_product' (for two arrays) or 'element_wise_multiply' (for element-wise multiplication without summation). No explicit when/when-not instructions or named alternatives are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a sum of squares, implying a read-only operation with no side effects, but does not disclose behavioral traits like error handling (e.g., for non-numeric strings in the input array), performance characteristics, or output format. The description is minimal and lacks necessary context for safe invocation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain/category tag is extraneous but does not significantly detract. There is no wasted verbiage, making it efficient for quick scanning.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is incomplete. It lacks details on input semantics (e.g., string-to-number conversion), error conditions, and output format (e.g., numeric result type). For a tool with 0% schema coverage and no annotations, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'numbers in a list', which aligns with the 'numbers' parameter in the schema, but adds no semantics beyond what the schema already shows (an array of strings). It does not explain what the strings represent (e.g., numeric values), expected format, constraints, or examples, leaving parameters poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sum of squares of numbers in a list.' It specifies the verb ('calculate'), resource ('sum of squares'), and input type ('numbers in a list'). However, it does not explicitly differentiate from sibling tools (e.g., 'sum_digit_powers', 'sum_of_two_squares'), which are also summation tools but with different mathematical operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It includes a domain/category tag ('Domain: arithmetic, Category: general'), but this is too vague to help an agent choose between similar sibling tools like 'sum_digit_powers' or 'sum_of_two_squares'. No explicit when/when-not instructions or named alternatives are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the mathematical method ('Sylvester's sequence') but doesn't disclose behavioral traits such as computational complexity, output format, error handling, or limitations (e.g., valid ranges for 'terms'). For a tool with no annotations, this leaves significant gaps in understanding its operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in one sentence. The domain/category tags add minimal but relevant context without verbosity. However, it could be more structured by explicitly addressing parameters or usage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It explains the mathematical goal but lacks details on parameters, behavior, output, and practical usage, making it inadequate for a tool with one undocumented parameter.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('terms') with 0% description coverage, and the tool description provides no information about it. The description doesn't explain what 'terms' represents (e.g., number of unit fractions, maximum value, constraints), failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Express 1 as sum of unit fractions using Sylvester's sequence.' It specifies the verb ('Express'), resource ('1'), and method ('using Sylvester's sequence'), though it doesn't explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'unit_fraction_sum' beyond the domain/category tags.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description includes domain/category tags ('arithmetic', 'egyptian_fractions'), but these are generic and don't specify prerequisites, constraints, or comparisons to sibling tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the calculation but does not disclose behavioral traits such as input validation (e.g., vector length must be 3), error handling, numerical precision, or output format. For a mathematical tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded in a single sentence, with no wasted words. It efficiently states the core purpose and includes domain/category information. However, it could be slightly more structured by separating usage notes or parameter details, but it's appropriately sized for its content.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical operation with 3 parameters), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on input validation, output format, error conditions, and practical usage examples. For a tool with no structured support, the description should provide more context to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not add any parameter semantics. It names the parameters ('three 3D vectors') but does not explain their format (e.g., arrays of numbers as strings), constraints (e.g., must have 3 elements), or examples. With 3 undocumented parameters, the description fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the triple scalar product of three 3D vectors.' It specifies the verb ('calculate'), resource ('triple scalar product'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'dot_product' or 'cross_product' beyond the domain/category hint, which is why it's not a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.vectors') and category ('general'), but does not specify scenarios, prerequisites, or comparisons to sibling tools (e.g., 'dot_product', 'cross_product', 'triple_vector_product'). This lack of explicit usage context limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the statistical test but does not describe key behaviors such as output format (e.g., t-statistic, p-value), assumptions (e.g., normality), or error handling. For a tool with no annotations and three parameters, this leaves significant gaps in understanding how it operates.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted text, and it efficiently communicates the core functionality without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test, three undocumented parameters, no annotations, and no output schema, the description is incomplete. It lacks details on inputs, outputs, assumptions, and usage context, making it inadequate for an agent to reliably invoke the tool without additional information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters ('data', 'population_mean', 'alpha') are documented in the schema. The description does not add any meaning beyond the schema—it does not explain what these parameters represent, their units, or valid ranges. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform one-sample t-test to test whether sample mean differs significantly from population mean.' It includes a specific verb ('Perform'), resource ('one-sample t-test'), and statistical context. However, it does not explicitly differentiate from sibling tools like 't_test_two_sample' or 'paired_t_test', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance, only stating the domain ('statistics') and category ('inference'). It does not specify when to use this tool versus alternatives (e.g., 't_test_two_sample' for comparing two samples) or any prerequisites. Without explicit when/when-not instructions, it offers limited practical guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details: it doesn't specify output format (e.g., list of gaps, statistics), performance characteristics (e.g., computational limits), error handling, or whether it's read-only or has side effects. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence states the core purpose, and the second adds domain/category context. There is no wasted verbiage, making it efficient. However, the domain/category annotation might be redundant if already inferred from tool name or context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on behavior, output, and parameter meaning, which are crucial for a tool performing a mathematical computation. The domain/category hint is insufficient to bridge these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('limit') with 0% description coverage. The tool description does not explain what 'limit' means (e.g., upper bound for twin prime pairs, number of gaps to compute) or its constraints (e.g., must be positive integer). With low schema coverage, the description fails to compensate, leaving parameter semantics unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find gaps between consecutive twin prime pairs.' It specifies the verb ('find') and resource ('gaps between consecutive twin prime pairs'), which is mathematically precise. However, it does not explicitly differentiate from sibling tools like 'prime_gap' or 'twin_prime_pairs', though the domain/category hints at specialization.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('prime_gaps'), but offers no explicit instructions, prerequisites, or comparisons to sibling tools such as 'prime_gap' or 'twin_prime_pairs'. Usage is implied by the name and description alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds representations but does not describe output format, performance characteristics (e.g., computational limits), error handling, or whether it's deterministic. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence, followed by domain/category context. There is no wasted verbiage, and it efficiently communicates the essential idea without unnecessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (finding mathematical representations), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not address return values, error conditions, or practical constraints, making it inadequate for an agent to use the tool effectively without additional context or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, so the description must compensate. It only implies parameters for numerator and denominator by mentioning 'small fraction' but does not explain their roles, valid ranges, or the purpose of the 'limit' parameter. This fails to add meaningful semantics beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all ways to represent a small fraction as sum of two unit fractions.' It specifies the verb ('find'), resource ('ways'), and scope ('small fraction'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'unit_fraction_sum', which are related but not identical, leaving room for ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify use cases, prerequisites, or exclusions. For example, it does not clarify what constitutes a 'small fraction' or when to choose this over other Egyptian fraction tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates data for visualization, implying a read-only operation that outputs structured data, but doesn't disclose behavioral traits such as computational complexity, output format, error handling, or any side effects. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence, followed by domain/category tags. There's no wasted text, but it could be more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of prime visualization, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what the output contains, how the Ulam spiral is constructed, or any limitations (e.g., performance with large sizes). This leaves significant gaps for an AI agent to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the tool description doesn't mention the parameter at all. It fails to explain what 'size' represents (e.g., spiral dimensions, number of primes, grid size) or provide any semantic context, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate data for Ulam spiral prime visualization.' It specifies the action ('generate data') and the resource ('Ulam spiral prime visualization'), and includes domain/category context. However, it doesn't differentiate from sibling tools like 'prime_counting_function' or 'prime_density_analysis' that might also involve prime number analysis.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't indicate specific scenarios, prerequisites, or comparisons to sibling tools like 'sieve_of_eratosthenes' or 'prime_factors' that might be relevant for prime-related tasks.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions what the tool does (calculates variance) and the conceptual measure, but it does not describe key behavioral traits such as input validation (e.g., handling non-numeric strings in the 'numbers' array), error handling, output format, or performance considerations (e.g., computational complexity for large lists). This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the tool's purpose, followed by a brief explanation and domain tags. There is no wasted verbiage, and it efficiently conveys the core idea in a single sentence with additional context. However, it could be slightly improved by integrating parameter hints without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical calculation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not address parameter details, behavioral expectations, or output information, leaving significant gaps for an AI agent to understand how to correctly invoke and interpret results from this tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the schema provides no descriptions for the parameters. The description does not compensate by explaining the parameters: it does not mention the 'numbers' array (e.g., expected format, numeric conversion) or the 'population' boolean (e.g., meaning of true/false for population vs sample variance). With two parameters and no schema descriptions, the description adds minimal semantic value beyond the tool's general purpose.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sample variance of a list of numbers. Measures how spread out the numbers are from the mean.' It specifies the verb ('calculate'), resource ('sample variance'), and provides a conceptual explanation. However, it does not explicitly differentiate from sibling tools like 'standard_deviation' or 'covariance', which are related statistical measures, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes a domain/category tag ('Domain: statistics, Category: general'), which implies usage in statistical contexts, but it does not provide explicit guidance on when to use this tool versus alternatives (e.g., 'population' vs 'sample' variance, or when to choose variance over standard deviation). No when-not-to-use or prerequisite information is given, leaving usage largely implicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks details on behavior: it doesn't mention error handling (e.g., for invalid inputs), performance characteristics, or output format (since there's no output schema). The domain/category hint at context but don't add actionable behavioral traits.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first phrase. The domain/category information is additional but not redundant. It avoids unnecessary words, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical operation with two parameters, one with a default), lack of annotations, and no output schema, the description is incomplete. It doesn't explain the 'p' parameter's role, potential constraints (e.g., p >= 1), or what the tool returns. For a tool with 0% schema coverage, more context is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'norm (magnitude)' and 'vector', which partially explains the 'vector' parameter, but does not clarify the 'p' parameter (e.g., that it's the p-norm order, with default 2 for Euclidean norm). The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the norm (magnitude) of a vector'. It specifies the verb ('calculate') and resource ('norm of a vector'), and includes domain/category context ('Domain: linear_algebra.vectors, Category: general'). However, it does not explicitly differentiate from sibling tools like 'euclidean_norm' or 'manhattan_norm', which are likely related but not directly named as alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if this is for general p-norms or specific cases, or when to choose it over sibling tools like 'euclidean_norm' (which might be a specific case with p=2).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates vector rejection but does not disclose behavioral traits such as input validation (e.g., handling non-numeric strings in arrays), error handling (e.g., zero vectors), output format, or computational characteristics. The description is minimal and lacks necessary operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first phrase. It avoids unnecessary words, though the domain and category annotations are appended efficiently. However, it could be more structured by separating usage notes from the core description.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on parameter semantics, behavioral transparency, and output expectations. For a mathematical tool with two parameters, more context is needed to guide effective use, such as input formats and result interpretation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It does not explain the parameters 'vector_a' and 'vector_b' beyond implying they are vectors. No details on array format (e.g., numeric strings, length requirements), meaning of the vectors in the rejection calculation, or examples are provided. The description adds little semantic value over the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate vector rejection (component perpendicular to another vector)'. It specifies the verb ('calculate'), resource ('vector rejection'), and defines the mathematical concept. However, it does not explicitly differentiate from sibling tools like 'vector_projection' or 'normalize_vector', which are related vector operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it includes a domain ('linear_algebra.vectors') and category ('general'), which implies context but does not specify when to use this tool versus alternatives like 'vector_projection' or 'cross_product' for perpendicular components. No explicit when-to-use, when-not-to-use, or prerequisite information is given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool checks orthogonality but does not disclose behavioral traits such as how it handles non-numeric inputs (since parameters are typed as arrays of strings), what the return value is (boolean or detailed result), or error conditions (e.g., vectors of different dimensions). The mention of 'tolerance' in the schema is not explained in the description.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence. It avoids unnecessary words, though it could be more structured by separating purpose from domain/category. Every part of the description serves a purpose, with no wasted content.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (3 parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameters, return values, error handling, and usage context. For a mathematical tool with input validation needs (e.g., vector dimensions, numeric parsing), this minimal description does not provide sufficient context for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It does not mention any parameters—'vector_a', 'vector_b', or 'tolerance'—leaving their semantics undocumented. The description fails to explain what these parameters represent (e.g., vector components as strings, tolerance for numerical precision) or their expected formats.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if two vectors are orthogonal (perpendicular)'. It specifies the verb ('check') and resource ('two vectors'), and includes the domain/category context. However, it does not explicitly differentiate from sibling tools like 'vectors_parallel' or 'dot_product', which are related vector operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.vectors') and category ('general'), but offers no explicit when/when-not instructions or references to sibling tools like 'dot_product' (which computes the dot product used in orthogonality checks) or 'vectors_parallel' (for checking parallel vectors).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions checking for parallel/anti-parallel status but doesn't disclose behavioral traits like numerical tolerance handling (implied by the 'tolerance' parameter), return format (boolean? details?), or edge cases (e.g., zero vectors, dimension mismatches). This leaves significant gaps for a tool with mathematical computations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with domain/category tags. It's front-loaded with the core purpose, though it could be more informative without losing efficiency. No wasted words, but under-specification limits its helpfulness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and 3 parameters, the description is incomplete. It doesn't cover parameter meanings, return values, error conditions, or usage context. For a mathematical tool with sibling alternatives, this leaves the agent poorly equipped to use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It doesn't explain parameters at all—no mention of what 'vector_a' and 'vector_b' represent (arrays of strings? numeric values?), what 'tolerance' does, or how inputs should be formatted. This fails to add meaning beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if two vectors are parallel (or anti-parallel)' with domain/category context. It specifies the verb ('Check') and resource ('two vectors'), though it doesn't explicitly differentiate from sibling tools like 'vectors_orthogonal' or 'vector_angle' that handle related vector relationships.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. With many sibling tools for vector operations (e.g., 'vectors_orthogonal', 'dot_product', 'cross_product'), the description lacks any context about when parallel checking is appropriate versus other vector analyses or comparisons.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the identity and domain but does not explain how the verification works (e.g., numerical computation with tolerance), what the output looks like (e.g., boolean or detailed result), or any error handling. This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise, consisting of a single sentence that states the identity and includes domain/category context. It is front-loaded with the core purpose. However, the parenthetical note could be integrated more smoothly, but overall, it avoids unnecessary verbosity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical verification tool with 2 parameters, no annotations, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral details, or output format, making it inadequate for an AI agent to fully understand how to invoke and interpret results from this tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (x and tolerance) with 0% schema description coverage, meaning no parameter details are provided in the schema. The description does not add any information about these parameters, such as what 'x' represents (e.g., a real number) or how 'tolerance' affects the verification. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: verifying the hyperbolic identity cosh²(x) - sinh²(x) = 1. It specifies the mathematical operation (verification) and the identity involved. However, it does not distinguish this tool from sibling tools like 'verify_identity' or 'comprehensive_identity_verification', which might handle similar mathematical verifications.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance by mentioning the domain (trigonometry) and category (hyperbolic), but it does not explicitly state when to use this tool versus alternatives like 'verify_identity' or other hyperbolic function tools. There is no information on prerequisites, limitations, or specific use cases beyond the identity verification.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'verification by comparison' but doesn't disclose what the tool actually returns (e.g., boolean result, numeric difference, error message), what happens with invalid inputs, or any computational constraints. For a verification tool with 4 parameters and no annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence plus domain/category) with zero wasted words. It's front-loaded with the core purpose and efficiently includes relevant context. Every element earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (4 parameters, verification logic), lack of annotations, and no output schema, the description is insufficient. It doesn't explain what constitutes successful verification, what format the result takes, or how the tolerance parameter affects the comparison. For a mathematical verification tool, users need to understand the verification criteria and output format.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the 4 parameters (a, b, operation, tolerance) are documented in the schema. The description adds no information about what these parameters represent (e.g., that a and b are angles, operation selects addition/subtraction formulas, tolerance is numerical precision). This fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Verify sum and difference formulas by comparison with direct calculation.' It specifies the verb ('verify'), resource ('sum and difference formulas'), and method ('comparison with direct calculation'), with domain/category context. However, it doesn't explicitly distinguish this from sibling tools like 'sum_difference_formulas' or 'comprehensive_identity_verification', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (trigonometry) and category (identities), but doesn't indicate whether this is for educational verification, numerical validation, or when other identity verification tools would be more appropriate. No explicit when/when-not statements or named alternatives are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'Generate points' but does not disclose behavioral traits such as output format (e.g., list of coordinates, time series), computational complexity, error handling, or default behaviors (e.g., wave_type defaults to 'sine'). This leaves significant gaps for an agent to understand how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a clear main purpose in the first phrase. The additional domain/category context is brief and relevant. There is no wasted verbiage, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (6 parameters, no annotations, no output schema), the description is insufficient. It lacks details on parameter semantics, behavioral traits, and output expectations. For a tool that generates data points, more context on the return format (e.g., array of (x,y) pairs) and usage is needed to be complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It does not add any meaning beyond the schema—no explanation of what parameters like 'amplitude', 'frequency', or 'wave_type' represent, their units, valid ranges, or interactions. For example, it does not clarify that 'duration' might be in seconds or that 'sample_rate' is in Hz, leaving parameters semantically ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate points for a sinusoidal wave equation.' It specifies the action (generate points) and the resource (sinusoidal wave equation), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'wave_amplitude_analysis' or 'wave_interference', which are related but distinct.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions domain and category but does not specify scenarios, prerequisites, or exclusions. For example, it does not indicate whether this is for simulation, visualization, or analysis, or how it differs from other wave-related tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions analysis but does not specify output format, computational constraints, error handling, or side effects. For a tool with no annotation coverage, this leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the purpose in a single sentence with no wasted words. The domain and category tags are efficiently appended. However, it could be more structured by separating usage notes or parameter hints, though brevity is appropriate for a simple tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on parameter semantics, behavioral traits, and output expectations. For a tool with two parameters and mathematical analysis complexity, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not explain what 'waves' or 'time_points' represent, their expected formats, or usage examples. It fails to compensate for the lack of schema documentation, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze wave interference patterns between two or more waves.' It specifies the verb ('analyze'), resource ('wave interference patterns'), and scope ('between two or more waves'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'wave_amplitude_analysis' or 'wave_equation', which are related but distinct, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context about prerequisites, typical use cases, or comparisons to sibling tools such as 'wave_amplitude_analysis' or 'wave_equation'. The domain and category tags ('trigonometry, applications') offer minimal implied usage but no explicit instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool 'checks' the conjecture but does not disclose behavioral traits such as what the output looks like (e.g., returns a boolean, a list of primes, or an error for invalid input), performance characteristics (e.g., computational limits for large n), or error handling. The description is minimal and lacks essential operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain context but is somewhat redundant. There is no wasted verbiage, but it could be more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical conjecture-checking tool, no annotations, no output schema, and low parameter coverage, the description is incomplete. It fails to explain what the tool returns, how it handles edge cases (e.g., n <= 5, even n), or any limitations. The agent lacks sufficient information to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description does not add any semantic information about 'n', such as its expected range (odd integer > 5), format, or constraints. For a tool checking a number theory conjecture, this is a significant gap, as the agent needs to know what input is valid.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check weak Goldbach conjecture: every odd integer > 5 is sum of three primes.' It specifies the verb ('Check'), the mathematical conjecture, and the domain/category. However, it does not explicitly differentiate from its sibling 'goldbach_conjecture_check' (which likely checks the standard Goldbach conjecture), so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic, Category: additive_number_theory'), but this is too vague to help an agent decide between this and other number theory tools like 'goldbach_conjecture_check' or 'goldbach_pairs'. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates numbers in a range but does not clarify key behaviors: whether the range is inclusive or exclusive, if it returns a list or sequence, error handling for invalid inputs, or performance characteristics. This leaves significant gaps in understanding how the tool operates beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category information. There is no unnecessary verbiage, and the structure is efficient, though the domain/category details could be considered slightly extraneous if not needed for tool selection.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (2 parameters, no annotations, no output schema), the description is insufficient. It lacks details on parameter usage, behavioral traits (e.g., output format, error handling), and differentiation from siblings. Without an output schema, the description should ideally hint at return values, but it does not, leaving the agent with incomplete context for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, so the description must compensate. It mentions 'a given range' but does not explain the 'start' and 'end' parameters—such as their default values (0 and 10), whether they are inclusive, or if they accept negative values. This lack of detail fails to adequately supplement the schema, resulting in incomplete parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate whole numbers (non-negative integers) in a given range.' It specifies the verb ('generate'), resource ('whole numbers'), and scope ('in a given range'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'integers_in_range' or 'natural_numbers', which might have overlapping functionality, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance by mentioning the domain ('arithmetic') and category ('number_systems'), but it does not specify when to use this tool versus alternatives. For example, it does not explain how it differs from sibling tools such as 'integers_in_range' or 'natural_numbers', leaving the agent without clear usage context or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'detailed calculation', which hints at output behavior, but does not disclose critical traits such as error handling (e.g., for non-prime inputs), computational complexity, or what 'detailed' entails. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no unnecessary verbiage, and the domain/category tags are efficiently appended. However, it could be slightly improved by integrating usage hints more seamlessly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of verifying a mathematical theorem, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on input validation, output format (what 'detailed calculation' means), error conditions, and differentiation from sibling tools, making it inadequate for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'p' of type integer. The description does not add any semantic details about 'p', such as that it should be a prime number, its valid range, or examples. With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Verify Wilson's theorem for a given prime with detailed calculation.' It specifies the verb ('verify'), the mathematical theorem, and the input resource ('a given prime'). However, it does not explicitly differentiate from sibling tools like 'wilson_theorem_check' or 'wilson_theorem_test', which appear to serve similar purposes, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance, mentioning the domain ('arithmetic') and category ('wilson_theorem'), but does not specify when to use this tool versus alternatives like 'wilson_theorem_check' or 'wilson_theorem_test'. There is no explicit advice on prerequisites, input constraints (e.g., that 'p' must be prime), or comparison with siblings, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions what the tool does but fails to describe how it behaves: no information on input format expectations (e.g., numeric strings vs. other types), error handling, output format, or computational characteristics. For a statistical tool with undocumented parameters, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence with supplementary tags. There's no wasted verbiage, and the structure is clear. However, the brevity contributes to underspecification in other dimensions, slightly reducing its effectiveness despite efficient wording.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical calculation with one undocumented parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It omits essential context: parameter details, behavioral traits, output expectations, and usage distinctions from siblings. For a tool in a crowded namespace, this leaves the agent with insufficient information to use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, documenting only that 'numbers' is a required array of strings. The description adds no parameter semantics—it doesn't explain what 'numbers' represents (e.g., numeric data points), expected format (e.g., comma-separated values), or validation rules. With low schema coverage, the description fails to compensate, leaving parameters largely unexplained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate z-scores for a dataset (standardized values)'. It specifies the verb ('calculate'), resource ('z-scores'), and provides clarifying context ('standardized values') with domain/category tags. However, it doesn't explicitly differentiate from sibling tools like 'standard_deviation' or 'normalize_vector', which might offer overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many statistical sibling tools (e.g., 'standard_deviation', 'normalize_vector', 'comprehensive_stats'), there's no indication of when z-score calculation is preferred, what prerequisites exist, or any limitations. The domain/category tags offer minimal contextual framing but no actionable usage rules.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it describes what the tool does (perform a z-test), it doesn't mention important behavioral aspects such as what the output format will be (since no output schema exists), whether it returns p-values, test statistics, or confidence intervals, or any assumptions about the data (e.g., normality). This leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in a single sentence. It efficiently communicates the statistical test and its application without unnecessary details. However, it could be slightly more structured by explicitly separating the purpose from domain/category information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical hypothesis test with 4 parameters, 0% schema description coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain parameter meanings, output format, or key assumptions (e.g., data should be normally distributed for z-test validity). For a tool with this level of complexity and poor structured documentation, the description should do much more to compensate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the parameters (data, population_mean, population_std, alpha) have descriptions in the schema. The tool description doesn't provide any additional information about what these parameters mean, their expected formats, or typical values. For example, it doesn't clarify that 'alpha' is the significance level or that 'data' should be a numeric sample array. This leaves parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform z-test for known population standard deviation to test whether sample mean differs from population mean.' It specifies the statistical test (z-test), its domain (statistics), and category (inference). However, it doesn't explicitly differentiate from sibling tools like 't_test_one_sample' or 'z_scores', which are related statistical tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain and category but doesn't specify when to use this tool versus alternatives like t-tests (when population standard deviation is unknown) or other hypothesis tests. No explicit when/when-not instructions or prerequisite conditions are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool calculates, with no information about error handling (e.g., for invalid inputs like |value| < 1), output format (degrees/radians), precision, or computational characteristics. For a mathematical function with potential domain restrictions, this is a significant gap in behavioral transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—just one sentence with parenthetical context—and front-loads the core purpose. Every word earns its place: 'Calculate arccosecant (inverse cosecant)' establishes the operation, and '(Domain: trigonometry, Category: inverse_functions)' provides helpful categorization without redundancy. No wasted words or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature and lack of annotations/output schema, the description is incomplete. It doesn't address key contextual elements: parameter semantics, return value (angle in radians/degrees?), domain restrictions, or error conditions. While concise, it leaves too many open questions for effective tool use, especially compared to more thoroughly documented sibling tools in the list.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description provides no information about the 'value' parameter. It doesn't explain what 'value' represents (e.g., a real number, the cosecant of an angle), valid ranges (|value| ≥ 1 for real arccosecant), units, or special cases. With one undocumented parameter and no compensation in the description, this falls below the baseline expectation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arccosecant (inverse cosecant)', which is a specific mathematical operation. It also provides domain context ('Domain: trigonometry, Category: inverse_functions'), which helps distinguish it from other mathematical tools. However, it doesn't explicitly differentiate from sibling tools like 'asec' or 'acot', which are also inverse trigonometric functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags imply it's for trigonometric calculations, there's no mention of when arccosecant is appropriate compared to other inverse trigonometric functions (like arcsin or arccos) or how it relates to sibling tools like 'csc' (cosecant). No prerequisites, input constraints, or typical use cases are described.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'extracts' amplitude, implying a read-only calculation, but does not specify output format, error handling, mathematical assumptions (e.g., handling of negative coefficients), or performance characteristics. This leaves significant gaps for a tool with undocumented parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category tags. There is no wasted verbiage, and every word contributes to understanding the tool's function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, two undocumented parameters, no annotations, and no output schema, the description is insufficient. It lacks details on the calculation method (e.g., amplitude = sqrt(A² + B²)), output format, error cases, or examples, making it incomplete for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two undocumented parameters ('a_coeff' and 'b_coeff'). The description mentions 'trigonometric coefficients A*cos(θ) + B*sin(θ)', which clarifies that 'a_coeff' corresponds to A and 'b_coeff' to B, adding meaningful context. However, it does not explain units, valid ranges, or interpretation, so it only partially compensates for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Extract amplitude from trigonometric coefficients A*cos(θ) + B*sin(θ).' It specifies the verb ('extract'), resource ('amplitude'), and mathematical context. However, it does not explicitly differentiate from potential sibling tools like 'wave_amplitude_analysis' or other trigonometric tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance by mentioning the domain ('trigonometry') and category ('wave_analysis'), which implies context. However, it lacks explicit instructions on when to use this tool versus alternatives (e.g., 'wave_amplitude_analysis' or other amplitude-related tools), prerequisites, or examples of appropriate scenarios.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates, without mentioning input constraints (e.g., valid range for 'value'), error handling, output format, or computational characteristics. For a mathematical function tool with no annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it directly states the tool's purpose in the first phrase, followed by brief domain/category context. There is no wasted verbiage, and every word contributes to understanding the tool's function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not cover input constraints, output format, error conditions, or mathematical properties, which are essential for correct usage. The domain/category hints are insufficient for full contextual understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not explain the 'value' parameter beyond what the schema provides (type: number). It lacks details on the parameter's meaning (e.g., input to arcsecant function), valid ranges (e.g., |value| ≥ 1 for real arcsecant), or units. With low schema coverage, the description fails to compensate adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arcsecant (inverse secant).' It specifies the verb ('calculate') and resource ('arcsecant'), and adds domain/category context. However, it does not explicitly differentiate from sibling tools like 'asech' (inverse hyperbolic secant) or 'acsc' (inverse cosecant), which are related inverse trigonometric functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('inverse_functions'), but does not specify use cases, prerequisites, or comparisons to sibling tools like 'asech' or 'acsc'. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'domain validation,' which hints at input constraints (likely for the arcsine function's domain of [-1, 1]), but does not detail what happens on invalid inputs (e.g., error messages, exceptions, or default behaviors). It also omits information about output format, precision, or any side effects. For a mathematical function tool with no annotations, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the core purpose in the first phrase and adds context in parentheses. There is no wasted language, and every word contributes to understanding the tool's function and domain. This efficiency makes it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a mathematical function with domain constraints), the lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not cover behavioral aspects like error handling, output details (e.g., range in radians), or usage distinctions from siblings. While concise, it fails to provide the necessary context for effective tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('value') with 0% description coverage, and the description does not add any semantic details about this parameter. It does not explain what 'value' represents (e.g., a sine ratio between -1 and 1), its expected units (radians vs. degrees), or the implications of domain validation. With low schema coverage and no compensation in the description, this leaves the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arcsine (inverse sine) with domain validation.' It specifies the verb ('calculate') and resource ('arcsine'), and distinguishes it from siblings like 'asin_degrees' by implying this version uses radians (though not explicitly stated). However, it does not explicitly differentiate from 'asin_degrees' in the description text, which holds it back from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions domain validation and categorizes the tool under 'trigonometry' and 'inverse_functions,' which gives some context. However, it does not specify when to use this tool versus alternatives like 'asin_degrees' or 'asinh,' nor does it provide any prerequisites, exclusions, or explicit usage scenarios. This lack of comparative guidance limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It only states what the tool calculates without describing behavior: no information about input domain restrictions (e.g., valid range for x), error handling, precision, or output format. For a mathematical function with zero annotation coverage, this is insufficient behavioral disclosure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence plus parenthetical) with zero wasted words. It's front-loaded with the core purpose and efficiently adds domain/category context. Every element earns its place in this minimal description.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical function with 1 parameter, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain the mathematical definition, input constraints, output interpretation, or relationship to sibling tools. The category label helps minimally, but key contextual information is missing.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It provides no parameter information beyond what's in the schema (single parameter 'x'). No explanation of what 'x' represents mathematically, acceptable values, units, or special cases. The description adds zero semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate inverse hyperbolic sine (area sine).' It specifies the mathematical function and provides domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'asinh' vs 'acosh' or 'atanh' beyond the category label.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the category 'inverse_hyperbolic', it doesn't explain when to choose asinh over other inverse hyperbolic functions or trigonometric functions. No usage context, prerequisites, or exclusions are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates without describing output format (e.g., radians vs. degrees), error handling (e.g., for invalid inputs), or mathematical properties (e.g., range of output values). For a mathematical function tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with no wasted words. The first phrase directly states the tool's purpose, and the parenthetical adds minimal but relevant context. Every sentence (effectively one) earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not address key contextual aspects like output format (radians/degrees), mathematical constraints, or how it differs from sibling tools. The description alone is insufficient for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'value' of type 'number'. The description adds no information about this parameter's meaning (e.g., that it represents the tangent value, expected range, or units). It does not compensate for the lack of schema documentation, leaving the parameter's semantics unclear beyond its basic type.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose as 'Calculate arctangent (inverse tangent)' with a specific mathematical verb ('calculate') and resource ('arctangent'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools like 'atan2' or 'atan_degrees', which handle related but distinct calculations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: trigonometry, Category: inverse_functions', but this is generic context rather than explicit usage instructions. There is no mention of when to prefer 'atan' over 'atan2' (for two-argument arctangent) or 'atan_degrees' (for degree output), which are directly relevant sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but lacks behavioral details: no mention of error handling (e.g., invalid base or number), performance characteristics, or output format. The description is functional but insufficient for a mutation-free tool with zero annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It front-loads the core purpose and includes helpful domain/category tags. Every element earns its place, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It doesn't explain the return value (decimal representation), error conditions, or how it differs from sibling tools like 'base_conversion'. For a 2-parameter tool with no structured support, more contextual detail is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'base' (2-36) but doesn't explain the 'number' parameter's format (e.g., string representation in the given base). The description adds minimal value beyond the bare schema, leaving key parameter semantics undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting a number from a specified base to decimal. It specifies the base range (2-36) and includes domain/category context. However, it doesn't differentiate from sibling tools like 'base_conversion' or 'binary_to_decimal', which perform similar base conversions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the base range (2-36) but offers no explicit when-to-use instructions, alternatives, or exclusions compared to sibling tools. The domain/category tags ('arithmetic', 'general') are too broad to serve as meaningful usage guidelines.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details: it doesn't explain the algorithm (e.g., based on continued fractions), performance characteristics, error handling, or output format. For a computational tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: one sentence stating the purpose, followed by domain/category in parentheses. Every word contributes directly to the tool's function, with no redundant information. It's front-loaded and efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain the approximation algorithm, output format (e.g., numerator/denominator pair), error bounds, or usage examples. For a tool that likely returns a rational number, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'x' and 'max_denom' but doesn't elaborate on their semantics: 'x' is described as the number to approximate, but 'max_denom' lacks clarification (e.g., must be positive integer). It adds minimal value beyond naming the parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find best rational approximation to x with denominator ≤ max_denom.' It specifies the verb ('Find'), resource ('best rational approximation'), and constraints (denominator bound). However, it doesn't explicitly differentiate from sibling tools like 'best_approximation_farey' or 'cf_to_rational', which appear related.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('continued_fractions'), which hints at context. However, it offers no explicit advice on when to use this tool versus alternatives (e.g., 'best_approximation_farey' or 'cf_to_rational' among siblings), nor does it specify prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the conversion action but does not describe error handling (e.g., invalid binary strings), performance characteristics, or output format. For a tool with zero annotation coverage, this leaves significant gaps in understanding how it behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by a domain/category tag. There is no wasted verbiage, and every part of the description contributes essential information efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no annotations, no output schema), the description is minimal but insufficient. It lacks details on parameter validation, error conditions, and output specifics, which are crucial for reliable use. While concise, it does not provide enough context for a complete understanding of the tool's behavior and limitations.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one required parameter 'binary_str' of type string. The description mentions 'binary number (base-2)' but does not elaborate on parameter semantics, such as valid formats (e.g., leading zeros, sign handling), constraints, or examples. It adds minimal value beyond the schema's type information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting a binary number to decimal. It specifies the input domain (binary, base-2) and output (decimal, base-10), and includes a domain/category tag for additional context. However, it does not explicitly differentiate from sibling tools like 'decimal_to_binary' or 'base_conversion', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'decimal_to_binary' (reverse operation) or 'base_conversion' (more general), nor does it specify any prerequisites, constraints, or typical use cases. Usage is implied by the purpose but not explicitly stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but does not describe how it behaves—e.g., whether it returns a list of approximations, a single best match, error handling, or computational limits. For a tool with no annotations, this lack of behavioral detail is a notable shortfall.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—two brief sentences that directly state the tool's function and domain/category without any fluff. It is front-loaded with the core purpose, making it efficient and easy to parse, though this conciseness comes at the cost of detail.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical approximation tool), lack of annotations, no output schema, and undocumented parameters, the description is incomplete. It does not explain what the tool returns, how approximations are calculated, or any limitations, making it insufficient for effective use by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('year_length') with 0% description coverage, and the tool description does not mention parameters at all. It fails to explain what 'year_length' represents (e.g., in days, decimal years) or its expected format, leaving the parameter undocumented. This is inadequate given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find calendar approximations using continued fractions.' It specifies the verb ('Find'), resource ('calendar approximations'), and method ('using continued fractions'), which is specific and informative. However, it does not distinguish this tool from its many siblings, as the sibling list includes numerous mathematical tools but no obvious alternatives for calendar approximations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('continued_fractions'), which implies context but does not specify use cases, prerequisites, or exclusions. With many sibling tools available, the lack of comparative guidance is a significant gap.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the mathematical definition but doesn't disclose behavioral traits: no information about input constraints (e.g., n must be positive integer), error handling, computational complexity, or output format. For a mathematical function tool with zero annotation coverage, this leaves significant gaps in understanding how the tool behaves operationally.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence containing the core purpose and domain/category context. Every word earns its place with zero redundancy. The mathematical definition is stated efficiently without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for the single parameter, the description is incomplete. While concise, it doesn't compensate for the missing structured information. For a mathematical function tool, users need to know input constraints, output format, and mathematical context—none of which are adequately addressed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description provides no parameter information beyond the schema's 'n: integer'. It doesn't explain what 'n' represents mathematically (positive integer? any integer?), valid ranges, or special cases. With one undocumented parameter at 0% coverage, the description adds minimal value over the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Carmichael function λ(n) - exponent of multiplicative group mod n.' It specifies the verb ('calculate'), the mathematical function (Carmichael function λ(n)), and provides domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'euler_totient' or 'order_modulo' which are related arithmetic functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('arithmetic_functions'), it doesn't indicate typical use cases, prerequisites, or when one might choose this over similar functions like Euler's totient function. The agent must infer usage from the mathematical definition alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does but doesn't disclose behavioral traits: it doesn't mention input constraints (e.g., valid continued fraction formats), error handling, performance characteristics, or what the output looks like (since there's no output schema). This leaves significant gaps for an agent to understand how to use it correctly.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence followed by domain/category tags—with zero wasted words. It's front-loaded with the core purpose, making it easy to parse. Every element (the conversion statement and tags) adds value without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical conversion with 1 parameter), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It states the purpose but doesn't provide enough context for an agent to reliably invoke the tool, such as explaining parameter semantics, output format, or error conditions. The domain/category tags help slightly but don't fill these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema only documents the parameter 'cf' as an array of integers without any semantic explanation. The description adds no parameter information beyond the tool's purpose—it doesn't explain what 'cf' represents, how the array should be structured, or provide examples. This fails to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Convert') and resource ('continued fraction to rational number'), making the purpose unambiguous. It also includes domain/category tags which help contextualize. However, it doesn't differentiate from potential siblings like 'rational_to_cf' (which appears in the sibling list) or explain how this conversion differs from other mathematical operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags hint at context, there's no explicit mention of when this conversion is appropriate, what prerequisites exist, or how it relates to sibling tools like 'rational_to_cf' (the inverse operation) or other continued fraction tools in the list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the mathematical domain but doesn't disclose any behavioral traits: no information about input constraints (e.g., valid ranges for 'n'), computational characteristics (e.g., iterative nature, potential for large sequences), error handling, or output format. For a tool with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose. There's no wasted text, and the domain/category tags are efficiently appended. Every word earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature and lack of annotations/output schema, the description is incomplete. It doesn't explain what the Collatz sequence is (though this might be assumed knowledge), provides no parameter details, and gives no indication of return values or behavior. For a tool with 1 parameter and no structured documentation, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It doesn't mention the parameter 'n' at all, leaving its meaning and constraints undocumented. The description should explain that 'n' is the starting integer for the Collatz sequence, but it provides no parameter semantics beyond what's implied by the tool name.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the maximum value reached in the Collatz sequence.' It specifies the verb ('Find'), resource ('maximum value'), and domain context ('Collatz sequence'). However, it doesn't explicitly differentiate from sibling tools like 'collatz_sequence' or 'collatz_stopping_time', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There are sibling tools like 'collatz_sequence' and 'collatz_stopping_time' that operate on the same mathematical concept, but the description doesn't mention them or explain when this specific tool is appropriate. The domain/category tags are generic and don't help with tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the algorithm and convergence trait but lacks critical behavioral details: required permissions, computational cost, output format (e.g., decimal string, rational approximation), error handling, or precision limits. For a computational tool with no annotations, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with parenthetical domain/category. It front-loads the core purpose and algorithm, with zero redundant information. Every word earns its place, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on behavior, parameters, return values, and comparative usage with siblings. For a mathematical computation tool with one parameter, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, with one parameter 'terms' undocumented. The description adds no parameter semantics—it doesn't explain what 'terms' means (e.g., number of iterations, series terms affecting precision), valid ranges, or default behavior. With low coverage and no compensation, the score reflects inadequate parameter clarification.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes pi using a specific algorithm (Chudnovsky) and mentions its key characteristic (extremely fast convergence). It distinguishes from siblings like compute_pi_leibniz, compute_pi_machin, and compute_pi_nilakantha by naming the algorithm, but doesn't explicitly differentiate performance or use cases beyond convergence speed.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternative pi-computation siblings. The description mentions 'extremely fast convergence' but doesn't explain practical implications (e.g., for high precision, fewer terms) or compare to other algorithms. Usage context is implied but not explicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool generates but doesn't disclose behavioral traits like computational complexity, error handling, output format, or whether it's deterministic. The description is minimal and lacks important operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with zero wasted words. It's a single sentence that efficiently communicates the core purpose and includes helpful domain/category metadata. Every element serves a clear purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a tool with no annotations, 0% schema coverage, and no output schema, the description is inadequate. It doesn't explain the required parameter, output format, or behavioral characteristics. Given the mathematical context and parameter requirement, more completeness is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions no parameters at all, while the input schema requires a 'depth' parameter. The description fails to explain what 'depth' means or how it affects the output, leaving a critical gap in parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate continued fraction representation of golden ratio' with a specific pattern '[1; 1, 1, 1, 1, 1, ...]'. It includes domain/category context, but doesn't explicitly differentiate from sibling tools like 'golden_ratio_cf' or 'compute_golden_ratio_continued_fraction'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided about when to use this tool versus alternatives. The description mentions the domain and category but gives no explicit usage context, prerequisites, or comparisons to sibling tools that might handle similar mathematical constant representations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool counts solutions within bounds but does not mention computational complexity, error handling, output format, or any side effects. For a tool with 7 parameters and no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category tags. There is no wasted verbiage, and every word contributes to understanding the tool's function efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (7 parameters, no annotations, no output schema), the description is incomplete. It does not explain the return value format, error conditions, or behavioral nuances. For a mathematical tool with multiple inputs, more context is needed to guide the agent effectively, making this description inadequate for the tool's complexity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description does not explain any parameters beyond implying 'a', 'b', 'c', and bounds for 'x' and 'y'. It lacks details on parameter constraints, units, or examples, failing to compensate for the schema's lack of descriptions. This leaves the agent guessing about parameter meanings and valid ranges.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Count integer solutions to ax + by = c within given bounds.' It specifies the verb ('count'), resource ('integer solutions'), and domain context ('diophantine_equations'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'solve_linear_diophantine' or 'diophantine_analysis', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit instructions on prerequisites, limitations, or comparisons with sibling tools such as 'parametric_solutions_diophantine' or 'solve_linear_diophantine'. This leaves the agent without clear usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the calculation but doesn't disclose behavioral traits: it doesn't mention input validation (e.g., handling non-numeric strings, 3D requirement), error conditions, performance characteristics, or output format. For a mathematical tool with no annotations, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose with domain/category tags. There is zero wasted text, and every word earns its place by specifying the operation and context efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical operation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't explain input requirements, output format, error handling, or usage context. For a tool that performs a specific vector calculation, more detail is needed to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'two 3D vectors' but doesn't explain parameter semantics: it doesn't specify that 'vector_a' and 'vector_b' are arrays of three strings representing vector components, expected formats (e.g., numeric strings), or units. The description adds minimal value beyond the parameter names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the cross product of two 3D vectors.' It specifies the mathematical operation (cross product), the resource (3D vectors), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'dot_product' or 'triple_vector_product', which are related vector operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (linear_algebra.vectors) and category (general), but doesn't specify use cases, prerequisites, or compare it to sibling tools like 'dot_product' or 'vector_angle' for different vector operations. The agent must infer usage from the name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description mentions the method is 'most accurate', which adds some context about performance, but it doesn't disclose other behavioral traits such as error handling, computational complexity, or what happens with invalid inputs (e.g., non-numeric 'func' strings). For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and key attribute ('most accurate'). There is no wasted verbiage, and the structure efficiently conveys the essential information without unnecessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical computation tool with 3 parameters), no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks details on parameter meanings, behavioral traits, and expected outputs. For a tool of this nature, the description should provide more context to guide effective use, but it falls short.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the parameters ('func', 'x', 'h') are documented in the schema. The description does not add any semantic information about these parameters—it doesn't explain what 'func' represents (e.g., a mathematical expression as a string), what 'x' is (the point at which to compute the derivative), or what 'h' is (the step size, with a default value). This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate numeric derivative using central difference method (most accurate)'. It specifies the verb ('calculate'), resource ('numeric derivative'), and method ('central difference'), and distinguishes it by noting it's 'most accurate'. However, it doesn't explicitly differentiate from its siblings 'derivative_backward' and 'derivative_forward', which are listed among the sibling tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the method is 'most accurate', which implies a preference over other derivative methods, but it doesn't explicitly state when to use this tool versus alternatives like 'derivative_backward' or 'derivative_forward', nor does it provide context on prerequisites or exclusions. No explicit alternatives or when-not-to-use scenarios are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('linear regression') but does not describe key behavioral traits such as what the output looks like (e.g., slope, intercept, p-value), whether it handles missing data, assumptions about the time series (e.g., equally spaced points), or any limitations (e.g., sensitivity to outliers). For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured, consisting of a single sentence that efficiently conveys the core purpose and context. It uses no unnecessary words and front-loads the essential information, making it easy to parse quickly. Every part of the sentence earns its place by specifying the action, resource, method, domain, and category.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of trend detection in time series, the description is incomplete. There is no output schema, and the description does not explain what the tool returns (e.g., trend metrics or statistical results). Combined with no annotations and poor parameter semantics, this makes it difficult for an agent to understand how to use the tool effectively or interpret its results, despite the concise purpose statement.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('data') with 0% description coverage, meaning the schema provides no semantic information. The description does not compensate by explaining what 'data' should contain (e.g., an array of numeric values representing time series points, expected format, or constraints like minimum length). This leaves the parameter's meaning unclear, which is inadequate given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Detect and quantify trend in time series using linear regression'. It specifies the verb ('detect and quantify'), resource ('trend in time series'), and method ('linear regression'), making it easy to understand what the tool does. However, it does not explicitly differentiate from sibling tools like 'linear_regression' or 'detrend', which are related but not identical, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('timeseries') and category ('analysis'), which implies context, but does not specify when to use this tool versus alternatives like 'linear_regression' (which might perform regression without trend detection) or 'detrend' (which might remove trends). There are no explicit instructions on when or when not to use it, leaving the agent to infer usage from the purpose alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what the tool calculates, without mentioning any behavioral traits: no information about computational complexity, error handling, input constraints (e.g., negative numbers?), output format, or whether it's deterministic. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by a domain/category tag. There's zero wasted text, and every element (calculation definition, domain context) earns its place efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical operation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It defines the concept but fails to provide necessary context about parameters, behavior, output, or relationship to sibling tools. For a tool with this level of structural underspecification, the description should do more to compensate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. The description mentions 'digital persistence' but doesn't explain what parameters 'n' (integer) and 'operation' (string with default 'multiply') mean in this context. It doesn't clarify what 'n' represents (starting number?), what 'operation' does (multiplication of digits?), or what alternatives to 'multiply' might be. The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate digital persistence (number of steps to reach single digit).' It specifies the verb ('calculate'), resource ('digital persistence'), and provides a concise definition. However, it doesn't explicitly differentiate from sibling tools like 'digital_root' or 'persistent_digital_root', which appear to be related concepts in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It includes a domain/category tag ('Domain: arithmetic, Category: special_numbers'), but this is generic classification rather than practical usage advice. There's no mention of when to choose this over similar tools like 'digital_root' or 'persistent_digital_root' from the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but does not disclose behavioral traits such as how it handles negative numbers, non-integer inputs, or large values, nor does it describe the output format (e.g., a dictionary of digit frequencies). For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Count frequency of each digit in a number.' The domain and category tags are efficiently appended without redundancy. Every word serves a purpose, and there is no wasted text, making it highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (2 parameters, no output schema, no annotations), the description is incomplete. It lacks details on parameter meanings, output format, edge cases (e.g., handling of zero or negative numbers), and behavioral context. While concise, it does not provide enough information for an agent to use the tool effectively without additional inference.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'n' (integer) and 'base' (integer, default 10) undocumented. The description mentions 'digit' and 'number' but does not explain that 'n' is the input number or that 'base' allows counting digits in different numeral systems (e.g., binary or hexadecimal). It adds minimal semantic value beyond the schema, failing to compensate for the low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Count frequency of each digit in a number.' It specifies the verb ('count'), resource ('frequency of each digit'), and target ('a number'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'digit_count' or 'digit_sum', which could have overlapping domains, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with the domain and category tags ('Domain: arithmetic, Category: digital_operations'), which imply a mathematical context. However, it lacks explicit instructions on when to use this tool versus alternatives (e.g., 'digit_count' for total digits or 'digit_sum' for sum of digits), and does not mention prerequisites or exclusions, offering only implied usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the method is 'naive' which implies inefficiency for large inputs, but doesn't specify computational complexity, time/space requirements, or what happens when no solution exists (e.g., returns null, error). For a computational tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence plus domain/category tags. Every word serves a purpose: it states the problem, method, and context without redundancy. It's front-loaded with the core functionality, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (solving discrete logarithms), lack of annotations, 0% schema coverage, and no output schema, the description is inadequate. It doesn't explain the algorithm's behavior, error conditions, performance characteristics, or output format. For a mathematical solver with four parameters, this leaves too much undefined for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description only implicitly defines g, h, n via the equation g^x ≡ h (mod n), but doesn't explain the optional max_exp parameter at all. It adds minimal semantic value beyond what's inferable from the equation, failing to compensate for the schema's lack of descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve discrete logarithm g^x ≡ h (mod n) using naive method.' It specifies the mathematical operation (solve discrete logarithm), the method (naive), and the domain/category context. However, it doesn't distinguish this tool from potential sibling discrete logarithm methods (like baby_step_giant_step which appears in the sibling list), so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the mathematical domain (arithmetic) and category (modular_arithmetic), but offers no explicit guidance on when to use this naive method versus alternatives (like baby_step_giant_step for the same problem), nor any prerequisites or limitations. The agent must infer usage from the method name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool calculates but doesn't disclose behavioral traits: no information about input constraints (e.g., valid ranges for n and k), performance characteristics, error handling, or output format. The description is purely functional without operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise - a single sentence with mathematical notation and domain tags. Every element earns its place: the mathematical definition is essential, and the domain/category provides helpful classification. No wasted words or redundant information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical function tool with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain parameter meanings, constraints, return values, or how this differs from related divisor functions. The mathematical notation alone is insufficient for an AI agent to use the tool correctly without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'n' and 'k' in the mathematical notation σ_k(n) but doesn't explain what these parameters represent (n=integer whose divisors are considered, k=exponent applied to each divisor). It provides minimal semantic context beyond the mathematical formula.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate σ_k(n) - sum of kth powers of divisors.' It specifies the mathematical function and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'divisor_sum' or 'divisor_count' that handle related divisor functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags ('arithmetic', 'arithmetic_functions') give broad context, there's no explicit comparison to sibling tools like 'divisor_sum' (which appears to be the k=1 case) or 'divisor_count' (k=0 case), nor any prerequisites or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates functions but does not describe how it behaves: e.g., whether it returns numeric values or symbolic expressions, handles angle units (radians/degrees), manages invalid inputs, or has performance considerations. For a calculation tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence stating the tool's purpose, followed by domain/category in parentheses. Every word earns its place, with no redundant or verbose language. It efficiently communicates the core functionality without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (trigonometric calculations with parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what the tool returns, how errors are handled, or provide enough context for reliable use. For a mathematical tool with inputs and implied outputs, more detail is needed to be fully actionable.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'angle' (number) and 'function' (enum: sin, cos, tan). The description does not add any semantic information about these parameters, such as what 'angle' represents (e.g., radians, degrees), the meaning of the 'function' enum, or default behavior. With low schema coverage, the description fails to compensate, leaving parameters poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate trigonometric functions using double angle formulas.' It specifies the verb ('calculate'), resource ('trigonometric functions'), and method ('using double angle formulas'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'half_angle_formulas' or 'sum_difference_formulas', which are related trigonometric identity tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('identities'), but does not specify scenarios, prerequisites, or compare it to sibling tools (e.g., 'half_angle_formulas' or basic trigonometric functions like 'sin', 'cos'). This lack of explicit usage context leaves the agent without clear decision-making criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates expansion lengths but doesn't explain what 'length' means (e.g., number of terms), whether it's a deterministic algorithm, if there are computational limits, or what the output format is. For a tool with zero annotation coverage, this is a significant gap in behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no wasted language, and the information is front-loaded. This efficiency makes it easy to parse, though it may lack necessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (involving Egyptian fraction expansions), lack of annotations, no output schema, and low parameter coverage, the description is insufficient. It doesn't explain the algorithm, output format, or behavioral traits, making it incomplete for effective use by an AI agent. More context is needed to understand how to interpret results or handle edge cases.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'max_n' with 0% description coverage, and the tool description provides no information about parameters. It doesn't explain what 'max_n' represents (e.g., maximum denominator to compute up to), its valid range, or how it affects the calculation. With low schema coverage, the description fails to compensate, leaving the parameter undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the length of Egyptian fraction expansion for fractions 1/n.' It specifies the verb ('calculate'), resource ('length of Egyptian fraction expansion'), and domain ('fractions 1/n'), making it easy to understand what the tool does. However, it doesn't explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('egyptian_fractions'), it doesn't specify use cases, prerequisites, or comparisons with sibling tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction'. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the operation type but does not disclose behavioral traits such as input validation (e.g., vector length matching), error handling, performance characteristics, or output format. The description is minimal and lacks necessary operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with no wasted words, front-loading the core operation. It efficiently communicates the purpose in a single sentence, though this brevity contributes to gaps in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical operation with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It lacks details on input validation, output format, error conditions, and usage context, making it incomplete for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description does not add any parameter semantics beyond naming 'vector_a' and 'vector_b'. It does not explain what these vectors represent, their expected format (e.g., numeric strings), length requirements, or constraints, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Multiply') and resource ('two vectors element-wise'), and specifies the mathematical operation as 'Hadamard product'. However, it does not explicitly differentiate from sibling tools like 'multiply' (which might be scalar multiplication) or 'dot_product', though the domain/category context helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'multiply', 'dot_product', or 'element_wise_divide'. The domain/category tags offer some context but no explicit usage instructions, prerequisites, or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. It only states what the tool calculates, without mentioning input constraints (e.g., rate > 0), output format, error handling, computational characteristics, or side effects. For a mathematical tool with parameters, this is a significant gap in behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It's front-loaded with the core purpose and includes supplementary domain/category information efficiently. Every element earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain the exponential distribution's context, parameter meanings, return value format, or usage examples. For a tool that performs a specific probability calculation, more contextual information is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters 'x' and 'rate' are completely undocumented in the schema. The description adds no parameter semantics—it doesn't explain what 'x' represents (e.g., value at which to evaluate CDF) or 'rate' (e.g., rate parameter λ of the distribution). With low coverage, the description fails to compensate, leaving parameters ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the cumulative distribution function (CDF) of the exponential distribution.' It specifies the verb ('calculate') and resource ('CDF of exponential distribution'), and includes domain/category context. However, it doesn't differentiate from sibling tools like 'exponential_pdf' or 'exponential_sample', which would require a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('probability') and category ('general'), but doesn't specify use cases, prerequisites, or when to choose this over related tools like 'normal_cdf' or 'binomial_cdf' from the sibling list. This leaves the agent with insufficient context for appropriate tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden but offers minimal behavioral insight. It mentions 'multiple representations' which suggests the tool might return different formats, but doesn't clarify what these are, whether computations are exact or approximate, error handling, or performance characteristics. For a mathematical tool with potential complexity, this is inadequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It front-loads the core functionality ('Extended GCD with Bézout coefficients') and adds supplementary context ('multiple representations') efficiently. The domain/category annotation is separate and doesn't clutter the main description.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is insufficient for a tool with 3 parameters and mathematical complexity. It doesn't explain return values, error conditions, or the 'multiple representations' feature. The agent lacks critical context to use this tool effectively beyond guessing from the name.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate but adds no parameter information. It doesn't explain what 'a' and 'b' represent (e.g., integers for GCD computation), the purpose of 'find_alternatives', or any constraints (e.g., non-negative, non-zero). This leaves parameters undocumented beyond their basic types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs 'Extended GCD with Bézout coefficients and multiple representations,' specifying the mathematical operation (extended GCD), outputs (Bézout coefficients), and feature (multiple representations). It distinguishes from the simpler 'extended_gcd' sibling tool by mentioning additional representations, though it doesn't explicitly contrast with other GCD-related tools like 'gcd' or 'bezout_identity'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description mentions 'multiple representations' which hints at broader functionality than basic extended GCD, but doesn't specify use cases, prerequisites, or compare it to siblings like 'extended_gcd' or 'bezout_identity'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but does not describe output format, error handling, performance characteristics, or limitations (e.g., valid ranges for 'n'). For a tool with no annotations, this is a significant gap, as the agent lacks critical operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted verbiage, and the additional domain/category note is brief and relevant. This efficiency makes it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of generating a Farey sequence, the description is incomplete. There are no annotations, no output schema, and low parameter coverage. The description does not explain what a Farey sequence is, the format of the output, or any mathematical properties. For a tool with no structured support, this leaves too many gaps for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer but no semantic explanation. The description mentions 'order n' but does not clarify what 'order' means, valid ranges, or constraints. Since schema coverage is low, the description fails to compensate adequately, leaving the parameter poorly defined.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the Farey sequence F_n of order n.' It specifies the verb ('Generate'), resource ('Farey sequence'), and parameter ('order n'), making the function unambiguous. However, it does not differentiate from sibling tools like 'farey_neighbors' or 'farey_sequence_length', which are related but distinct, preventing a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), which implies context, but does not specify use cases, prerequisites, or comparisons to sibling tools such as 'farey_neighbors' or 'farey_sequence_properties'. This lack of explicit direction limits its utility for an agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'applications to modular arithmetic', which adds some context, but fails to describe critical behaviors such as input constraints (e.g., denominators must be positive, fractions must be in lowest terms), error handling, or output format. For a mathematical tool with 4 parameters, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that efficiently conveys the core purpose and domain. It is front-loaded with the main action and avoids unnecessary details. Every word earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (4 parameters with 0% schema coverage, no annotations, no output schema), the description is incomplete. It does not compensate for the lack of structured data by explaining parameter meanings, behavioral traits, or output expectations. For a tool performing a specialized mathematical operation, this leaves too many gaps for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description does not explain what p1, q1, p2, q2 represent (e.g., numerators and denominators of two fractions), their constraints (e.g., integers, non-zero denominators), or their relationship. This leaves parameters undocumented, making it difficult for an agent to use the tool correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Farey sum of two fractions with applications to modular arithmetic.' It specifies the verb ('Calculate'), resource ('Farey sum of two fractions'), and provides domain context. However, it does not explicitly differentiate from sibling tools like 'farey_mediant_path' or 'farey_neighbors' which might involve similar concepts, so it's not a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'applications to modular arithmetic' but does not specify scenarios, prerequisites, or compare it to related tools like 'farey_sequence' or 'mediant'. This lack of explicit usage context limits its helpfulness for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It states the tool calculates distance, implying a read-only, non-destructive operation, but does not elaborate on output format (e.g., units), error handling, or computational characteristics (e.g., precision, limitations). For a tool with no annotations, this is insufficient to guide the agent effectively.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category tags are efficiently appended. This is a model of brevity and clarity in structure.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (4 required parameters, no output schema, no annotations), the description is incomplete. It lacks details on parameter semantics, behavioral traits, and output expectations. While conciseness is high, the description does not provide enough context for the agent to use the tool confidently without additional inference or trial.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'GPS coordinates' and 'two points', which hints at the parameters (lat1, lon1, lat2, lon2), but does not explain their semantics (e.g., units, valid ranges, coordinate systems). This leaves critical parameter details undocumented, failing to adequately supplement the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate great circle distance between two points on Earth (GPS coordinates)'. It specifies the verb ('calculate'), resource ('great circle distance'), and domain context ('GPS coordinates'). However, it does not explicitly differentiate from sibling tools like 'distance_haversine' or 'geom_distance', which may serve similar purposes, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('geometry') and category ('general'), but does not specify when to use this tool versus alternatives (e.g., 'distance_haversine' or 'geom_distance'), nor does it outline prerequisites or exclusions. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states the calculation method (Shoelace formula) but lacks critical details: it doesn't specify input format (e.g., coordinate pairs as strings), error handling (e.g., for invalid polygons), performance characteristics, or output format. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and method. There is no wasted language or redundancy, making it efficient for quick comprehension. The structure is clear, with the core action ('Calculate the area') presented immediately.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical calculation with a single but semantically rich parameter), no annotations, and no output schema, the description is incomplete. It lacks details on input format, output structure, error conditions, and usage context relative to siblings like 'geom_triangle_area'. This makes it inadequate for reliable agent invocation without additional assumptions or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'vertices' implicitly but provides no details on their format (e.g., 'x,y' strings), ordering (clockwise/counterclockwise), or constraints (minimum vertices, non-self-intersecting). This fails to add meaningful semantics beyond the bare schema, leaving the single parameter poorly explained.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the area of a polygon' with a specific method ('using the Shoelace formula'). It distinguishes itself from sibling tools like 'geom_triangle_area' by handling general polygons. However, it doesn't explicitly contrast with 'geom_triangle_area' or other geometry tools, keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance: it mentions the domain (geometry) and category (general), but offers no explicit when-to-use instructions, prerequisites, or alternatives. For example, it doesn't clarify when to use this versus 'geom_triangle_area' for triangles or other polygon-related tools, leaving the agent with little contextual direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a calculation but doesn't describe what 'gnomon numbers' are mathematically, the output format, error handling, or computational constraints. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with domain/category tags—and front-loaded with the core purpose. There's no wasted verbiage, and the structure efficiently communicates the essential information in minimal space.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical calculation tool with 2 undocumented parameters, no annotations, and no output schema, the description is insufficient. It doesn't explain what gnomon numbers are, how they relate to s-gonal numbers, the parameter roles, or the return format, leaving too much ambiguity for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (n, s) with 0% description coverage, and the tool description provides no information about what these parameters represent. Without any parameter semantics in the description, users must infer that 'n' and 's' relate to s-gonal numbers, but the exact meaning (e.g., s = number of sides, n = index) is undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate gnomon numbers for s-gonal numbers.' It specifies both the action ('calculate') and the mathematical object ('gnomon numbers for s-gonal numbers'), and provides domain/category context. However, it doesn't explicitly differentiate from sibling tools (e.g., 'polygonal_number' or 'polygonal_sequence'), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category hints at mathematical contexts, there's no explicit mention of use cases, prerequisites, or comparisons to sibling tools like 'polygonal_number' or 'centered_polygonal_number' that might handle related calculations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the tool 'checks' a number, implying a read-only operation, but doesn't disclose behavioral traits like error handling (e.g., for non-integer inputs), performance characteristics, or what the output looks like (e.g., boolean or detailed result). This leaves significant gaps for an agent to understand how to invoke it correctly.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—two sentences with zero waste. The first sentence states the purpose, and the second adds domain context. It's front-loaded and efficiently structured, making it easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a mathematical check with one parameter), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain the return value, error conditions, or parameter semantics, which are essential for correct usage. The domain/category hint is insufficient to fill these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The tool description adds no information about what 'n' represents (e.g., an integer to test) or its constraints (e.g., non-negative, range limits). This fails to compensate for the lack of schema documentation, leaving the parameter's meaning ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a Catalan number.' It specifies the verb ('Check') and resource ('a number'), and the domain/category context helps clarify it's about combinatorial numbers. However, it doesn't explicitly differentiate from sibling tools like 'catalan' or 'catalan_number', which might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With many sibling tools (e.g., 'catalan', 'catalan_number', 'catalan_sequence'), there's no indication of how this tool differs or when it's preferred. The domain/category hint is minimal and doesn't address usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks for optimality but does not explain what 'optimal' entails beyond 'shortest possible,' nor does it describe the return value (e.g., boolean or detailed analysis), error conditions, or computational constraints. This is inadequate for a tool with three parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the additional domain/category information is efficiently appended. Every word earns its place, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (checking optimality of Egyptian fractions), the lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not compensate for these gaps by explaining parameters, return values, or behavioral details. The agent would struggle to use this tool correctly without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool description does not explain the parameters at all. It mentions 'Egyptian fraction representation' but does not clarify what 'numerator', 'denominator', and 'representation' mean or how they relate. With low schema coverage and no parameter details in the description, the agent lacks essential semantic context.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if Egyptian fraction representation is optimal (shortest possible).' It specifies the verb ('Check'), resource ('Egyptian fraction representation'), and criterion ('optimal (shortest possible)'). However, it does not explicitly differentiate from sibling tools like 'shortest_egyptian_fraction' or 'egyptian_fraction_properties', which is why it doesn't achieve a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('egyptian_fractions'), but offers no explicit when-to-use, when-not-to-use, or alternative tool recommendations. This leaves the agent without context for selecting this tool among related siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('Check if a number is an s-gonal number') without describing how it performs the check, what it returns (e.g., boolean, details), error handling, or performance considerations. This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with a parenthetical domain/category. It is front-loaded with the core purpose and wastes no words. Every part of the description earns its place by adding context without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical check with two parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not explain the mathematical definition of an s-gonal number, parameter roles, return type, or edge cases. The domain/category hint is insufficient to make the tool fully understandable.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'num' and 's' undocumented. The description does not explain what these parameters mean (e.g., 'num' is the integer to test, 's' is the number of sides/polygon type) or their constraints (e.g., s >= 3). It fails to compensate for the lack of schema documentation, leaving parameters semantically unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is an s-gonal number.' It specifies the verb ('Check') and resource ('s-gonal number'), and includes a domain/category for context. However, it does not explicitly differentiate from sibling tools like 'is_triangular_number' or 'is_pentagonal_number', which are specific cases of polygonal numbers.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'is_triangular_number' (for s=3) or 'is_pentagonal_number' (for s=5), nor does it explain when to prefer this general tool over specific ones. The domain/category hint is minimal and does not constitute actionable usage advice.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks for vampire numbers and finds fangs, but doesn't describe what happens for non-vampire numbers (e.g., returns false/empty), performance characteristics, or error handling. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the core functionality in one clear sentence, followed by domain/category in parentheses. Every word earns its place with no redundancy or fluff, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (checking a mathematical property), lack of annotations, no output schema, and 0% parameter coverage, the description is insufficient. It doesn't explain the return format (e.g., boolean plus fang pairs), edge cases, or mathematical definition of vampire numbers, leaving the agent with incomplete context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the tool description does not explain the parameter 'n' at all. It doesn't specify what 'n' represents (e.g., an integer to test), valid ranges, or constraints. With low schema coverage, the description fails to compensate, leaving the parameter's meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a vampire number and find its fangs.' It specifies the verb ('check'), resource ('number'), and outcome ('find its fangs'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'vampire_numbers' (which likely lists vampire numbers), so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but this is generic context that doesn't help an agent choose between this and similar tools (e.g., 'is_vampire_number' vs. 'vampire_numbers'). No explicit when-to-use or when-not-to-use instructions are present.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full behavioral disclosure burden. It states the computation and the odd-n constraint, but doesn't describe error handling (e.g., what happens if n is even), input validation, performance characteristics, or output format. For a mathematical function with no annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—one sentence plus domain/category tags—with zero wasted words. It front-loads the core purpose and constraint efficiently. Every element (computation, symbol notation, constraint, tags) earns its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain the Jacobi symbol's definition, return values (-1, 0, 1), or edge cases. The domain/category tags help but don't substitute for functional completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It names the parameters implicitly via '(a/n)' and adds the constraint 'for odd n', giving some semantic meaning to n. However, it doesn't explain what a and n represent mathematically (integer arguments to the Jacobi symbol), their valid ranges beyond the odd requirement, or the relationship between them.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute Jacobi symbol (a/n) for odd n.' It specifies the mathematical operation (compute), the resource (Jacobi symbol), and includes a domain constraint (odd n). However, it doesn't explicitly differentiate from sibling tools like 'legendre_symbol' or 'is_quadratic_residue', which are related modular arithmetic functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance through the constraint 'for odd n', but offers no explicit when-to-use advice, no comparison with alternatives (like legendre_symbol for prime modulus), and no prerequisites. The domain/category tags ('arithmetic, modular_arithmetic') give some context but aren't actionable guidelines.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool computes but doesn't disclose behavioral traits like error handling for non-prime p, performance characteristics, return format, or mathematical conventions (e.g., standard Legendre symbol values of -1, 0, 1). The domain/category tags add minimal context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
Extremely concise with zero wasted words. The single sentence directly states the computation, and the domain/category tags are efficiently appended. Every element earns its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical tool with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It lacks details on return values, error conditions, mathematical assumptions, and how it relates to sibling tools like jacobi_symbol or is_quadratic_residue, making it inadequate for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It names the parameters (a and p) and specifies p must be prime, which adds meaning beyond the schema's integer types. However, it doesn't explain what a represents (integer modulo p) or constraints like p > 0, leaving significant gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes the Legendre symbol (a/p) for prime p, specifying both the mathematical operation and domain/category. It distinguishes itself from siblings like jacobi_symbol by explicitly mentioning 'prime p', but doesn't contrast with other modular arithmetic tools like is_quadratic_residue or tonelli_shanks.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives. The description mentions the domain and category but doesn't provide context about when Legendre symbols are needed versus other modular arithmetic operations, nor does it mention prerequisites like p being prime (though implied).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe output format, error handling, performance characteristics, or any side effects. For a computational tool with zero annotation coverage, this leaves significant gaps in understanding how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose. It is front-loaded with the core functionality and includes domain/category tags efficiently. There is no wasted verbiage, making it highly readable and to-the-point.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not address parameter details, return values, error conditions, or usage distinctions from similar tools. For a tool with one parameter and no structured support, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not mention the 'vector' parameter at all. It fails to explain what the vector input should contain (e.g., numeric values as strings), its expected format, or any constraints. With one undocumented parameter, the description adds no semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Manhattan norm (L1 norm) of a vector'. It specifies the verb ('calculate'), resource ('Manhattan norm'), and domain context ('linear_algebra.vectors'), but does not explicitly differentiate from sibling tools like 'euclidean_norm' or 'chebyshev_norm' beyond naming them differently.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('linear_algebra.vectors') and category ('general'), but offers no explicit advice on when to use this tool versus alternatives like 'euclidean_norm' or 'p_norm', nor does it specify prerequisites or exclusions. The context is implied but not elaborated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe any behavioral traits such as error handling (e.g., invalid matrix inputs), computational limits, or output format. For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, stating the core purpose in a single sentence. The additional domain and category information is minimal and does not detract from clarity. There is no wasted verbiage, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical calculation tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks essential details such as parameter explanations, error conditions, and return value information, which are necessary for effective tool use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning the input schema provides no descriptions for the 'matrix' parameter. The description does not compensate by explaining the parameter's semantics, such as the expected format (e.g., a 2x2 array of numbers as strings), constraints, or examples. This leaves the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the determinant of a 2x2 matrix.' It specifies the verb ('calculate'), resource ('determinant'), and scope ('2x2 matrix'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'matrix_det_3x3' or 'matrix_solve_2x2', which would require a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.matrices') and category ('general'), but this is not actionable usage advice. There is no mention of prerequisites, limitations, or comparisons to sibling tools like 'matrix_det_3x3' or 'matrix_solve_2x2'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the method ('Cramer's rule') but does not describe key behavioral traits such as numerical stability limitations, error handling for singular matrices, input format expectations (e.g., string arrays for numbers), or output structure. This leaves significant gaps for a tool that performs mathematical computations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and method. Every word earns its place, with no redundant or verbose language, making it efficient for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of solving linear equations, lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not cover critical aspects like input validation, error cases (e.g., non-invertible matrices), output format, or performance considerations, leaving the agent under-informed for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It does not explain the parameters 'matrix_a' and 'vector_b' beyond implying they represent the matrix A and vector b in Ax=b. No details on array dimensions (e.g., 3x3 for matrix_a, length 3 for vector_b), data types (strings likely for numerical values), or formatting are provided, failing to adequately clarify parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve a 3x3 system of linear equations Ax = b using Cramer's rule'. It specifies the verb ('solve'), resource ('3x3 system of linear equations'), and method ('Cramer's rule'). However, it does not explicitly differentiate from sibling tools like 'matrix_solve_2x2' or 'gaussian_elimination', which are also linear algebra solvers, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('linear_algebra.matrices') and category ('general'), but does not specify when to use this tool versus alternatives (e.g., for 3x3 systems only, or when Cramer's rule is appropriate). No explicit when/when-not instructions or sibling tool comparisons are included, leaving the agent with little contextual direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While 'transpose' implies a mathematical transformation, the description doesn't clarify whether this operation is read-only or mutative, what happens with invalid input (e.g., non-rectangular arrays), or any performance considerations. It lacks essential context for safe and effective use.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—just one sentence plus domain/category annotations. It front-loads the core functionality ('Transpose a matrix') and avoids any redundant or verbose language. Every word earns its place, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a matrix operation with 1 parameter), lack of annotations, 0% schema coverage, and no output schema, the description is insufficient. It doesn't explain input format, output structure, error handling, or mathematical assumptions (e.g., real numbers only). For a tool with no structured support, more descriptive detail is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no parameter information beyond the tool name. The input schema defines a 'matrix' parameter as an array of strings, but the description doesn't explain the expected format (e.g., how rows/columns are represented), constraints, or examples. This leaves critical gaps in understanding how to structure input.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Transpose a matrix (swap rows and columns)'. It uses a specific verb ('transpose') and resource ('matrix'), making the function unambiguous. However, it doesn't differentiate from sibling tools beyond the domain/category annotation, which is why it doesn't reach a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It includes domain/category annotations ('linear_algebra.matrices, Category: general'), but these are structural metadata rather than usage instructions. There's no mention of prerequisites, limitations, or sibling tools for comparison.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds the maximum value but does not mention how it handles edge cases (e.g., empty lists, non-numeric strings in the array), performance characteristics, or error behavior. This leaves significant gaps in understanding the tool's behavior beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Find the maximum value in a list of numbers.' The additional domain and category information is brief and does not detract from clarity. Every sentence earns its place, with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (1 parameter, no output schema, no annotations), the description is minimal. It states the basic purpose but lacks details on parameter handling, edge cases, or output format. For a tool with undocumented parameters and no annotations, this is insufficient to ensure reliable use by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('numbers') with 0% description coverage, and the description does not add any parameter-specific information. It does not explain what format the numbers should be in (e.g., as strings in the array), whether they must be numeric, or any constraints. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the maximum value in a list of numbers.' It specifies the verb ('Find') and resource ('maximum value in a list of numbers'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'maximum' or 'max_float', which might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: comparison,' but this is generic and does not help distinguish it from sibling tools like 'maximum' or 'max_float'. There are no explicit instructions on prerequisites, limitations, or when to choose this tool over others.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe output format, error handling, or constraints (e.g., integer inputs, non-zero denominators). For a tool with 4 parameters and no annotations, this leaves significant behavioral gaps, such as whether it returns a simplified fraction or raw numerator/denominator.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted verbiage, and every part (calculation, fractions, domain) earns its place efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (4 parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameter meanings, output format, and behavioral traits. While conciseness is high, the description does not provide enough context for an agent to confidently invoke the tool without guessing at semantics.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters p1, q1, p2, q2 undocumented. The description does not explain these parameters at all—it does not clarify that they represent numerators and denominators of two fractions. With low schema coverage, the description fails to compensate, leaving parameter meanings ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the mediant of two fractions.' It specifies the verb ('calculate') and resource ('mediant of two fractions'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'farey_mediant_path' or 'farey_neighbors', which might also involve mediants in Farey sequences, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), which hints at context, but does not specify scenarios, prerequisites, or comparisons to sibling tools like 'farey_mediant_path' or 'best_approximation_farey'. Without explicit usage instructions, the agent must infer applicability.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it states what the tool computes, it doesn't describe important behavioral aspects: computational complexity, input constraints (e.g., valid ranges for n and k), error handling, or output format. For a mathematical computation tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the core purpose is stated in the first sentence, with domain context efficiently added in parentheses. There is zero wasted verbiage, and every word earns its place. This is a model of conciseness for a mathematical tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of the Waring's problem computation, the lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the output represents (e.g., an integer count, or possibly a representation), error conditions, or performance characteristics. For a non-trivial number theory tool, more context is needed for effective agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning neither parameter (n, k) has descriptions in the schema. The tool description mentions 'n' and 'k' but provides no semantic clarification beyond what's implied by the problem statement. It doesn't explain what n represents (the target number) or k (the exponent), nor any constraints (e.g., n must be positive, k typically ≥ 2). With low schema coverage, the description fails to compensate adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find minimum number of k-th powers needed to represent n.' It specifies both the verb ('Find minimum number') and the resource ('k-th powers needed to represent n'), and provides domain context ('Domain: arithmetic, Category: additive_number_theory'). However, it doesn't explicitly differentiate from sibling tools like 'waring_representation' or 'sum_of_four_squares', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There are no explicit when/when-not statements, no mention of prerequisites, and no named alternatives. The domain/category tags offer some context but don't constitute actionable usage guidelines for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does ('Calculate') but doesn't disclose behavioral traits like input constraints (e.g., n must be positive integer), computational characteristics, error handling, or output format. For a mathematical function tool with zero annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with zero wasted words. The first sentence directly states the purpose, and the parenthetical adds domain context efficiently. Every element earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. For a mathematical function tool, it should at minimum specify the parameter meaning and typical return values (e.g., returns -1, 0, or 1). The current description leaves too much undefined for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'μ(n)' which implies a single integer parameter n, but doesn't explain what n represents (e.g., positive integer), valid ranges, or special cases (e.g., n=1 returns 1, n with squared prime factor returns 0). The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Möbius function μ(n)' with specific verb ('Calculate') and resource ('Möbius function μ(n)'). It distinguishes from siblings by specifying the mathematical function, though it doesn't explicitly contrast with similar arithmetic tools like 'mobius_function_range' or 'liouville_function'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It includes domain/category tags ('Domain: arithmetic, Category: arithmetic_functions'), but these are generic and don't help differentiate from many sibling tools in the same categories. No explicit when/when-not instructions or named alternatives are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the sequence involves 'cows that reproduce,' hinting at a recursive or generative process, but fails to detail computational behavior (e.g., recursion depth, performance, or output format). This is inadequate for a tool with no structured annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted verbiage, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a tool with no annotations, 0% schema coverage, and no output schema, the description is insufficient. It lacks details on parameter meaning, behavioral traits, return values, and usage context, making it incomplete for effective agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one required parameter 'n' of type integer. The description does not explain what 'n' represents (e.g., term index, count of cows) or its constraints (e.g., range, typical values). Given the low schema coverage, the description fails to compensate, leaving the parameter's meaning ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Narayana's cow sequence (cows that reproduce).' It specifies the verb ('calculate'), resource ('Narayana's cow sequence'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools like 'narayana_number' or 'narayana_triangle_row', which are related but distinct, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context about typical use cases, prerequisites, or comparisons to sibling tools (e.g., 'narayana_number' or 'narayana_triangle_row'), leaving the agent without direction for selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the domain ('arithmetic') and category ('digital_operations'), but does not disclose behavioral traits such as performance characteristics (e.g., computational complexity for large n), error handling (e.g., invalid inputs), or output format (e.g., integer or string). The base parameter is hinted at but not explained behaviorally.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core functionality, and the parenthetical adds domain context without redundancy. Every word earns its place, with no wasted sentences or vague phrasing.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (arithmetic operation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not cover parameter details, behavioral aspects, or output expectations, leaving significant gaps for an AI agent to understand and invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'n' and implies 'base' via the domain note, but does not explain parameter semantics: what 'n' represents (e.g., integer input), what 'base' does (e.g., numeral system for palindrome checking), valid ranges, or default behavior. The description adds minimal value beyond the schema's property names.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the next palindromic number greater than n.' It specifies the verb ('Find'), resource ('palindromic number'), and condition ('greater than n'). However, it does not explicitly differentiate from sibling tools like 'is_palindromic_number' or 'palindromic_numbers', which check or list palindromes, rather than finding the next one.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it implies usage when you need the next palindrome after a given number. It does not specify when to use this tool versus alternatives (e.g., 'is_palindromic_number' for verification, 'palindromic_numbers' for listing), nor does it mention any prerequisites, exclusions, or edge cases (e.g., handling negative numbers or different bases).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks critical details: it doesn't specify the standard range (e.g., [0, 2π) for positive radians or [-π, π) for symmetric), whether it handles edge cases like large angles, or what the output format is. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with a parenthetical note—and front-loaded with the core purpose. Every word earns its place, with no redundant or verbose phrasing. It efficiently communicates the essential idea without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (3 parameters, no annotations, no output schema), the description is incomplete. It doesn't explain the normalization behavior, output format, or parameter interactions. While conciseness is high, it sacrifices necessary context for a tool that performs a non-trivial mathematical operation with multiple configuration options.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It adds no information about the three parameters (angle, unit, range_type) beyond what the schema provides (types, enums, defaults). The description doesn't explain what 'normalize' means in terms of these parameters or their interactions, leaving semantics unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Normalize an angle to a standard range.' It specifies the domain (trigonometry) and category (angle_conversion), making the intent unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'convert_angle' or 'angle_difference', which could have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit when/when-not instructions or references to sibling tools. The agent must infer usage from the tool name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the operation but lacks behavioral details such as what algorithm is used (e.g., Gram-Schmidt), whether it modifies inputs or returns a new vector, error handling for linearly dependent vectors, or performance characteristics. This leaves significant gaps for a mutation-like operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It is front-loaded with the core purpose and includes domain/category context efficiently, making it easy to parse despite its brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a linear algebra operation with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is insufficient. It lacks details on behavior, parameters, return values, and error conditions, making it incomplete for reliable tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description provides no parameter details. It doesn't explain what 'vector' and 'basis_vectors' represent (e.g., numeric arrays, format expectations), their dimensions, or constraints. For a tool with 2 required parameters and no schema descriptions, this is inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('Orthogonalize') and the resource ('a vector with respect to a set of vectors'), with a specific domain and category. It distinguishes from siblings by focusing on orthogonalization, which is not directly covered by other tools like 'normalize_vector' or 'vectors_orthogonal'. However, it doesn't explicitly differentiate from potential similar linear algebra operations beyond the domain hint.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The domain and category hints imply usage in linear algebra contexts, but there's no mention of prerequisites, when not to use it, or how it compares to sibling tools like 'gram_schmidt' or 'vector_projection' that might handle related operations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a p-norm for p >= 1, implying a mathematical computation, but does not disclose behavioral traits such as error handling (e.g., for invalid inputs like non-numeric vectors or p < 1), performance characteristics, or output format. This leaves significant gaps for a tool with two required parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and domain. There is zero wasted text, and every word earns its place by conveying essential information efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with two required parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to explain parameter details, behavioral expectations, or output format, leaving the agent with inadequate information to use the tool correctly beyond a basic understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'vector' and 'p >= 1', adding basic semantics: p is a number >= 1, and vector is implied to be an array. However, it does not explain the vector's expected format (e.g., numeric values, handling of strings in the array) or constraints (e.g., p as integer vs. real). With two undocumented parameters, this is insufficient compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the p-norm of a vector for any p >= 1'. It specifies the verb ('calculate'), resource ('p-norm of a vector'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'euclidean_norm' or 'manhattan_norm', which are specific cases of p-norms, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain 'linear_algebra.vectors' and category 'general', but offers no explicit when/when-not instructions or references to sibling tools like 'euclidean_norm' (p=2) or 'manhattan_norm' (p=1), leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the action ('Find') but does not describe what the tool returns (e.g., a list of gaps, their sizes, or associated primes), any computational limits, or error conditions. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single, direct sentence that states the tool's purpose. There is no wasted language, and the parenthetical domain/category note adds context without verbosity. It efficiently communicates the core function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (involving prime gaps), lack of annotations, no output schema, and undocumented parameters, the description is insufficient. It does not explain the return format, computational behavior, or parameter meaning, leaving the agent with inadequate information to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('limit') with 0% description coverage, meaning its purpose is undocumented. The description does not explain what 'limit' represents (e.g., upper bound for prime search, maximum gap size to consider, or number of gaps to return). This lack of semantic information hampers effective tool invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find record prime gaps (first occurrence of each gap size).' It specifies the verb ('Find'), resource ('record prime gaps'), and scope ('first occurrence of each gap size'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'prime_gap' or 'prime_gaps_analysis', which is why it doesn't achieve a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, context, or comparisons with sibling tools such as 'prime_gap' or 'prime_gaps_analysis'. This absence of usage instructions leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates numbers but lacks details on behavior: no information on output format (e.g., list, array), error handling (e.g., for negative n), performance, or limits. The description is minimal and doesn't compensate for the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: a single sentence directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and every part serves to clarify the tool's function efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a sequence generator with one parameter), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain what pronic numbers are, the output format, or any behavioral aspects, making it inadequate for full understanding despite its conciseness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description doesn't add any parameter semantics. It mentions 'n' implicitly ('first n pronic numbers') but doesn't explain what 'n' represents (e.g., count, integer > 0), its range, or constraints. With low schema coverage, the description fails to compensate, leaving parameters poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n pronic numbers.' It specifies the verb ('Generate') and resource ('pronic numbers') with a parameter constraint ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'is_pronic_number' or 'pronic_sequence' (if present), which slightly limits its distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), but offers no explicit instructions on context, prerequisites, or comparisons with sibling tools like 'is_pronic_number' or other sequence generators.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'Find[s] all quadratic residues modulo n,' which implies a read-only operation that returns a list, but it does not specify output format (e.g., list of integers), handling of edge cases (e.g., negative n, n=0, or n=1), performance characteristics, or error conditions. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the core purpose in the first phrase, followed by domain and category metadata. There is no wasted verbiage or redundancy, making it efficient for quick understanding. Every sentence (or phrase) earns its place by providing essential information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical function with one parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not cover parameter semantics, output format, error handling, or usage context relative to siblings. While concise, it lacks the depth needed for an agent to use the tool effectively without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, and the description does not add any semantic details about it. It does not explain what 'n' represents (e.g., a positive integer modulus), valid ranges, or constraints (e.g., n > 1 for meaningful residues). With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all quadratic residues modulo n.' It specifies the verb ('Find'), resource ('quadratic residues'), and domain context ('modulo n'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'is_quadratic_residue' or 'jacobi_symbol', which are related modular arithmetic tools, so it misses the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('modular_arithmetic'), but this is too general and does not help an agent choose between this and similar tools like 'is_quadratic_residue' (which checks a single residue) or 'jacobi_symbol' (which computes a related symbol). No explicit when-to-use or when-not-to-use instructions are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates random numbers but doesn't disclose behavioral traits such as the range of random numbers (e.g., integers, floats, distribution), whether the output is deterministic or seeded, or any performance considerations. The description is minimal and lacks essential context for a tool that produces random data.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose. There is no wasted language or redundancy, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (generating random arrays), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't address key aspects like the type of random numbers, distribution, or output format, leaving significant gaps for an AI agent to understand and use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, so the description must compensate. It mentions 'specified dimensions' but doesn't explain what 'rows' and 'cols' represent (e.g., array shape, constraints like positive integers). The description adds minimal meaning beyond the schema, failing to clarify parameter roles or usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate an array of random numbers with specified dimensions.' It includes a specific verb ('Generate'), resource ('array of random numbers'), and scope ('with specified dimensions'). However, it doesn't explicitly differentiate from sibling tools like 'random_float' or 'random_int', which generate single random values rather than arrays.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('general'), but offers no explicit when/when-not instructions or references to sibling tools like 'random_float' or 'random_int' for comparison. Usage is implied rather than stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the domain ('linear_algebra.vectors') and category ('general'), but fails to describe key behavioral traits such as input validation (e.g., handling of non-numeric strings in the vector array), error conditions, or the format of the output (since there is no output schema). This leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted language, and the domain/category information is efficiently appended. This makes it easy to parse and understand quickly, earning a high score for conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical operation with two parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It fails to provide necessary context such as parameter details, behavioral expectations, or output format. While the domain/category hint is helpful, it does not compensate for the lack of essential information needed for correct tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the input schema provides no descriptions for the 'vector' and 'scalar' parameters. The description adds minimal semantic value by naming the parameters ('vector' and 'scalar') but does not explain their expected formats, constraints, or usage. For example, it does not clarify that 'vector' is an array of strings (likely representing numbers) or how the scalar multiplication is applied. This insufficient compensation for the low schema coverage results in a low score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Multiply a vector by a scalar value.' It specifies the verb ('Multiply') and the resources ('vector' and 'scalar'), and the domain/category context ('linear_algebra.vectors, Category: general') provides additional clarity. However, it does not explicitly differentiate from sibling tools like 'element_wise_multiply' or 'matrix_scalar_multiply', which could cause confusion in selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context about when this operation is appropriate, such as for linear algebra computations, and does not mention sibling tools like 'element_wise_multiply' or 'matrix_scalar_multiply' that might be relevant for similar tasks. This absence of usage instructions leaves the agent without clear direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'brute force search', which implies potential computational intensity or limitations, but does not elaborate on performance characteristics, error handling, or output format. For a tool with three parameters and no output schema, this lack of detail is a significant gap, leaving the agent uncertain about what to expect.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the core purpose in the first clause and adds domain/category context efficiently. Every sentence earns its place without redundancy or fluff, making it easy for an agent to parse quickly. The structure is optimal for a tool description of this complexity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (three parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameter meanings, behavioral traits like performance or limitations, and output expectations. While conciseness is high, the description fails to compensate for the missing structured data, making it insufficient for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the three parameters (numerator, denominator, max_terms) are documented in the schema. The description does not add any information about these parameters, such as their roles, constraints, or how they interact. This leaves the agent with no guidance beyond the raw schema types, which is inadequate for effective tool use.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the shortest Egyptian fraction representation by brute force search.' It specifies the verb ('Find'), resource ('shortest Egyptian fraction representation'), and method ('brute force search'), making it easy to understand. However, it does not explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'fibonacci_greedy_egyptian', which might offer alternative methods or outputs, so it misses the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: arithmetic, Category: egyptian_fractions'), but this is too vague to help an agent choose between sibling tools like 'egyptian_fraction_decomposition' or 'is_optimal_egyptian_fraction'. There are no explicit instructions on when or when not to use it, or what prerequisites might be needed.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions 'probabilistic,' implying potential for false positives/negatives, but lacks details on accuracy, error rates, performance characteristics, or output format. For a tool with mathematical complexity and no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that efficiently states the tool's purpose and domain/category. Every word earns its place, with no redundant information, making it front-loaded and easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (probabilistic primality test), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the probabilistic nature, parameter roles, expected outputs, or error handling, leaving critical gaps for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It adds no information about parameters 'n' (the number to test) or 'k' (iterations/confidence parameter). Without this, users must infer parameter meanings from context, which is insufficient for a tool with two parameters, one optional with a default.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs a 'Solovay-Strassen probabilistic primality test using Jacobi symbols,' specifying both the algorithm (Solovay-Strassen) and mathematical components (Jacobi symbols). It distinguishes from simpler primality tests like 'is_prime' but doesn't explicitly differentiate from sibling probabilistic tests like 'miller_rabin_test' or 'deterministic_miller_rabin.'
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description mentions it's a 'probabilistic primality test' and categorizes it as 'advanced_primality,' which implies usage for advanced primality testing, but doesn't specify scenarios, prerequisites, or compare it to other primality tests like 'aks_primality_test' or 'miller_rabin_test.'
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions generating a 'path' but doesn't disclose what the output format looks like, whether the algorithm has computational limits, what happens with invalid inputs (like zero denominators), or any error conditions. For a computational tool with no annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence plus domain/category tags—with zero wasted words. It front-loads the core purpose immediately. Every element (action, resource, target, context) earns its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, and no output schema, the description is inadequate. It doesn't explain the output (what a 'path' entails), error handling, or mathematical assumptions. For a tool that performs a non-trivial algorithm on two integer inputs, more context is needed to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'target fraction' but doesn't explain that target_p and target_q represent numerator and denominator, nor does it specify constraints (e.g., positive integers, q ≠ 0). While it implies the parameters define a fraction, this is minimal compensation for the complete lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate path through Stern-Brocot tree to reach target fraction.' It specifies both the action ('generate path') and the resource ('Stern-Brocot tree'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'farey_mediant_path' or 'best_rational_approximation' that might involve similar fraction-related operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('farey_sequences'), it doesn't specify use cases, prerequisites, or contrast with sibling tools like 'calkin_wilf_tree' or 'farey_sequence' that also handle rational numbers. The agent must infer usage from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool's function but does not describe what the test returns (e.g., boolean result, details on pseudoprimality), performance characteristics, error handling, or limitations (e.g., input constraints, computational complexity). For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category annotation is efficiently appended. Every word earns its place, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (advanced primality test), lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not cover parameter meanings, return values, behavioral traits, or usage context. For such a specialized mathematical tool, more detail is needed to ensure the agent can invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'n' (the number) and 'bases' implicitly but does not explain their roles, valid ranges, or interactions (e.g., that 'bases' is an array of integers used for testing). Without this semantic detail, the agent cannot understand parameter purposes beyond the schema's basic types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Test if a number is a strong pseudoprime to given bases.' It specifies the verb ('Test'), resource ('number'), and context ('strong pseudoprime to given bases'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'miller_rabin_test' or 'solovay_strassen_test', which are also primality-related tests.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('advanced_primality'), which implies context but does not specify scenarios, prerequisites, or comparisons to sibling tools such as 'aks_primality_test' or 'deterministic_miller_rabin'. Without explicit when-to-use or when-not-to-use instructions, the agent lacks practical usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description states what the tool does but does not cover important behavioral aspects such as performance characteristics (e.g., computational complexity for large limits), error handling, or output format. It mentions 'up to limit' but does not clarify if the limit is inclusive or how results are returned (e.g., list, count). This leaves gaps for an AI agent to understand operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage or redundancy. The additional domain and category information in parentheses is brief and relevant, making the description efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical computation tool with 2 parameters, 0% schema description coverage, no annotations, and no output schema, the description is insufficient. It does not explain parameter details, behavioral traits, or what the output will look like (e.g., list of numbers, their cube representations). For a tool that performs a non-trivial arithmetic search, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'up to limit' which partially explains the 'limit' parameter, but does not define what 'limit' represents (e.g., maximum number value, count of results). It does not mention the 'min_ways' parameter at all, leaving its purpose undocumented. Thus, the description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all taxi numbers (sums of two cubes in multiple ways) up to limit.' It specifies the verb ('Find'), resource ('taxi numbers'), and domain context ('sums of two cubes in multiple ways'), which is specific and informative. However, it does not explicitly differentiate from sibling tools, as the sibling list contains many arithmetic/number theory tools but none specifically for taxi numbers, so the distinction is implicit rather than explicit.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but does not specify prerequisites, exclusions, or recommend other tools for related tasks. For example, it does not indicate if this is for mathematical exploration, verification, or if other tools might handle similar number sequences.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool sums unit fractions and returns a reduced fraction, but doesn't disclose behavioral traits such as error handling (e.g., for zero denominators), input constraints (e.g., positive integers), performance characteristics, or what happens with empty lists. This leaves significant gaps for a mutation-like operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's function and output. It's front-loaded with the core purpose and includes a domain/category hint without unnecessary elaboration, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't explain input constraints (e.g., valid denominators), error conditions, or the format of the reduced fraction result. For a tool with one parameter and mathematical complexity, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'denominators' (array of integers) undocumented. The description mentions 'list of unit fractions,' which implies denominators, but doesn't clarify semantics (e.g., that these are the denominators of unit fractions 1/n, or that they must be positive). It adds minimal value beyond the schema's type information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Sum a list of unit fractions and return the result as a reduced fraction.' It specifies the verb ('sum'), resource ('list of unit fractions'), and output format ('reduced fraction'), though it doesn't explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction' beyond the domain/category hint.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('egyptian_fractions'), but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'egyptian_fraction_decomposition' or 'farey_sum', leaving the agent without clear usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool validates a number string in a base, implying a read-only check with no side effects, but does not disclose behavioral traits like error handling (e.g., invalid inputs), return format (e.g., boolean or detailed message), or performance considerations. For a validation tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's function without unnecessary words. It is front-loaded with the core purpose, and the domain/category annotation is efficiently appended. Every part of the description earns its place, making it highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (validation with two parameters), lack of annotations, and no output schema, the description is incomplete. It does not cover behavioral aspects, parameter details, or return values, leaving the agent with insufficient information to use the tool effectively beyond a basic understanding of its purpose.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'number string' and 'given base', aligning with the parameters 'number' (string) and 'base' (integer), but adds minimal semantic context. It does not explain expected formats (e.g., alphanumeric for bases >10), valid ranges for 'base', or examples, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Validate if a number string is valid in the given base.' It specifies the verb ('validate'), resource ('number string'), and context ('in the given base'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'is_valid_base' or 'base_conversion', which handle related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context on prerequisites, typical use cases, or comparisons with siblings such as 'is_valid_base' (which might check base validity) or 'base_conversion' (which might handle conversions). Without this, the agent must infer usage from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the operation ('Add two vectors element-wise') but does not describe any behavioral traits such as input validation (e.g., vectors must be of equal length), error handling, performance characteristics, or output format. This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category information. There is no wasted verbiage, and every part of the sentence contributes to understanding the tool's function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical operation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not provide enough context for safe and correct usage, such as parameter details, behavioral expectations, or output information. The domain/category hint is insufficient to fill these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not add any parameter semantics. It mentions 'two vectors' but does not explain what 'vector_a' and 'vector_b' represent, their expected formats (e.g., arrays of numbers), constraints (e.g., must be same length), or examples. With low schema coverage, the description fails to compensate for the lack of parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Add two vectors element-wise' with a specific verb ('Add') and resource ('vectors'), and it includes domain/category context ('Domain: linear_algebra.vectors, Category: general'). However, it does not explicitly distinguish this from sibling tools like 'matrix_add' or 'add', which might handle different types of addition, so it misses full sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.vectors') but does not specify when this tool is appropriate compared to other addition-related tools in the sibling list (e.g., 'add', 'matrix_add', 'element_wise_add'). There is no explicit when/when-not or alternative tool naming.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the operation ('Subtract one vector from another element-wise') but does not describe critical behaviors such as input validation (e.g., vector length matching), error handling, or output format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded with the core purpose in a single sentence. There is no wasted text, and the domain/category hints are efficiently appended. It earns its place by being direct and to the point.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (vector operation with two parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not cover parameter details, behavioral traits, or output expectations, making it inadequate for an AI agent to use the tool effectively without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not add any parameter semantics—it does not explain what 'vector_a' and 'vector_b' represent, their expected formats (e.g., arrays of numbers), or constraints (e.g., same length). This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Subtract one vector from another element-wise.' It specifies the verb ('Subtract'), resource ('vectors'), and operation type ('element-wise'), which is specific. However, it does not explicitly distinguish it from sibling tools like 'subtract' (scalar subtraction) or 'matrix_subtract', though the domain hint ('linear_algebra.vectors') provides some context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.vectors') and category ('general'), but does not specify use cases, prerequisites, or comparisons to sibling tools like 'subtract' or 'vector_add', leaving the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs numerical verification at test points, which implies a read-only, computational operation without side effects. However, it lacks details on error handling, performance characteristics (e.g., computational cost), output format, or limitations (e.g., accuracy of numerical methods), leaving significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted language or unnecessary elaboration, making it efficient for quick comprehension by an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of verifying trigonometric identities (which involves mathematical computations and potential numerical errors), the description is incomplete. With no annotations, 0% schema coverage, and no output schema, it fails to provide essential details: parameter meanings, behavioral traits (e.g., tolerance interpretation), and output structure. This leaves the agent poorly equipped to use the tool effectively in practice.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning none of the three parameters (identity_name, test_angles, tolerance) are documented in the schema. The description does not explain what these parameters mean, their expected formats (e.g., how test_angles should be specified), or their roles in the verification process. This leaves the agent with no semantic understanding beyond parameter names, failing to compensate for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Verify a trigonometric identity numerically at multiple test points.' It specifies the verb ('verify'), resource ('trigonometric identity'), and method ('numerically at multiple test points'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'comprehensive_identity_verification' or 'verify_sum_difference_formulas', which prevents a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('trigonometry') and category ('identities'), which implies context but does not specify when to use this tool versus alternatives. There is no explicit mention of when-not-to-use scenarios or direct references to sibling tools, leaving the agent with insufficient direction for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool 'applies custom weights to recent observations', which implies a calculation but does not describe output format, error handling, performance characteristics, or any constraints (e.g., weight normalization). For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. Every word earns its place with no redundancy or unnecessary elaboration, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical operation with two parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain the calculation method, output format, error conditions, or practical usage examples. For a tool in a domain like timeseries analysis, this leaves too much unspecified for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'custom weights' and 'recent observations', which loosely map to 'weights' and 'data' parameters, but does not explain their semantics (e.g., weight array length matching data, numerical constraints, or handling of invalid inputs). The description adds minimal value beyond the bare parameter names, failing to adequately address the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute Weighted Moving Average (WMA) - applies custom weights to recent observations'. It specifies the verb ('Compute'), resource ('Weighted Moving Average'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'simple_moving_average' or 'exponential_moving_average', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('timeseries') and category ('analysis'), it does not specify scenarios, prerequisites, or comparisons to sibling tools like 'simple_moving_average' or 'exponential_moving_average'. This lack of explicit usage context limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool uses 'wheel factorization for improved efficiency,' which hints at performance characteristics but lacks critical details: what the tool returns (e.g., list of primes), computational complexity, memory usage, or error handling. For a tool with no annotations, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence plus domain/category tags—with zero wasted words. It is front-loaded with the core purpose and efficiently includes relevant metadata. This is a model of brevity without sacrificing essential clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a specialized sieve algorithm), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain the tool's behavior, output format, or parameter meanings, leaving significant gaps for an AI agent to understand and invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters 'limit' and 'wheel_primes' are undocumented in the schema. The description adds no information about these parameters—it does not explain what 'limit' represents (e.g., upper bound for primes) or what 'wheel_primes' should contain. This fails to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Wheel sieve using wheel factorization for improved efficiency.' It specifies the verb ('sieve'), resource (implied prime numbers), and domain context ('arithmetic, Category: sieve_algorithms'). However, it does not explicitly differentiate from sibling sieve tools like 'sieve_of_eratosthenes' or 'incremental_sieve', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'improved efficiency' but does not specify scenarios where wheel factorization is preferred over other sieve algorithms, nor does it reference sibling tools. This leaves the agent without practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'efficiently,' hinting at performance, but doesn't disclose critical behavioral traits: computational limits (e.g., large k/m), error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding its operation and constraints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: one sentence states the core function, followed by a parenthetical domain/category. Every word earns its place with zero waste, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with two parameters), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It lacks details on behavior, parameter meanings, return values, and error conditions, leaving the agent under-informed for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter details. The description adds minimal semantics: 'k' and 'm' are implied as inputs for factorial modulo calculation, but it doesn't explain their roles (e.g., k is the factorial base, m is the modulus), constraints (e.g., non-negative integers), or examples. This insufficiently compensates for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate k! mod m efficiently for Wilson's theorem.' It specifies the verb ('calculate'), resource (factorial modulo), and context (Wilson's theorem). However, it doesn't explicitly differentiate from sibling tools like 'wilson_theorem_check' or 'wilson_theorem_test', which appear related to Wilson's theorem but have different functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain (arithmetic) and category (primality_tests), implying use in primality testing contexts. However, it lacks explicit when-to-use instructions, alternatives (e.g., vs. other Wilson's theorem tools), or exclusions. The agent must infer usage from the category alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'domain validation,' which implies input constraints (likely -1 ≤ value ≤ 1), but does not detail error handling, output format (radians vs. degrees), or performance characteristics. For a mathematical function with no annotations, this is a significant gap in behavioral disclosure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it states the core function in the first phrase and adds domain/category context efficiently. Every sentence earns its place with no wasted words, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical function with domain validation), no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on output (e.g., radians), error cases, and sibling differentiation, making it inadequate for reliable tool invocation without additional inference.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The description adds some context by implying domain validation for the 'value' parameter, but does not specify the exact domain or units. Since schema coverage is low, the description partially compensates but not fully, aligning with the baseline for minimal param info.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arccosine (inverse cosine) with domain validation.' It specifies the mathematical operation (arccosine) and mentions domain validation, which is a key aspect. However, it does not explicitly differentiate from siblings like 'acos_degrees' or 'asin', though the domain/category hints at trigonometry.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions 'domain validation' but does not specify when to use this tool versus alternatives (e.g., 'acos_degrees' for degrees output, 'asin' for arcsine). No explicit when/when-not instructions or prerequisites are given, leaving the agent to infer from context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'domain validation', which is a useful behavioral trait, but doesn't disclose other important aspects like error handling (e.g., what happens if x < 1), performance characteristics, or output format. For a mathematical function tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that states the core functionality and key feature (domain validation), followed by a parenthetical category. Every word earns its place with no redundancy or fluff.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the tool returns, error conditions, or mathematical context beyond the basic operation. For a tool that performs a specific mathematical calculation, more context about behavior and results would be helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'domain validation' which adds context about the parameter 'x' (likely requiring x ≥ 1 for real results), but doesn't explicitly explain the parameter's role or constraints. The description provides some semantic value beyond the bare schema, but not enough to fully document the single parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate inverse hyperbolic cosine (area cosine) with domain validation.' It specifies the verb ('calculate'), resource ('inverse hyperbolic cosine'), and includes domain validation as a key feature. However, it doesn't explicitly differentiate from sibling tools like 'acosh' vs 'asinh' or 'atanh', though the category 'inverse_hyperbolic' provides some context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions domain validation, which implies the tool handles input validation, but doesn't specify when to use this tool versus alternatives like 'cosh' or other inverse hyperbolic functions. No explicit when/when-not instructions or alternative tool references are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'domain validation', which implies input constraints (likely x ≠ 0 for inverse hyperbolic cotangent) and error handling, adding useful behavioral context. However, it doesn't disclose other traits like performance, error messages, or output format, leaving gaps for a tool with no structured annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that states the core functionality and adds domain/category context. There's no wasted verbiage, and every part contributes to understanding the tool's purpose, though it could be slightly more informative without losing efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, 1 parameter, no annotations, and no output schema, the description is incomplete. It mentions domain validation but doesn't detail the domain constraints, error behavior, or return values. For a tool performing a specialized calculation, more context on inputs and outputs is needed to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (x) with 0% description coverage, and the tool description adds no information about the parameter. It doesn't explain what 'x' represents (e.g., a real number, domain restrictions like |x| > 1 for acoth), its units, or valid ranges beyond the vague 'domain validation'. This fails to compensate for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate inverse hyperbolic cotangent with domain validation.' It specifies the verb ('calculate'), resource ('inverse hyperbolic cotangent'), and includes domain validation as an additional feature. However, it doesn't explicitly differentiate from sibling tools like 'acoth' vs 'acot' or 'acsch', though the domain/category hints help.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions domain validation and categorizes it under 'trigonometry' and 'inverse_hyperbolic', but doesn't specify use cases, prerequisites, or compare it to related siblings like 'acot' or 'acsch'. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates the 'shortest angular difference,' implying a mathematical computation, but does not describe output format (e.g., range of results, handling of negative values, or unit consistency). For a tool with no annotations, this is a significant gap in behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context, which is useful but not essential. There is no wasted text, making it efficient, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (mathematical computation with 3 parameters), no annotations, and no output schema, the description is minimally adequate. It states what the tool does but lacks details on behavior, output, and parameter usage. For a tool in a server with many siblings, more context would help distinguish it, but it meets a basic threshold.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not mention any parameters, while the input schema covers 3 parameters (angle1, angle2, unit) with 0% schema description coverage. The description adds no semantic information about what the parameters represent or how they interact (e.g., that unit applies to both angles). With low schema coverage, the description fails to compensate, but the tool's purpose inherently implies the parameters, so a baseline 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the shortest angular difference between two angles.' It specifies the verb ('calculate') and resource ('angular difference'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'convert_angle' or 'normalize_angle', which might handle related angle operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('angle_conversion'), but does not specify scenarios, prerequisites, or comparisons to sibling tools (e.g., 'convert_angle' for unit conversion, 'normalize_angle' for angle wrapping). This leaves the agent without explicit usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While 'Get' implies a read-only operation, the description doesn't specify what 'properties and equivalent representations' actually means in practice, nor does it mention any constraints, limitations, or output format expectations. This leaves significant behavioral questions unanswered.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with just one sentence containing the core functionality and domain/category context. There's zero wasted language, and the information is front-loaded appropriately for a simple tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a tool with 2 parameters, no annotations, no output schema, and 0% schema description coverage, the description is inadequate. It doesn't explain what 'properties and equivalent representations' means, doesn't guide usage relative to similar sibling tools, and provides minimal parameter context. The conciseness comes at the expense of necessary completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the schema provides no parameter descriptions. The tool description mentions 'angle properties and equivalent representations' but doesn't explain what the 'angle' and 'unit' parameters actually do or how they relate to the tool's functionality. The description adds minimal semantic value beyond what's implied by the parameter names themselves.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Get') and resource ('angle properties and equivalent representations'), and it provides domain/category context. However, it doesn't differentiate from sibling tools like 'convert_angle' or 'normalize_angle', which appear to be related angle manipulation tools in the same server.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. With sibling tools like 'convert_angle' and 'normalize_angle' available, there's no indication of what distinguishes this tool's functionality from those similar tools, leaving the agent without usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions handling 'floating-point precision issues,' which hints at behavior, but doesn't disclose details like the default tolerance value (1e-9 from the schema), how tolerance is applied (e.g., absolute vs. relative), or what the output looks like (e.g., boolean). This leaves significant gaps for a tool with no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise and front-loaded, with two sentences that directly state the purpose and key behavior. There is no wasted text, and the domain/category in parentheses is efficiently included without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema description coverage (0%), the description is incomplete. It lacks details on behavioral traits (e.g., output format, error handling), parameter usage, and differentiation from siblings. For a comparison tool with three parameters, this is inadequate to guide an AI agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate. It implies parameters 'a' and 'b' as the numbers to compare and 'tolerance' as the threshold, but doesn't explain their semantics beyond 'floating-point numbers' and 'tolerance.' This adds some meaning over the bare schema but doesn't fully clarify usage (e.g., tolerance units or typical values).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if two floating-point numbers are approximately equal within a tolerance.' It specifies the verb ('check'), resource ('two floating-point numbers'), and scope ('within a tolerance'), though it doesn't explicitly differentiate from sibling tools like 'equal' or 'is_close' beyond mentioning floating-point precision handling.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance, stating it 'Handles floating-point precision issues' and includes a domain/category, but it doesn't specify when to use this tool versus alternatives like 'equal' or 'is_close' (which is a sibling tool). No explicit when/when-not instructions or prerequisites are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates a sequence but does not disclose behavioral traits such as output format (e.g., list of numbers), error handling for invalid inputs, or computational limits. This leaves significant gaps in understanding how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's function and parameters, with no wasted words. It is appropriately sized and front-loaded, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (3 parameters, no annotations, no output schema), the description is incomplete. It lacks information on output format, error conditions, and usage context, which are crucial for an agent to invoke the tool correctly. The description does not compensate adequately for the missing structured data.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaningful context by naming the parameters ('first term, common difference, and number of terms') and implying their roles in sequence generation. However, it doesn't provide details on constraints (e.g., valid ranges for 'num_terms') or examples, so it only partially compensates for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate an arithmetic sequence with given first term, common difference, and number of terms.' It specifies the verb ('generate') and resource ('arithmetic sequence'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'arithmetic_series' or 'arithmetic_sum', which is why it doesn't reach a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain and category but gives no explicit when/when-not instructions or references to sibling tools, leaving the agent to infer usage context independently.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation method but does not cover critical aspects such as error handling (e.g., for invalid inputs like negative 'num_terms'), performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first clause. The formula and domain/category tags are relevant but could be slightly more integrated. There is no redundant information, and every sentence contributes to understanding the tool's function, though minor improvements in flow could enhance structure.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical calculation with three parameters), no annotations, and no output schema, the description is incomplete. It lacks details on error conditions, output format, and practical usage examples. While the formula provides some context, it does not fully compensate for the absence of structured metadata, leaving the agent with insufficient information for reliable invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It implicitly defines the parameters through the formula 'n/2 * (2a + (n-1)d)', where 'a' corresponds to 'first_term', 'd' to 'common_diff', and 'n' to 'num_terms'. This adds meaningful context beyond the schema's type definitions. However, it does not explicitly map formula variables to parameter names or explain constraints (e.g., 'num_terms' must be positive), limiting the score to baseline adequacy.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sum of an arithmetic sequence' using a specific formula. It specifies the verb ('calculate'), resource ('sum of an arithmetic sequence'), and provides the formula for clarity. However, it does not explicitly distinguish this tool from its sibling 'arithmetic_series', which likely serves a similar purpose, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('general'), but these are too vague to inform usage decisions. There is no mention of prerequisites, limitations, or comparisons to sibling tools like 'arithmetic_series', leaving the agent without practical usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions what the tool does but doesn't describe key behaviors: whether it returns a list or sequence, if there are performance considerations for large limits, or what happens with invalid inputs (e.g., negative limits). The description lacks details on output format, error handling, or computational characteristics.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context efficiently. There's no wasted text, and it's appropriately sized for a simple tool, though it could benefit from more detail given the lack of annotations and schema coverage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a computational tool with no annotations, 0% schema coverage, and no output schema), the description is incomplete. It doesn't explain the return value (e.g., list of integers), error conditions, or performance implications. For a tool that generates sequences, more context on output behavior is needed to be fully usable.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description doesn't add any parameter semantics. It mentions 'limit' but doesn't explain its meaning (e.g., inclusive/exclusive, valid range, units). The description fails to compensate for the low schema coverage, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all Armstrong numbers (narcissistic numbers) up to limit.' It specifies the verb ('Find'), resource ('Armstrong numbers'), and scope ('up to limit'), and distinguishes it from sibling tools like 'is_narcissistic_number' (which tests individual numbers) and 'narcissistic_numbers' (which might generate them differently). However, it doesn't explicitly differentiate from 'narcissistic_numbers' in the sibling list, which could cause ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage by stating the domain ('arithmetic') and category ('special_numbers'), which provides some context. However, it doesn't give explicit guidance on when to use this tool versus alternatives like 'is_narcissistic_number' (for testing individual numbers) or 'narcissistic_numbers' (a sibling tool with potentially different behavior). No exclusions or prerequisites are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. While it mentions 'full quadrant determination' (which hints at the tool's behavior with respect to quadrant signs), it doesn't disclose important behavioral traits like: what coordinate system is assumed, whether inputs can be zero/negative, what output range/units are used (radians vs degrees), or error handling. The description is insufficient for a mathematical function with potential edge cases.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise - just one sentence plus a parenthetical. It's front-loaded with the core purpose. However, the parenthetical '(Domain: trigonometry, Category: inverse_functions)' adds minimal value and could be considered somewhat redundant given the tool name and obvious mathematical context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given that there are no annotations and no output schema, the description is incomplete. For a mathematical function tool, users need to know: output units (radians implied but not stated), behavior with special inputs (like x=0), and mathematical properties. The description mentions 'full quadrant determination' which is helpful, but doesn't provide enough context for reliable use, especially compared to the extensive sibling tool list that includes similar trigonometric functions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, providing only parameter names (y, x) and types. The description adds no parameter semantics whatsoever - it doesn't explain what y and x represent (typically Cartesian coordinates), their relationship, or any constraints. However, since this is a standard mathematical function with well-known parameters, the baseline of 3 is appropriate despite the lack of explicit parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate two-argument arctangent for full quadrant determination.' It specifies the mathematical operation (arctangent) and its key feature (full quadrant determination). However, it doesn't explicitly differentiate from its sibling 'atan2_degrees', which appears to be a similar tool with degree output.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. The parenthetical '(Domain: trigonometry, Category: inverse_functions)' gives some context about the mathematical domain, but offers no explicit guidance on when to use this tool versus alternatives like 'atan' (single-argument arctangent) or 'atan2_degrees'. There's no mention of specific use cases or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool generates Bell numbers but does not disclose behavioral traits such as computational complexity, input constraints (e.g., valid range for 'n'), error handling, or output format. This leaves significant gaps for a tool with a single parameter.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose. It is front-loaded with the core functionality and includes domain/category context efficiently, with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on behavior, parameter constraints, and return values, which are critical for a computational tool. The domain/category hint is helpful but insufficient for full understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameter 'n' undocumented. The description mentions 'the first n Bell numbers', implying 'n' is a count, which adds basic semantics. However, it does not specify constraints (e.g., n must be positive integer) or examples, providing only minimal value beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n Bell numbers.' It specifies the verb ('Generate') and resource ('Bell numbers'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'bell_number' or 'bell_triangle', which appear related.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools (e.g., 'bell_number' or 'bell_triangle'), leaving the agent without context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It states the tool generates Bell's triangle, implying a read-only computation, but does not mention performance characteristics (e.g., computational complexity for large n), error handling, or output format. For a tool with no annotations, this is insufficient behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: a single sentence that directly states the tool's function and includes domain/category metadata. There is no wasted verbiage, and the key information is front-loaded, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on output format (e.g., list of lists, matrix), error conditions, and performance limits. For a tool that generates combinatorial structures, more context is needed for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description adds that 'n' specifies the row limit ('up to row n'), which clarifies its meaning beyond the schema's type annotation. However, it does not detail constraints (e.g., n must be non-negative integer) or examples, leaving some ambiguity. With low schema coverage, this partial compensation warrants a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate Bell's triangle up to row n.' It specifies the verb ('Generate'), resource ('Bell's triangle'), and scope ('up to row n'). However, it does not explicitly differentiate from sibling tools like 'bell_number' or 'bell_sequence', which are related combinatorial tools, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('combinatorial_numbers'), but does not specify use cases, prerequisites, or comparisons to siblings like 'bell_number' or 'bell_sequence'. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'generates' something but doesn't clarify what the output looks like (e.g., list of fractions, tree structure), whether it's deterministic, if there are computational limits, or how it handles invalid inputs. The description is too vague about the tool's behavior beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence with additional domain/category tags. It's front-loaded with the core purpose and wastes no words. However, the parentheses with 'Domain: arithmetic, Category: farey_sequences' feel slightly tacked-on rather than integrated, preventing a perfect score.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of generating a mathematical tree structure, no annotations, no output schema, and minimal parameter documentation, the description is inadequate. It doesn't explain what the output contains, how the tree is represented, or any behavioral constraints. For a tool that likely produces structured mathematical data, this leaves too many gaps for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('levels') with 0% description coverage. The description doesn't mention this parameter at all, so it adds no semantic information beyond the schema. However, since there's only one parameter and the tool's purpose implies it generates tree levels, the baseline score of 3 is appropriate—the schema is minimal but the description doesn't compensate for the lack of parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate levels of Calkin-Wilf tree related to Farey sequences.' It specifies the verb ('Generate'), resource ('levels of Calkin-Wilf tree'), and provides domain context ('Domain: arithmetic, Category: farey_sequences'). However, it doesn't explicitly differentiate from sibling tools like 'farey_sequence' or 'stern_brocot_tree', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions Farey sequences but doesn't explain why one would choose this over tools like 'farey_sequence', 'farey_neighbors', or 'stern_brocot_tree'. There's no mention of prerequisites, typical use cases, or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not mention error handling (e.g., for negative or large n), performance characteristics, or output format. For a computational tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the purpose and formula. Every word earns its place, with no redundant information, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, and no output schema, the description is incomplete. It lacks details on return values, error conditions, and behavioral traits, which are crucial for an AI agent to invoke it correctly. The formula is provided, but operational context is missing.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description adds meaning by specifying 'nth Catalan number', implying 'n' is an integer index, but does not detail constraints (e.g., non-negative, range limits). With low schema coverage, it partially compensates but not fully, warranting a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Catalan number' with the explicit formula C_n = (2n)!/(n+1)!n!. It specifies the domain (arithmetic) and category (combinatorial_numbers), making the verb+resource clear. However, it does not distinguish from sibling tools like 'catalan' or 'catalan_sequence', which might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks explicit instructions on when to choose this over 'catalan' or 'catalan_sequence', and does not mention any prerequisites or exclusions, leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates numbers but does not describe output format (e.g., list of integers), performance characteristics (e.g., computational limits for large n), error handling, or any side effects. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The additional domain and category information is brief and relevant. There is no wasted text, making it efficient for quick understanding, though it could be slightly more structured with bullet points or examples.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It does not explain what the tool returns (e.g., a list of Catalan numbers), any limitations (e.g., maximum n), or error conditions. For a tool with no structured support, the description should provide more context to ensure the agent can use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'n' as the parameter but does not explain its meaning beyond 'first n'. No details on constraints (e.g., n must be positive integer), default values, or examples are provided. The description adds minimal semantics, so it meets the baseline for a tool with one parameter but does not fully address the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n Catalan numbers.' It specifies the verb ('Generate'), resource ('Catalan numbers'), and scope ('first n'), which is specific and unambiguous. However, it does not explicitly distinguish this tool from sibling tools like 'catalan' or 'catalan_number', which might serve similar functions, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('combinatorial_numbers'), but this is too generic to help an agent choose between this and sibling tools like 'catalan' or 'catalan_number'. There are no explicit instructions on prerequisites, constraints, or comparative use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a value but does not describe any behavioral traits such as input validation (e.g., handling negative 'n'), performance characteristics, error conditions, or output format. For a computational tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence stating the core purpose, followed by domain/category in parentheses. Every word earns its place with no redundancy or unnecessary elaboration, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on behavior, parameter semantics, output format, and usage context. While concise, it does not provide sufficient information for an agent to confidently invoke the tool without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, so the schema provides no semantic context. The description adds minimal value by implying 'n' is an index ('nth'), but does not explain its meaning (e.g., integer position in the sequence), constraints (e.g., non-negative), or examples. With low schema coverage, the description compensates inadequately, warranting a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth centered hexagonal number.' It specifies the verb ('calculate') and resource ('centered hexagonal number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'centered_polygonal_number' or 'centered_square_number', which would require more specific guidance on when to use this particular figurate number tool.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or comparisons with sibling tools (e.g., 'centered_polygonal_number', 'centered_square_number'). Without explicit when-to-use or when-not-to-use instructions, the agent lacks contextual direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it mentions the test type and purpose, it doesn't describe key behavioral aspects: what the tool returns (test statistic, p-value, degrees of freedom), whether it performs validation (e.g., checking for non-negative frequencies, sample size adequacy), or any computational characteristics (e.g., handling of small expected frequencies). For a statistical test tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. The domain/category tags add context without verbosity. However, it could be slightly more structured by separating usage notes from the core description, but overall it's appropriately concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test (3 parameters, no output schema, no annotations), the description is incomplete. It lacks details on parameter semantics, return values, assumptions, and behavioral traits. While it identifies the test type, it doesn't provide enough context for an agent to use it correctly without external knowledge of chi-square tests.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so parameters 'observed', 'expected', and 'alpha' are undocumented in the schema. The description only vaguely references 'observed frequencies' and 'expected frequencies' without explaining their format (arrays of numbers), relationships (same length), or meaning (counts or proportions). It doesn't mention 'alpha' at all. With low schema coverage, the description fails to compensate adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform chi-square goodness-of-fit test to test whether observed frequencies match expected frequencies.' It specifies the statistical test type (chi-square goodness-of-fit), the action (perform test), and the goal (test match between observed and expected frequencies). However, it doesn't differentiate from potential statistical testing siblings like 'fishers_exact_test' or 'proportion_test' that might also handle categorical data comparisons.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides some implied usage context through the domain/category tags ('Domain: statistics, Category: inference'), suggesting it's for statistical inference tasks. However, it lacks explicit guidance on when to use this specific test versus alternatives like proportion tests or exact tests, nor does it mention prerequisites (e.g., sample size requirements, independence assumptions) or typical scenarios for application.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool calculates but doesn't describe behavioral traits like error handling (e.g., what happens with empty arrays or invalid data), computational characteristics (e.g., performance, precision), or output format (e.g., numeric value, interpretation). For a statistical tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose without unnecessary words. Every part earns its place: the calculation action, the specific metric, the input context, and domain/category tags for additional context. It's appropriately sized for a straightforward statistical tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a statistical calculation with two required array parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on output (what the effect size value represents, units), error conditions, and practical usage notes. The domain/category tags help, but more context is needed for effective agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description mentions 'two samples' and 'standardized difference between two means', which implicitly maps to the two array parameters (data1, data2) as the sample datasets. However, it doesn't detail parameter constraints (e.g., array lengths, numeric types) or usage semantics beyond the basic mapping. The description adds some value but doesn't fully compensate for the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Cohen's d effect size for two samples (standardized difference between two means)'. It specifies the verb ('Calculate'), resource ('Cohen's d effect size'), and scope ('for two samples'), making the intent unambiguous. However, it doesn't explicitly differentiate from sibling tools, though the statistical nature is implied by the domain/category tags.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (statistics) and category (inference), which hints at context, but offers no explicit when-to-use, when-not-to-use, or named alternatives. The agent must infer usage from the tool's name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool calculates but doesn't disclose behavioral traits like input constraints (e.g., n must be positive integer), computational complexity, error handling, or output format. For a mathematical tool with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence with domain/category context. However, the domain/category annotations could be considered redundant since they don't add operational value for tool selection.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and a single parameter tool, the description is inadequate. It doesn't explain what the stopping time represents, input constraints, output format, or edge cases. For a mathematical calculation tool, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description provides no parameter information beyond what's implied by the tool name. The single parameter 'n' is completely undocumented in both schema and description, leaving its meaning and constraints unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific verb ('Calculate') and resource ('Collatz stopping time'), with additional domain/category context. It distinguishes from sibling tools like 'collatz_sequence' (which generates the full sequence) and 'collatz_max_value' (which finds the maximum value).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. While the purpose is clear, there's no mention of when this calculation is appropriate compared to other Collatz-related tools or mathematical sequence tools in the extensive sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden but only states the mathematical formula. It doesn't disclose behavioral traits like precision limitations, performance characteristics (e.g., time/complexity for many terms), error handling for invalid inputs, or output format. The description is purely declarative without operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The additional domain/category information is brief and relevant. There's no wasted verbiage, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the tool returns (e.g., a numeric approximation, error estimate), how accuracy scales with terms, or any limitations. For a computational tool, this leaves significant gaps for an AI agent to understand its behavior fully.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description doesn't mention the 'terms' parameter at all, and schema description coverage is 0%, so it adds no parameter semantics beyond the bare schema. However, with only one parameter and a straightforward tool, the baseline is 3 as the schema alone might be minimally sufficient, though the description fails to compensate for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes e using the infinite series formula, specifying the mathematical method and domain/category. It distinguishes itself from sibling tools like 'e' or 'compute_e_limit' by explicitly mentioning the series approach, though it doesn't explicitly contrast with those alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives like 'compute_e_limit' or 'e'. The description mentions the domain and category but gives no practical context about accuracy trade-offs, computational cost, or typical use cases for series approximation versus other methods.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the formula but lacks behavioral details: it doesn't mention that this is a slow-converging series (important for performance), doesn't specify output format or precision, and omits any error handling or limitations. The description adds minimal context beyond the basic formula.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the purpose and formula in one sentence. The parenthetical domain/category adds minor metadata without verbosity. However, it could be more structured by separating usage guidance or parameter details, but as-is, it avoids waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical computation with performance implications), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It omits critical context: expected output (e.g., float approximation of pi), convergence behavior, accuracy trade-offs with 'terms', and comparison to other pi-computation tools. This leaves significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'terms' of type integer. The description does not explain what 'terms' means (e.g., number of series terms to sum), its typical range, or its impact on accuracy. Since schema coverage is low, the description fails to compensate adequately, providing no parameter semantics beyond what the bare schema indicates.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes pi using the Leibniz formula, specifying the mathematical method. It distinguishes itself from other pi-computation siblings (e.g., compute_pi_chudnovsky, compute_pi_machin) by naming the specific algorithm. However, it does not explicitly contrast with these siblings in the description text, missing full differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (arithmetic) and category (mathematical_constants), but offers no explicit when/when-not instructions or references to sibling tools like compute_pi_chudnovsky for different precision needs or contexts.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe output format, error handling, assumptions (e.g., normal approximation conditions), or computational characteristics. For a statistical inference tool with zero annotation coverage, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It is front-loaded with the core purpose and includes domain/category tags efficiently. Every part of the description earns its place by conveying essential information without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical inference with 3 parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is insufficient. It does not compensate for the missing structured data by explaining return values, assumptions, or usage context, making it inadequate for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description does not mention any parameters explicitly, but implies 'sample proportion' via 'successes' and 'n', and 'confidence level' via 'confidence interval'. It adds minimal semantic context (e.g., 'population proportion', 'sample proportion') but does not detail parameter roles, units, or constraints, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate confidence interval for population proportion from sample proportion', specifying the verb ('calculate'), resource ('confidence interval'), and domain/category. It distinguishes the tool from siblings like 'confidence_interval_mean' by focusing on proportions rather than means, but does not explicitly contrast them in the description text.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('inference'), but offers no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools like 'proportion_test' or 'bootstrap_confidence_interval' that might serve similar purposes.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a conversion 'in one operation', implying a straightforward, read-only calculation without side effects. However, it lacks details on error handling (e.g., invalid inputs), performance characteristics, or output format, which are important for a tool with three parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: one sentence stating the purpose, followed by domain and category in parentheses. Every word earns its place, with no redundancy or fluff. It is front-loaded with the core functionality, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (three parameters, no annotations, no output schema), the description is insufficient. It does not explain the return values, error conditions, or practical usage examples. While the schema provides parameter details, the lack of behavioral context and output information leaves gaps for an AI agent to operate effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate, but it does not mention any parameters. The input schema clearly defines 'angle', 'from_unit', and 'to_unit' with enums, so the agent can infer usage from the schema alone. The description adds no semantic context beyond the schema, resulting in a baseline score of 3 due to the schema's clarity despite the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert between different angle units in one operation.' It specifies the verb ('convert'), resource ('angle units'), and scope ('in one operation'), making it easy to understand. However, it does not explicitly differentiate from sibling tools like 'degrees_to_radians' or 'radians_to_gradians', which perform similar conversions but are more specific.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('trigonometry') and category ('angle_conversion'), but does not specify when to use this tool versus alternatives like 'degrees_to_radians' or 'radians_to_gradians'. There is no explicit advice on when-not-to-use or prerequisites, leaving the agent to infer usage from context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a conversion but does not describe any behavioral traits such as error handling (e.g., invalid units), precision, or output format. For a tool with no annotations, this is a significant gap, as the agent lacks critical operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose followed by domain/category in parentheses. There is no wasted text, and every part of the sentence contributes essential information, making it highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (3 parameters, no annotations, no output schema), the description is insufficient. It lacks details on parameter semantics, behavioral traits, and output format. While concise, it does not provide enough context for the agent to reliably invoke the tool without ambiguity, especially with 0% schema description coverage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, meaning the schema provides no semantic information. The description adds some value by listing example units ('mph, kph, m/s, knots, etc.'), which helps clarify the 'from_unit' and 'to_unit' parameters. However, it does not fully document all parameters (e.g., 'value' is not explained), so it partially compensates but not completely, aligning with the baseline for moderate schema coverage gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert speed between different units: mph, kph, m/s, knots, etc.' It specifies the verb ('convert'), resource ('speed'), and provides examples of units. However, it does not explicitly distinguish this tool from sibling conversion tools like convert_angle, convert_area, etc., which reduces the score from a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('conversions') and category ('general'), but does not specify when to choose speed conversion over other conversion tools or any prerequisites. This lack of explicit usage context results in a low score.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not mention any behavioral traits such as input validation (e.g., handling of non-numeric inputs), error handling, performance characteristics, or output format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's function, followed by domain and category in parentheses. There is no wasted text, and every part contributes to understanding the tool's purpose efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is incomplete. It lacks information on output (e.g., returns a numeric value), error conditions, and behavioral context. While concise, it does not provide enough detail for an agent to fully understand how to invoke and interpret results without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'angle_degrees' of type 'number'. The description adds minimal semantics by specifying 'an angle in degrees', which clarifies the unit beyond the parameter name. However, it does not provide details on allowed ranges, special values, or examples, leaving the schema to carry most of the parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate cosine of an angle in degrees.' It specifies the verb ('calculate'), resource ('cosine'), and domain ('trigonometry, Category: basic_functions'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'cos' (which likely calculates cosine in radians) or 'cos_series', so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify when to choose it over similar tools (e.g., 'cos' for radians, 'cos_series' for series approximation) or any prerequisites. This lack of comparative context leaves usage decisions unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the conversion action but does not mention any behavioral traits such as error handling (e.g., for negative or non-integer inputs), performance characteristics, or output format details. The description is minimal and lacks context beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Convert decimal to octal (base-8) number system.' It wastes no words and directly states the core functionality. The domain and category tags are additional but not verbose. Every sentence earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, output schema, and minimal parameter coverage, the description is incomplete. It does not explain what the tool returns (e.g., a string or integer), how errors are handled, or any limitations. For a tool with no structured support, the description should provide more context to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('decimal') with 0% description coverage. The tool description does not add any parameter-specific information beyond what the schema name implies. Since there is only one parameter and its purpose is inferred from the tool name, the baseline score of 3 is appropriate, but no additional semantics are provided.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert decimal to octal (base-8) number system.' It specifies the verb ('convert'), resource ('decimal'), and target ('octal'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'decimal_to_binary' or 'decimal_to_hexadecimal', though the domain/category tags provide some context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('number_systems'), but does not specify scenarios, prerequisites, or comparisons with sibling tools like 'base_conversion' or 'decimal_to_base'. Usage is implied by the name and description alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'high precision,' which adds some context about output quality, but fails to describe other critical behaviors such as error handling (e.g., for invalid inputs), performance characteristics, or return format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Convert degrees to radians with high precision.' It wastes no words and immediately conveys the core function. The domain and category tags in parentheses are additional but non-essential, maintaining efficiency without clutter.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is incomplete. It lacks details on behavioral traits, parameter semantics, and usage guidelines, which are necessary for an agent to use it effectively. While the purpose is clear, the overall context is insufficient for a well-informed invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'degrees' of type 'number' but no semantic details. The description does not add any parameter-specific information beyond the tool's purpose, such as expected units, valid ranges, or examples. Since schema coverage is low, the description does not compensate, resulting in a baseline score of 3 due to the simple, single-parameter nature.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert degrees to radians with high precision.' It specifies the verb ('convert'), resource ('degrees to radians'), and quality ('high precision'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'convert_angle' or 'radians_to_degrees', which would be needed for a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance through the domain and category tags ('trigonometry, angle_conversion'), which imply context but do not explicitly state when to use this tool versus alternatives. There is no mention of when not to use it or direct references to sibling tools like 'radians_to_radians' or 'convert_angle', leaving the agent with little practical direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool analyzes density as n increases, implying it might compute or compare density metrics, but it does not describe what the analysis entails (e.g., returns a value, a plot, or a table), any computational constraints, or error handling. This leaves significant gaps for a tool with no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It is front-loaded with the core purpose, and the domain/category note is brief and relevant. Every part earns its place, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical analysis tool), lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what the analysis outputs, how density is defined or computed, or any prerequisites. For a tool with these contextual gaps, more detail is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'max_n' with 0% description coverage, and the description does not add any parameter-specific information. It mentions 'as n increases', which loosely relates to 'max_n', but does not explain what 'max_n' represents (e.g., upper bound for n, integer limit) or its valid range. Since schema coverage is low, the description fails to compensate, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Analyze density of Farey sequences as n increases.' It specifies the verb ('analyze'), resource ('density of Farey sequences'), and scope ('as n increases'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'farey_sequence' or 'farey_sequence_properties', which is why it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), but this is too vague to help an agent choose between this and sibling tools like 'farey_sequence' or 'farey_sequence_length'. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the calculation but does not disclose behavioral traits such as error handling (e.g., for negative numbers or non-integer inputs), performance characteristics, or output format. The description is minimal and lacks necessary operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted text, and it efficiently communicates the core functionality without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical operation with two parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain the return value, error conditions, or detailed parameter usage, leaving significant gaps for an AI agent to understand and invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'number' and 'base' implicitly in the calculation context but does not explain parameter meanings beyond the schema's type definitions. The description adds marginal value by hinting at the base parameter's role, but it does not fully document the two parameters' semantics or usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the product of digits of a number.' It specifies the verb ('calculate'), resource ('product of digits'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'digital_product_sequence' or 'digit_sum', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions domain and category but gives no explicit when/when-not instructions or references to sibling tools. Usage is implied by the description's content but lacks actionable context for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the sorting behavior but doesn't disclose important details: how negative numbers or zero are handled, whether non-integer inputs are accepted, what happens with leading zeros, or the return format. For a tool with no annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—one sentence plus domain/category tags. Every word contributes: the first sentence states the core functionality, and the parenthetical adds context. No wasted words, though it could be argued it's too brief given the lack of annotations.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, no output schema, and 2 parameters, the description is incomplete. It doesn't explain the return value (e.g., integer or string?), edge cases, or error handling. For a tool with digital manipulation, more context is needed for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions both parameters implicitly ('number' for 'n', 'ascending or descending order' for 'descending'), but doesn't explain parameter constraints (e.g., valid ranges for 'n', that 'descending' defaults to false). The description adds some meaning but doesn't fully document the two parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Sort the digits of a number in ascending or descending order.' It specifies the verb ('sort'), resource ('digits of a number'), and direction options. However, it doesn't explicitly differentiate from sibling tools like 'sort_numbers' or 'digit_reversal' beyond the domain/category tags.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided about when to use this tool versus alternatives. The description mentions domain/category ('arithmetic, digital_operations'), but this doesn't help choose between similar tools like 'sort_numbers' (which sorts lists of numbers) or 'digit_reversal' (which reverses digit order). No prerequisites, constraints, or explicit alternatives are stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation method but does not describe behavioral traits such as error handling (e.g., for invalid coordinates), performance characteristics, or output format. For a tool with no annotations, this is a significant gap in transparency, as it omits key operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first sentence. The additional domain and category information is brief and does not add unnecessary length. However, it could be more structured by separating usage notes or parameter details, but overall, it is efficient with minimal waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical calculation tool with 5 parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It fails to explain parameter meanings, output format (e.g., distance units), or any behavioral context. For a tool with these gaps, the description should provide more comprehensive information to aid the agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not add any parameter semantics; it does not explain what 'lat1', 'lon1', etc., represent (e.g., latitude/longitude in degrees), the role of 'radius' (default Earth radius in kilometers), or units. With low coverage and no compensation in the description, the baseline score is appropriate but reflects a lack of added value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate great circle distance between two points using Haversine formula.' It specifies the verb ('calculate'), resource ('great circle distance'), and method ('Haversine formula'), which is precise. However, it does not explicitly differentiate from sibling tools like 'geom_distance' or 'geom_great_circle_distance', which might offer similar functionality, so it lacks sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: trigonometry, Category: applications'), but this does not indicate specific use cases, prerequisites, or exclusions. Without explicit when-to-use or alternative tool references, the agent has minimal guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool counts partitions with distinct parts, implying a read-only operation, but doesn't mention computational limits (e.g., performance for large n), error handling, or output format. For a tool with zero annotation coverage, this is a significant gap in behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the core functionality in one clear sentence, followed by domain and category in parentheses. Every word earns its place, with no redundancy or unnecessary elaboration, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical partition counting), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't explain the return value (e.g., integer count), handle edge cases, or provide usage examples. For a tool with these contextual gaps, more detail is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, so the schema provides no semantic information. The description adds minimal context by implying 'n' is the integer to partition, but doesn't specify constraints (e.g., n must be non-negative) or examples. This partially compensates but leaves key details undocumented, aligning with the baseline for low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Count partitions of n into distinct parts (no repeated values).' It specifies the verb ('count'), resource ('partitions of n'), and constraint ('distinct parts, no repeated values'), making the operation unambiguous. However, it doesn't differentiate from sibling tools like 'partition_count' or 'restricted_partitions', which likely handle different partition types, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('partitions'), but doesn't specify prerequisites, typical use cases, or comparisons to sibling tools such as 'partition_count' or 'restricted_partitions'. This lack of context leaves the agent without clear usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a value but doesn't disclose behavioral traits such as input validation (e.g., whether 'n' must be non-negative), error handling, performance characteristics, or output format. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence stating the purpose, followed by domain/category context. Every word earns its place with no redundancy or unnecessary elaboration, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and minimal parameter documentation, the description is incomplete. It doesn't cover what a dodecahedral number is, the formula used, output format, or error conditions. For a tool with no structured support, more context is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description doesn't add any parameter semantics beyond the input schema. With 0% schema description coverage and one parameter ('n'), the schema only indicates it's an integer. The description doesn't explain what 'n' represents (e.g., index, order) or any constraints. However, since there's only one parameter and the purpose is clear, the baseline is 3, but it doesn't compensate for the lack of schema details.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth dodecahedral number.' It specifies the verb ('Calculate') and resource ('dodecahedral number'), and the domain/category context helps distinguish it from siblings. However, it doesn't explicitly differentiate from similar figurate number tools (e.g., 'icosahedral_number' or 'tetrahedral_number') in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't indicate specific use cases, prerequisites, or comparisons to sibling tools like 'icosahedral_number' or 'polygonal_number'. The agent must infer usage from the name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe output format, performance characteristics, error handling, or computational limits. For a tool with no annotations, this is a significant gap in transparency about how it behaves when invoked.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core functionality, and the second adds domain/category context. There's no wasted verbiage, and every word contributes to understanding the tool's purpose efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what Dudeney numbers are, how results are returned, or any limitations. For a tool that likely generates a list of numbers, more context is needed to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions the 'limit' parameter, which aligns with the single required parameter in the schema. However, schema description coverage is 0%, and the description doesn't add details like valid ranges, units, or examples. It provides basic semantics but doesn't compensate for the lack of schema documentation, meeting the baseline for minimal parameter information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all Dudeney numbers up to limit.' It specifies the verb ('Find'), resource ('Dudeney numbers'), and scope ('up to limit'). However, it doesn't differentiate from siblings like 'armstrong_numbers' or 'narcissistic_numbers' beyond the domain/category tags, which is why it doesn't reach a perfect 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but doesn't specify use cases, prerequisites, or compare it to similar tools like 'armstrong_numbers' or 'happy_numbers' in the sibling list. This leaves the agent with minimal context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'high-precision arithmetic', hinting at computational intensity, but fails to detail critical aspects: performance expectations (e.g., time/complexity for high precision), error handling (e.g., invalid precision values), or output format (e.g., string vs. number). For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with no wasted words. The first sentence directly states the tool's function, and the parenthetical adds domain context efficiently. Every part earns its place, making it easy to parse quickly without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical constant generation with precision control), lack of annotations, and no output schema, the description is insufficient. It doesn't explain the return value (e.g., a string of digits, a number), error conditions, or performance implications. For a tool that likely involves computational trade-offs, more context is needed to use it effectively, resulting in a low score.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('precision') with 0% description coverage, so the description must compensate. It adds meaning by specifying that precision controls the generation of 'e digits', implying it determines the number of decimal places or digits output. However, it doesn't clarify units (e.g., decimal places vs. total digits), valid ranges, or default behavior, leaving some ambiguity. Given the low schema coverage, this is a minimal but adequate explanation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate e digits to specified precision using high-precision arithmetic.' It specifies the verb ('Generate'), resource ('e digits'), and method ('high-precision arithmetic'), making the function unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'e' or 'compute_e_series', which could provide similar functionality, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: arithmetic, Category: mathematical_constants'), but this is generic and doesn't help distinguish it from siblings like 'e' or 'compute_e_series'. There are no explicit instructions on prerequisites, limitations, or scenarios favoring this tool over others.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the algorithm ('greedy algorithm') but lacks critical details: it doesn't specify input constraints (e.g., valid fraction ranges), output format, error handling, performance characteristics, or whether the operation is deterministic. For a computational tool with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence directly states the tool's purpose and method, and the second adds domain/category context without redundancy. Every word serves a purpose, making it efficient and easy to parse for an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of fraction decomposition and the lack of annotations, output schema, and low schema description coverage, the description is incomplete. It doesn't address input validation, output structure, algorithmic limitations, or error cases. For a mathematical tool with two required parameters, more context is needed to ensure reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate. It implies parameters for numerator and denominator by mentioning 'a fraction', but doesn't explicitly name them or explain their roles (e.g., that they must be integers, with denominator non-zero). The description adds minimal value beyond the schema's property names, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Decompose a fraction into Egyptian fractions using greedy algorithm.' It specifies the verb ('decompose'), resource ('a fraction'), and method ('greedy algorithm'), making the intent unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'egyptian_expansion_lengths' or 'shortest_egyptian_fraction', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('egyptian_fractions'), but offers no explicit advice on when to use this tool versus alternatives like 'egyptian_fraction_lcm' or 'fibonacci_greedy_egyptian'. There's no mention of prerequisites, constraints, or typical use cases, leaving the agent with insufficient context for optimal selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the mathematical operation but doesn't mention important behavioral aspects: input constraints (e.g., n must be non-negative integer, potential overflow for large n), error handling, performance characteristics, or return format. The description is mathematically correct but operationally incomplete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in two parts: the mathematical definition and domain/category metadata. Both sentences earn their place - the first defines the operation, the second provides classification. It's appropriately sized for a simple mathematical function, though it could be slightly more front-loaded with usage context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical computation tool with no annotations and no output schema, the description is insufficient. It explains what factorial is mathematically but doesn't cover: input validation (what happens with negative n?), output format (integer, potential overflow), error conditions, or performance considerations. The context signals show 1 parameter with 0% schema coverage - the description doesn't fully compensate for these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage (just 'n' as integer). The description adds the mathematical meaning of 'n' in the factorial formula, which provides essential semantic context beyond the bare schema. However, it doesn't specify constraints like n ≥ 0 or handling of edge cases (n=0, negative n). Given the low schema coverage, the description partially compensates but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the mathematical operation: 'Calculate factorial n! = n × (n-1) × ... × 2 × 1.' It specifies the verb ('calculate') and resource ('factorial') with the mathematical definition. However, it doesn't explicitly differentiate from sibling tools like 'double_factorial' or 'subfactorial', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: basic_sequences' which gives some context but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'double_factorial' or 'fibonacci'. There's no explicit when-to-use or when-not-to-use information.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates numbers but lacks behavioral details: it doesn't specify output format (e.g., list of integers), handling of large indices (potential overflow), performance characteristics, or error conditions (e.g., negative limits). The description is minimal and misses key operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence directly states the tool's function with the mathematical formula, followed by domain/category tags. There is no wasted text, and every part contributes to understanding the tool's purpose efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical computation with potential for large numbers), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address output format, error handling, or practical constraints (e.g., index limits due to computational limits). The domain/category tags add minimal context but don't compensate for these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds some semantics: it clarifies that 'limit' refers to an 'index limit' for generating Fermat numbers up to that index. However, it doesn't specify valid ranges (e.g., non-negative integers), default behavior, or examples. With one parameter, the baseline is 4, but the description only partially compensates for the lack of schema details.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate Fermat numbers F_n = 2^(2^n) + 1 up to index limit.' It specifies the mathematical formula and the action (generate), but does not differentiate from siblings like 'fermat_primality_check' or 'known_fermat_primes', which are related but distinct tools. The domain/category tags add context but aren't part of the core purpose statement.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives is provided. The description mentions a 'limit' parameter but doesn't explain when to choose this over other Fermat-related tools (e.g., 'fermat_primality_check' for testing primality). Usage is implied by the tool's name and formula, but no context or exclusions are stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('efficient matrix exponentiation') but does not describe key behaviors such as input constraints (e.g., n must be non-negative, integer limits), performance characteristics (e.g., time complexity), error handling, or output format. For a computational tool with no annotation coverage, this lack of detail is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and method. There is no wasted verbiage, and the parenthetical domain/category adds useful metadata without cluttering the core message. It efficiently communicates essential information in minimal space.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on input constraints (e.g., n must be non-negative), behavioral traits (e.g., performance, error handling), and output specifics (e.g., integer result, potential overflow). For a tool that performs mathematical calculations, more context is needed to ensure correct and safe usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds minimal semantics by implying 'n' represents the position in the Fibonacci sequence ('nth Fibonacci number'), but it does not elaborate on valid ranges, constraints, or examples. Since schema coverage is low, the description partially compensates but falls short of fully clarifying parameter meaning.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Fibonacci number using efficient matrix exponentiation.' It specifies the verb ('calculate'), resource ('nth Fibonacci number'), and method ('efficient matrix exponentiation'). However, it does not explicitly differentiate from sibling tools like 'fibonacci_sequence' or 'binet_formula' (which also compute Fibonacci-related values), leaving room for ambiguity about when to choose this specific tool.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the method ('efficient matrix exponentiation') but does not specify scenarios where this is preferable (e.g., for large n, performance considerations) or when other Fibonacci-related tools might be more appropriate. Without such context, users must infer usage from the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the action ('find all amicable number pairs') but does not describe key behaviors such as output format (e.g., list of pairs, JSON structure), performance characteristics (e.g., time complexity for large limits), error handling, or any side effects. This leaves significant gaps for an agent to understand how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain and category in parentheses are slightly redundant but not wasteful. It avoids unnecessary elaboration, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It does not explain what the tool returns (e.g., list of pairs, error messages) or behavioral aspects like performance limits. For a tool with no structured metadata, the description should provide more context to be fully helpful, but it falls short.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds minimal semantics beyond the input schema. It mentions 'up to limit,' which clarifies the parameter's role but does not provide details like valid ranges, units, or examples (e.g., must be positive integer). With 0% schema description coverage and only one parameter, this is adequate but not informative, aligning with the baseline expectation for such coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all amicable number pairs up to limit.' It specifies the verb ('find'), resource ('amicable number pairs'), and scope ('up to limit'), which is clear and specific. However, it does not explicitly differentiate from sibling tools like 'is_amicable_number' or other number-theoretic tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context about prerequisites, when-not-to-use scenarios, or comparisons to sibling tools such as 'is_amicable_number' or 'amicable_numbers' (if they existed). The domain and category tags ('arithmetic, special_numbers') are too generic to offer meaningful usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the tool is 'useful for pattern analysis' but doesn't disclose critical behavioral traits: what format the differences are returned in (array of numbers?), whether the input sequence must be numeric (schema allows strings), what happens with invalid inputs, or any limitations. The description adds minimal behavioral context beyond the basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences and a parenthetical. The first sentence states the core purpose, the second provides usage context, and the parenthetical adds domain information. No wasted words, though it could be more front-loaded with critical details about parameter expectations.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and many sibling tools, the description is incomplete. It doesn't explain what the tool returns, how differences are calculated (subtraction? absolute difference?), input requirements, or error handling. For a tool with mathematical operations, this leaves significant gaps for an AI agent to use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'sequence' but doesn't explain what constitutes a valid sequence (numbers? strings that represent numbers?), expected length, or format. The description adds no parameter details beyond what's implied by the tool name, leaving the single parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the differences between consecutive terms in a sequence.' It specifies the verb ('find') and resource ('differences'), and the parenthetical adds domain context ('arithmetic, general'). However, it doesn't explicitly differentiate from sibling tools like 'differencing' or 'gap_analysis' that might have overlapping functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides some usage context with 'Useful for pattern analysis' and domain hints, but doesn't explicitly state when to use this tool versus alternatives. With many sibling tools (like 'differencing', 'gap_analysis', 'arithmetic_sequence'), there's no guidance on when this specific tool is preferred or what distinguishes it from similar operations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'generates' Ford circles, implying a computational or output-producing operation, but does not describe what the output looks like (e.g., graphical data, coordinates, or mathematical representations), any performance considerations, or error conditions. For a tool with no annotations and no output schema, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage or redundancy, making it efficient for quick comprehension. The parenthetical domain and category add useful metadata without cluttering the core message.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of generating Ford circles (a mathematical visualization tool), the description is insufficient. There are no annotations, no output schema, and minimal parameter guidance. The description does not explain what Ford circles are, what the output entails, or how to interpret results. For a tool that likely produces structured or graphical data, this lack of context makes it incomplete for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, and the description does not add any parameter-specific information. It mentions 'F_n' (Farey sequence of order n), which implicitly relates to the parameter, but does not explain the meaning of 'n' (e.g., that it's a positive integer defining the sequence order) or constraints. With low schema coverage, the description provides minimal compensation, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate Ford circles for fractions in Farey sequence F_n.' It specifies the verb ('Generate'), resource ('Ford circles'), and domain context ('fractions in Farey sequence F_n'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'ford_circle_properties' or 'farey_sequence', which are related but distinct, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), but does not specify prerequisites, typical use cases, or comparisons to siblings like 'ford_circle_properties' or 'farey_sequence'. This lack of explicit when-to-use or when-not-to-use information limits its utility for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates frequency but does not describe how it handles invalid inputs (e.g., negative periods), units (e.g., seconds for period, Hz for frequency), or error conditions. This lack of detail makes it difficult for an agent to predict behavior accurately.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the purpose in a single sentence. It efficiently includes domain and category information without unnecessary details. However, it could be slightly improved by integrating usage hints to enhance clarity without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical calculation with one parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not explain the calculation method (e.g., frequency = 1/period), return values, or error handling, leaving significant gaps for an agent to invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('period') with 0% description coverage, so the description must compensate. It mentions 'period' but does not explain its meaning, units, or constraints (e.g., must be positive). The description adds minimal semantics beyond the schema, so it meets the baseline for low coverage but doesn't fully clarify parameter usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate frequency from period and related wave properties.' It specifies the verb ('calculate'), resource ('frequency'), and input ('period'), and mentions the domain ('trigonometry, wave_analysis'). However, it does not explicitly differentiate from sibling tools like 'angular_velocity_from_period_or_frequency' or 'wave_amplitude_analysis', which could cause confusion in selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if it's for simple frequency calculation or when other wave properties are needed, leaving usage ambiguous.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the algorithm ('Euclidean algorithm'), which adds some behavioral context, but does not disclose other traits such as error handling, input constraints (e.g., negative numbers), performance characteristics, or output format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and method, followed by domain and category tags. There is no wasted verbiage, and every element serves a clear purpose, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical function with no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on behavior, parameter semantics, return values, and error conditions. While concise, it does not provide enough context for an agent to fully understand and invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'a' and 'b' documented only as integers. The description does not add any semantic details about these parameters, such as their meaning, valid ranges, or examples. Since the schema coverage is low, the description fails to compensate, resulting in minimal added value beyond the basic schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the Greatest Common Divisor (GCD) of two integers using Euclidean algorithm.' It specifies the verb ('Calculate'), resource ('GCD'), and method ('Euclidean algorithm'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'extended_gcd' or 'gcd' variants, which slightly limits its distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('number_theory'), but does not specify scenarios, prerequisites, or comparisons to sibling tools like 'extended_gcd' or 'is_coprime'. This leaves the agent without explicit usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe how it behaves: no information on performance characteristics (e.g., computational complexity for large n), output format (e.g., list of lists, sorted order), error handling (e.g., for negative n), or any side effects. The description is minimal and lacks behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise—a single sentence plus domain/category tags. It's front-loaded with the core purpose. However, the domain/category note might be redundant if the tool name is clear, and the brevity comes at the cost of completeness, but it's efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (generating all partitions is computationally intensive), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address output format, performance limits, or error conditions. For a tool with potential high computational cost, more context is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the schema provides no semantic information. The description adds minimal context by naming the parameter 'n' and implying it's an integer for partition generation, but doesn't explain its meaning (e.g., 'n is the integer to partition, must be non-negative') or constraints. This partially compensates but leaves gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate all integer partitions of n.' It specifies the verb ('generate'), resource ('integer partitions'), and domain context ('arithmetic, Category: partitions'). However, it doesn't explicitly differentiate from sibling tools like 'distinct_partitions' or 'restricted_partitions', which are related but distinct partition functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't explain when to choose this over similar partition tools (e.g., 'distinct_partitions' for partitions without repetition, 'restricted_partitions' for constraints). There's no mention of prerequisites, limitations, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe any behavioral traits like error handling, precision, or output format. This is a significant gap for a tool with no structured annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted text, and the domain/category information is efficiently included without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, no output schema, and minimal parameter information, the description is incomplete. It does not address key contextual aspects like the return value (e.g., area as a number), units, or error conditions, which are essential for a calculation tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not add any parameter semantics beyond the input schema, which has 0% description coverage. However, with only one parameter ('radius'), the baseline is 4, but since the description provides no additional meaning (e.g., units, constraints), it does not fully compensate, resulting in a score of 3.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Calculate') and resource ('area of a circle'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'geom_circle_circumference' or 'geom_polygon_area', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: geometry, Category: general', but this is generic context rather than explicit usage instructions, such as when to prefer this over other area calculation tools or geometric functions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full behavioral disclosure burden. It states what the tool does but doesn't describe any behavioral traits: no information about error handling, precision, units, or what happens with invalid inputs. The description is purely functional without operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence) and front-loaded with the core purpose. Every word earns its place, and there's no redundant information. The domain/category annotation is efficiently appended without disrupting the main message.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the tool returns, what units are involved, error conditions, or mathematical assumptions. For a calculation tool with one parameter, more context would be helpful for proper agent usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description needs to compensate. It mentions 'radius' implicitly through the calculation context but doesn't provide any semantic details about the parameter. The baseline is 3 since the schema covers the parameter structure, but the description adds minimal value beyond what's obvious from the tool name.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Calculate') and resource ('circumference of a circle'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'geom_circle_area' or 'geom_circle_intersection' beyond the different calculation type.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. There's no mention of when this calculation is appropriate, what inputs are expected beyond the schema, or how it differs from related geometry tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the infinite series capability for |r| < 1, which is useful context about the tool's behavior. However, it fails to describe critical aspects: whether it handles edge cases (e.g., r = 1, negative terms), what happens with invalid inputs (e.g., non-numeric values), the return format (e.g., number, error message), or performance considerations. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the purpose. The second sentence adds useful context about infinite series, and the parenthetical note ('Domain: arithmetic, Category: general') is brief though not highly informative. There is no wasted text, and it efficiently conveys core information in two sentences.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical calculation tool with 3 parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on parameter meanings, error handling, return values, and edge cases. While it hints at infinite series behavior, it doesn't provide enough context for reliable use, especially compared to well-documented siblings like 'arithmetic_sum' or 'geometric_sequence'.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, meaning the schema provides no semantic information. The description does not mention any parameters by name or explain their roles (e.g., 'first_term' as the initial value, 'common_ratio' as the multiplier, 'num_terms' as optional for finite sums). It only implies the use of a common ratio ('r') for infinite sums. With low schema coverage, the description fails to compensate adequately, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sum of a geometric sequence.' It specifies the verb ('calculate') and resource ('sum of a geometric sequence'), and distinguishes it from siblings like 'geometric_sequence' (which generates terms) and 'geometric_series' (which might refer to series representation). However, it doesn't explicitly differentiate from 'series_sum' or 'power_series_sum', which could also compute sums, though those are more general.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides some implied usage context: it mentions 'For |r| < 1, can calculate infinite series sum,' which hints at when to use it for infinite vs. finite sums. However, it lacks explicit guidance on when to choose this tool over alternatives like 'arithmetic_sum' or 'series_sum', and doesn't specify prerequisites or exclusions (e.g., handling of divergent series). The mention of 'Domain: arithmetic, Category: general' is vague and doesn't offer practical usage rules.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does conceptually but lacks behavioral details: it doesn't specify the output format (e.g., boolean result, error handling for invalid inputs), performance characteristics, or any side effects. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in one sentence and adding domain context in parentheses. There is no wasted verbiage, and the structure is clear. However, it could be slightly more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical conjecture-checking tool, no annotations, no output schema, and low schema description coverage, the description is incomplete. It lacks details on input validation, output format, error conditions, and how it differs from sibling tools. This makes it inadequate for an agent to use the tool effectively without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description implies 'n' should be an even integer > 2 but does not explicitly state this requirement or explain the parameter's role. It adds minimal semantic context beyond the schema, so the baseline score of 3 is appropriate given the schema's lack of descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: checking the Goldbach conjecture for a given even integer. It specifies the mathematical domain (arithmetic) and category (additive_number_theory), which helps contextualize the tool. However, it does not explicitly differentiate from sibling tools like 'goldbach_pairs' or 'weak_goldbach_check', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the mathematical context but does not specify prerequisites, constraints (e.g., input must be an even integer > 2), or compare it to siblings like 'goldbach_pairs' (which might return the prime pairs) or 'weak_goldbach_check' (for odd numbers). This leaves the agent without clear usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks details on performance (e.g., computational limits for large inputs), error handling (e.g., what happens if 'n' is odd), or output format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information in parentheses is brief and relevant, adding context without unnecessary elaboration. Every part of the description earns its place efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (involving number theory computations), lack of annotations, no output schema, and low schema description coverage, the description is insufficient. It does not cover behavioral aspects like performance limits, error conditions, or what the output looks like (e.g., list of pairs). For a tool with these gaps, more detail is needed to be complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds meaning by specifying that 'n' must be an even number, which is crucial context not in the schema. However, it does not explain the range or constraints (e.g., minimum value, handling of non-integers), leaving some ambiguity. Given the low schema coverage, this partial compensation earns a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all Goldbach pairs for an even number.' It specifies the verb ('Find'), resource ('Goldbach pairs'), and constraint ('for an even number'). However, it does not explicitly differentiate from sibling tools like 'goldbach_conjecture_check', which might have overlapping functionality but isn't directly distinguished here.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('additive_number_theory'), but does not specify prerequisites, when-not-to-use scenarios, or refer to sibling tools like 'goldbach_conjecture_check' for comparison. This leaves the agent without clear usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates a continued fraction expansion but does not explain what the output looks like (e.g., format, length, precision), whether it's deterministic, or if there are any limitations (e.g., maximum terms). For a computational tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core functionality in the first sentence. The parenthetical metadata ('Domain: arithmetic, Category: continued_fractions') is slightly extraneous but not wasteful. Overall, it is efficiently structured with no redundant phrasing.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It does not explain the output format, behavioral traits, or usage context, which are critical for an agent to invoke it correctly. The description alone is insufficient for effective tool use without external assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('terms') with 0% description coverage, so the schema provides no semantic context. The description does not mention parameters at all, failing to compensate for the schema's lack of documentation. However, since there is only one parameter and its purpose (number of terms) is somewhat inferable from the tool's name and description, it meets the baseline for minimal viability without adding value beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate continued fraction expansion of golden ratio φ.' It specifies the verb ('Generate'), resource ('continued fraction expansion'), and target ('golden ratio φ'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'continued_fraction_golden_ratio' or 'compute_golden_ratio_continued_fraction', which appear to serve similar purposes, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a 'Domain' and 'Category' in parentheses, but this is generic metadata rather than practical usage advice. There is no indication of prerequisites, constraints, or comparisons to sibling tools like 'continued_fraction_golden_ratio', leaving the agent without clear direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the conversion action but does not describe any behavioral traits such as error handling, input validation, output format, or computational limits. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with zero wasted words. The first sentence directly states the tool's purpose, and the additional domain/category information is efficiently appended. Every sentence earns its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema description coverage, the description is incomplete. It lacks details on behavior, parameter semantics, output format, and usage context. For a conversion tool, this leaves critical gaps in understanding how to invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds minimal value by naming the parameter ('gradians'). It does not explain the parameter's meaning, units, constraints, or conversion formula. With one undocumented parameter, the description partially compensates but remains inadequate for full clarity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert gradians to degrees.' It specifies the verb ('convert'), resource ('gradians'), and target ('degrees'), and includes domain/category context. However, it does not explicitly differentiate from its sibling 'degrees_to_gradians' or other angle conversion tools, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('angle_conversion'), but does not specify scenarios, prerequisites, or compare with sibling tools like 'degrees_to_gradians' or 'convert_angle', leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but lacks behavioral details such as input validation (e.g., handling negative values or non-numeric inputs), output format, error handling, or performance characteristics. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and context. There is no wasted verbiage, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It does not cover behavioral aspects, parameter details beyond naming, or output information. For a simple conversion tool, more context on input handling and result format would improve completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, but the description adds minimal value by naming the parameter ('gradians'). However, it does not explain the parameter's semantics (e.g., units, expected range, or conversion formula). With one parameter and low schema coverage, the description partially compensates but leaves key details undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting gradians to radians, specifying the domain (trigonometry) and category (angle_conversion). It uses a specific verb ('Convert') and resource ('gradians'), but does not explicitly differentiate from sibling tools like 'degrees_to_radians' or 'radians_to_gradians', which are similar angle conversion tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or compare it to sibling tools like 'degrees_to_radians' or 'gradians_to_degrees', leaving the agent without usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds happy numbers up to a limit, implying a read-only operation that returns a list, but does not disclose critical behaviors such as performance characteristics (e.g., computational complexity for large limits), error handling (e.g., invalid limits), output format, or any side effects. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Find all happy numbers up to a limit.' The additional domain and category in parentheses are efficient and relevant. Every word earns its place, with no redundancy or unnecessary elaboration, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (iterative sequence generation), lack of annotations, no output schema, and low schema description coverage, the description is incomplete. It does not explain what happy numbers are, the return format (e.g., list of integers), handling of edge cases, or performance considerations. For a tool that likely involves computation and returns structured data, this leaves the agent with insufficient context to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one required parameter 'limit' of type integer. The description adds minimal semantics by mentioning 'up to a limit,' which clarifies the parameter's role but does not specify constraints (e.g., positive integers, maximum value) or examples. Since schema coverage is low, the description compensates slightly but not fully, meeting the baseline for marginal added value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all happy numbers up to a limit.' It specifies the verb ('Find'), resource ('happy numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_happy_number' (which tests a single number), though the domain/category context helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('iterative_sequences'), but does not specify prerequisites, constraints, or when to choose it over similar tools like 'is_happy_number' or 'happy_numbers' vs. other number sequence tools. This leaves the agent without explicit usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full behavioral disclosure burden. It states the tool 'returns as fraction,' which is useful behavioral information about output format. However, it doesn't mention computational characteristics (e.g., performance with large n, precision limitations, memory usage), error conditions, or whether n must be positive. For a mathematical tool with no annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core functionality in the first clause. The parenthetical domain/category information is secondary but potentially useful. No wasted words, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for the single parameter, the description is incomplete. It explains what the tool does and the return format but lacks crucial context: parameter semantics, computational behavior, error handling, and differentiation from sibling tools. For a mathematical calculation tool, users need more guidance about valid inputs and expected behavior.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% description coverage. The description doesn't explicitly mention the parameter or add any semantic context beyond what's implied by 'harmonic number' (n is typically a positive integer index). Since schema coverage is 0%, the description should compensate more by explaining parameter meaning, constraints, or examples, but it only provides minimal implicit context.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate harmonic number using exact fractions (returns as fraction).' It specifies the verb ('calculate'), resource ('harmonic number'), and method ('exact fractions'), distinguishing it from generic harmonic number calculations. However, it doesn't explicitly differentiate from sibling tools like 'harmonic_number' or 'harmonic_partial_sum', which slightly reduces clarity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('harmonic_series'), but doesn't explain when to choose this exact-fraction method over other harmonic number tools or mathematical approaches. No explicit when/when-not instructions or sibling tool comparisons are present.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the conversion action without detailing error handling (e.g., invalid hex input), output format, or performance characteristics. This is a significant gap for a tool with no structured safety or behavioral hints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and it efficiently communicates the core functionality without unnecessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, output schema, and low schema description coverage, the description is incomplete. It does not address behavioral aspects like error handling or output format, and while the tool is simple, more context would help the agent use it correctly, especially with no sibling differentiation or parameter guidance.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'hex_str' of type string. The description does not add any parameter-specific semantics beyond implying it expects a hexadecimal string. It does not clarify format (e.g., case sensitivity, prefix like '0x'), examples, or constraints, leaving the schema to define the parameter minimally.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting hexadecimal to decimal numbers, specifying the domain (arithmetic) and category (number_systems). It uses a specific verb ('convert') and identifies the resource (hexadecimal number). However, it does not explicitly differentiate from sibling tools like 'binary_to_decimal' or 'octal_to_decimal', though the naming implies the distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or compare it to related sibling tools (e.g., 'binary_to_decimal', 'decimal_to_hexadecimal'), leaving the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions that it calculates 'all hyperbolic functions simultaneously', which implies a batch operation, but it does not disclose details like what specific functions are included, the output format, error handling for invalid inputs, or computational constraints. This leaves significant gaps in understanding the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with two sentences that directly state the purpose and context. It is front-loaded with the main action and avoids unnecessary details, though it could be slightly more informative without losing efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of calculating multiple hyperbolic functions, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on what functions are computed, the return structure, error conditions, or usage examples, making it inadequate for effective tool selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description mentions 'a given x' but does not add meaning beyond the schema (e.g., valid ranges, units, or examples). Since schema coverage is low, the description should compensate more but only provides basic context, resulting in a baseline score due to the single parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('calculate') and resource ('all hyperbolic functions for a given x simultaneously'), making the purpose specific and understandable. However, it does not explicitly distinguish this tool from sibling tools like 'sinh', 'cosh', 'tanh', etc., which calculate individual hyperbolic functions, so it doesn't fully differentiate from siblings.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance by mentioning the domain ('trigonometry') and category ('hyperbolic'), but it does not specify when to use this tool versus alternatives like individual hyperbolic function tools (e.g., 'sinh', 'cosh') or other mathematical tools. No explicit when/when-not or alternative recommendations are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions accuracy advantage over trapezoid rule, which is useful behavioral context. However, it doesn't disclose important traits: error behavior, computational complexity, handling of edge cases (e.g., singularities), convergence properties, or what happens with invalid inputs. For a numerical integration tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise - one sentence stating the core purpose with a parenthetical accuracy comparison and domain tags. It's front-loaded with the main functionality. The domain/category tags might be slightly redundant but don't significantly detract from efficiency. No wasted words or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a numerical integration tool with 4 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain parameter meanings, return values, error conditions, or practical usage considerations. The accuracy comparison adds some value, but doesn't compensate for the missing information needed to use the tool effectively. The domain tags provide minimal contextual framing.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so parameters are undocumented in the schema. The description provides no information about the four parameters (func, a, b, n_steps). It doesn't explain what 'func' should contain (mathematical expression format), that 'a' and 'b' are integration limits, what 'n_steps' controls, or the default value. The description fails to compensate for the complete lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate definite integral using Simpson's rule'. It specifies the mathematical operation (calculate definite integral) and the method (Simpson's rule), and distinguishes it from trapezoid rule by noting it's 'more accurate than trapezoid'. However, it doesn't explicitly differentiate from sibling integration tools like integrate_midpoint or integrate_trapezoid beyond the accuracy comparison.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies when to use this tool through the accuracy comparison ('more accurate than trapezoid'), suggesting it's preferred over trapezoid rule for better precision. The domain/category tags ('Domain: calculus, Category: general') provide some context about applicability. However, there's no explicit guidance on when to choose Simpson's rule over other integration methods available as siblings (midpoint, trapezoid), nor any prerequisites or limitations mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation method but does not describe key behavioral traits such as error handling, numerical precision, performance characteristics (e.g., computational cost with n_steps), or what the output looks like (e.g., numeric result, error estimate). For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first phrase. The additional context ('Domain: calculus, Category: general') is brief and relevant. There is no wasted verbiage, making it efficient, though it could be slightly more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (numerical integration with 4 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral details, or output format, leaving significant gaps for an AI agent to understand and invoke the tool correctly. The minimal description is inadequate for the tool's requirements.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for undocumented parameters. It does not add any meaning beyond the schema, failing to explain what 'func' represents (e.g., mathematical expression string), the roles of 'a' and 'b' as integration limits, or the purpose of 'n_steps' (e.g., number of trapezoids, default 1000). With 4 parameters and no schema descriptions, the description provides no parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate definite integral using the trapezoidal rule', specifying the verb ('calculate'), resource ('definite integral'), and method ('trapezoidal rule'). It distinguishes from siblings like 'integrate_midpoint' and 'integrate_simpson' by naming the specific numerical integration method. However, it does not explicitly differentiate from all siblings (e.g., general calculus tools), keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context with 'Domain: calculus, Category: general', suggesting it's for calculus problems. However, it lacks explicit guidance on when to use this tool versus alternatives like 'integrate_midpoint' or 'integrate_simpson', and does not mention prerequisites or exclusions. The context is implied but not detailed enough for full clarity.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks for Carmichael numbers but does not describe what happens for invalid inputs (e.g., negative n), performance characteristics, error handling, or the return format (e.g., boolean, string). This leaves significant gaps in understanding how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no wasted text, and every element serves to inform the tool's function efficiently, making it easy for an AI agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical check with no output schema and 0% schema description coverage), the description is insufficiently complete. It lacks details on input validation, output format, error conditions, and how it differs from similar tools. Without annotations or an output schema, the description should provide more context to ensure the agent can use it correctly, but it does not.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds minimal semantics by specifying 'n' as the input to check, but does not explain what 'n' represents (e.g., a positive integer, composite number) or any constraints. Given the low schema coverage, the description partially compensates but does not fully clarify parameter meaning, aligning with the baseline for this scenario.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if n is a Carmichael number (absolute Fermat pseudoprime)'. It specifies the verb ('Check'), resource ('n'), and domain context ('arithmetic, Category: pseudoprimes'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'carmichael_number_test' or 'is_fermat_pseudoprime', which might serve similar purposes, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify prerequisites, input constraints (e.g., n must be integer > 2), or compare it to siblings like 'carmichael_number_test' or primality tests. This lack of contextual usage information limits its effectiveness for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a 'Check', implying a read-only operation, but does not elaborate on computational complexity, error handling, or output format. For a mathematical verification tool with zero annotation coverage, this is insufficient to inform the agent adequately.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise, consisting of a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted verbiage, and the information is front-loaded, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It does not explain what a Fermat pseudoprime is, the mathematical condition being checked, or the return value (e.g., boolean or detailed result). For a specialized mathematical tool with no structured support, more explanatory context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with parameters 'n' and 'a' documented only by type. The description adds minimal context by naming the parameters in the phrase 'n is a Fermat pseudoprime to base a', which clarifies their roles but does not provide constraints, typical values, or examples. This partial compensation justifies a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if n is a Fermat pseudoprime to base a.' It specifies the verb ('Check') and the mathematical concept, and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'fermat_primality_check' or 'fermat_primality_test', which might have overlapping functionality, so it misses the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks information on prerequisites, typical use cases, or comparisons to sibling tools such as 'fermat_primality_check' or 'strong_pseudoprime_test'. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks Fibonacci membership but doesn't describe what happens with invalid inputs (e.g., negative numbers), performance characteristics, error handling, or the return format (e.g., boolean, string). For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category context. Every word earns its place with zero redundancy or fluff, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is incomplete. It lacks details on return values (e.g., boolean result), error conditions, and usage context. While minimalism can be appropriate, for a tool with no structured metadata, the description should provide more operational context to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, documenting only that 'n' is an integer. The description adds no parameter-specific information beyond implying 'n' is the number to check. It doesn't clarify valid ranges (e.g., non-negative?), units, or examples. With low schema coverage, the description compensates minimally, meeting the baseline for adequate but incomplete parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a Fibonacci number.' It specifies the verb ('Check') and resource ('a number'), and the domain/category context helps clarify it's about mathematical sequences. However, it doesn't explicitly differentiate from sibling tools like 'fibonacci' or 'fibonacci_sequence', which might generate or list Fibonacci numbers rather than test membership.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category hints at mathematical contexts, there's no mention of when to choose this over sibling tools like 'fibonacci' (which might generate Fibonacci numbers) or 'is_triangular_number' (a similar membership test for different sequences). No prerequisites, limitations, or typical use cases are specified.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks and shows a sequence, implying a read-only operation, but doesn't detail aspects like error handling (e.g., for invalid inputs), performance characteristics, or output format. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core functionality in a single sentence. The additional domain and category information is brief and doesn't detract from clarity. There's no wasted text, making it efficient, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is adequate but incomplete. It covers the basic purpose but lacks details on usage, parameters, and behavioral traits. Without annotations or an output schema, more context on what 'show the sequence' entails would improve completeness for effective agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('n') with 0% description coverage, so the schema provides no semantic context. The description doesn't add any parameter-specific information beyond implying 'n' is the number to check. It doesn't explain constraints (e.g., positive integers only) or provide examples. Given the low schema coverage, the description compensates minimally, meeting the baseline but not adding substantial value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a Keith number and show the sequence.' It specifies the verb ('check'), resource ('number'), and output ('show the sequence'), making the function unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'keith_numbers' (which likely lists Keith numbers), leaving room for improvement in sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but offers no explicit context, prerequisites, or comparisons to sibling tools (e.g., 'keith_numbers'). This lack of usage instructions limits its effectiveness in guiding the agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does without mentioning any behavioral traits such as performance considerations, error handling, or output format (e.g., returning a boolean). For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single clear sentence followed by domain/category metadata. There is no wasted verbiage, and the core purpose is stated immediately. However, the metadata in parentheses, while informative, could be considered slightly extraneous for tool selection.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is minimally adequate but incomplete. It lacks details on output (e.g., boolean result), error cases, or mathematical definition of pentagonal numbers, which would help users understand the tool's behavior fully. For a basic arithmetic tool, more context would improve usability.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, so the schema provides no semantic information. The description adds minimal context by implying 'n' is the number to check, but does not specify constraints (e.g., integer range, handling of non-integers) or examples. With low schema coverage, the description compensates only partially.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a pentagonal number.' It specifies the verb ('Check') and resource ('pentagonal number'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'pentagonal_number' or 'pentagonal_sequence', which might be related but serve different purposes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context such as prerequisites, typical use cases, or comparisons to sibling tools like 'pentagonal_number' (which might compute pentagonal numbers) or 'is_polygonal_number' (which might be more general). Without this, users must infer usage from the name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool's function but does not disclose behavioral traits such as input constraints (e.g., handling of negative numbers, zero, or large integers), performance characteristics, or error handling. This leaves significant gaps for a mutation-free tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category note is brief and relevant.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is minimal. It lacks details on behavior, edge cases, or output format (e.g., boolean result), which are necessary for an agent to use it correctly. While the tool is straightforward, the description does not provide enough context for reliable invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds no parameter-specific semantics beyond implying 'n' is the number to check. Since schema coverage is low, the description does not compensate by explaining constraints or examples, but the tool is simple with only one parameter, so a baseline 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose ('Check if a number is a power of two') with a specific verb ('Check') and resource ('a number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'nth_power_of_two' or 'powers_of_two', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain and category ('arithmetic, basic_sequences'), but this is too vague to help an agent choose between this and sibling tools like 'is_perfect_square' or 'is_triangular_number' for number property checks.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'checks' a number, implying a read-only operation, but does not specify what the output looks like (e.g., boolean, string), error conditions, or performance characteristics. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Check if a number is a pronic number.' The additional domain/category note is brief and relevant. There is no wasted verbiage, and every word serves a purpose, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, no output schema, and minimal parameter guidance, the description is incomplete. It does not explain what a pronic number is, what the return value signifies, or any edge cases. For a tool that performs a specific mathematical check, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not mention the parameter 'num' at all. However, since there is only one parameter and its type is clear (integer), the baseline is 3. The description does not add any semantic context beyond what the schema minimally provides (e.g., explaining what a 'pronic number' is or valid ranges).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a pronic number.' It specifies the verb ('Check') and the resource ('a pronic number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., other number-checking tools like is_triangular_number), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), but this is too vague to help an agent choose between similar sibling tools like is_triangular_number or is_pentagonal_number. No explicit when/when-not instructions or named alternatives are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('Check if a number is a triangular number') without describing how it behaves: e.g., what input range is valid, whether it handles negative numbers, what the output looks like (likely boolean), or any error conditions. For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category metadata. There is zero wasted verbiage, and every word earns its place. The structure is clear and efficient, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is incomplete. It doesn't explain the return value (likely boolean), input constraints, or error handling. While the tool is straightforward, the description lacks necessary context for reliable invocation, especially with no annotations to fill behavioral gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' of type integer with 0% description coverage. The tool description adds no parameter-specific information beyond implying 'n' is the number to check. Since schema coverage is low, the description doesn't compensate by explaining constraints (e.g., non-negative integers) or examples. However, with only one parameter, the baseline is higher, but the lack of additional semantics keeps it at a minimal viable score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a triangular number.' It specifies the verb ('Check') and resource ('triangular number'), and the domain/category context helps distinguish it from siblings like 'triangular_number' (which likely generates triangular numbers) or 'is_perfect_square' (a different property test). However, it doesn't explicitly differentiate from 'triangular_numbers' or 'triangular_sequence' in the sibling list, which could be ambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('basic_sequences'), but this is generic context rather than specific usage instructions. There's no mention of prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'triangular_number' or 'triangular_numbers'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool checks validity within a range (2-36), implying a read-only, non-destructive operation, but lacks details on error handling, return format, or performance characteristics. For a tool with no annotations, this is insufficient behavioral disclosure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: a single sentence directly states the tool's purpose and parameter constraint, followed by domain/category tags. Every word earns its place with zero waste, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on return values, error conditions, and behavioral nuances. For a validation tool in a complex sibling set, more context is needed to ensure proper agent usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It clarifies that the 'base' parameter must be 'between 2 and 36,' adding meaningful constraints beyond the schema's generic integer type. However, it does not explain edge cases or validation logic, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a base value is valid (between 2 and 36).' It specifies the verb ('Check'), resource ('base value'), and domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., 'validate_number_in_base'), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('number_systems'), but offers no explicit when-to-use rules, prerequisites, or alternatives. Without clear usage context or differentiation from similar tools, it falls short of adequate guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool 'finds' numbers, implying a read-only operation, but does not disclose behavioral traits such as performance characteristics (e.g., computational complexity for large limits), output format (e.g., list of integers), or error handling (e.g., invalid limit values). The description adds minimal context beyond the basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first. The additional domain and category information in parentheses is brief and relevant. There is no wasted verbiage, though it could be more structured with explicit sections for usage or parameters.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (finding special numbers up to a limit), lack of annotations, no output schema, and low schema coverage, the description is insufficient. It does not explain the return values (e.g., list format), edge cases, or performance considerations, making it incomplete for effective agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('limit') with 0% description coverage. The description adds meaning by specifying 'up to limit', clarifying that the tool returns numbers less than or equal to this value. However, it does not detail constraints (e.g., limit must be positive) or examples, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all Kaprekar numbers up to limit.' It specifies the verb ('Find'), resource ('Kaprekar numbers'), and scope ('up to limit'). However, it does not explicitly differentiate from sibling tools like 'is_kaprekar_number' or 'kaprekar_sequence', which might handle individual checks or sequences differently.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but offers no explicit instructions on prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'is_kaprekar_number' for single-number checks.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds numbers 'up to limit,' implying it returns a list or sequence, but does not describe the output format, performance characteristics, error handling, or any side effects. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose and parameter. There is no wasted verbiage; every word contributes essential information. It is front-loaded with the core functionality, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with one parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not explain what Keith numbers are, the return format, potential performance issues, or error conditions. For a tool with no structured support, more descriptive detail is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions the parameter 'limit' and its role ('up to limit'), but the input schema has 0% description coverage, providing only the type (integer). The description adds basic semantic context (it's an upper bound), but does not specify constraints like minimum value, whether it's inclusive/exclusive, or typical ranges. This partially compensates for the low schema coverage but remains minimal.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all Keith numbers up to limit.' It specifies the verb ('Find'), resource ('Keith numbers'), and scope ('up to limit'), which is a well-defined mathematical operation. However, it does not explicitly differentiate from sibling tools like 'is_keith_number' or 'keith_numbers' (if present elsewhere), though the domain/category tags help.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not indicate prerequisites, typical use cases, or comparisons with related tools (e.g., 'is_keith_number' for checking a single number). The agent must infer usage from context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details like computational complexity, performance expectations for large ranges, error handling for invalid inputs, or output format. This is a significant gap for a tool with mathematical computations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and to the point, with no wasted words. It's front-loaded with the core purpose and includes domain/category context efficiently. However, the lack of additional details makes it feel under-specified rather than optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address key aspects like what the tool returns (e.g., gap size, prime pair), performance considerations, or error cases. For a mathematical tool with potential complexity, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds no parameter semantics beyond implying a range via 'in a given range'. It doesn't explain what 'start' and 'end' represent (e.g., inclusive/exclusive, valid ranges, integer constraints). With low schema coverage, this is inadequate compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the largest prime gap in a given range.' It specifies the verb ('find') and resource ('largest prime gap'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'prime_gap' or 'prime_gaps_analysis' that might handle similar concepts.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't specify scenarios, prerequisites, or comparisons with sibling tools such as 'prime_gap' or 'prime_gaps_analysis'. Users must infer usage from the name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the function definition but does not disclose behavioral traits such as input constraints (e.g., n must be a positive integer), error handling, performance characteristics, or output format. This leaves significant gaps for an agent to understand how to invoke it correctly.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core function definition in a single sentence, followed by domain and category. There is no wasted text, making it efficient, though it could benefit from slightly more detail to improve usability.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical function tool with no annotations, 0% schema coverage, and no output schema, the description is incomplete. It defines the function but lacks essential context such as parameter explanations, usage examples, error conditions, and output details, making it insufficient for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not add any parameter semantics. It mentions 'n' in the function but does not explain its meaning, constraints (e.g., must be a positive integer), or examples. With one undocumented parameter, the description fails to compensate for the lack of schema details.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific mathematical function: 'Calculate the Liouville function λ(n) = (-1)^Ω(n).' It includes the domain (arithmetic) and category (arithmetic_functions), which distinguishes it from siblings like 'mobius_function' or 'big_omega' by specifying the exact formula and context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify use cases, prerequisites, or comparisons to sibling tools like 'mobius_function' or 'big_omega', which are related arithmetic functions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the test is performed but does not disclose behavioral traits such as computational complexity, typical runtime, error handling (e.g., for non-prime 'p'), or output format. For a primality test tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain and category annotations are efficiently appended. There is no wasted verbiage, though it could benefit from additional context without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a primality test, lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It does not explain what the test returns (e.g., boolean result, intermediate steps), performance considerations, or edge cases. For a tool with mathematical significance, more context is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('p') with 0% description coverage, and the tool description adds no parameter semantics. It does not explain what 'p' represents (e.g., exponent in 2^p - 1), valid ranges, or constraints (e.g., must be a prime integer). With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Lucas-Lehmer primality test for Mersenne numbers.' It specifies the exact mathematical test (Lucas-Lehmer primality test) and the target numbers (Mersenne numbers), which distinguishes it from sibling tools like 'aks_primality_test', 'fermat_primality_test', or 'is_mersenne_prime'. The domain and category annotations further clarify its niche in arithmetic/special primes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no explicit guidance on when to use this tool versus alternatives. It does not mention prerequisites (e.g., that 'p' must be prime for Mersenne numbers), nor does it compare it to sibling tools like 'is_mersenne_prime' or general primality tests. The domain/category hints at context but lacks actionable usage rules.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe error handling (e.g., for negative or large 'n'), computational limits, or output format. For a mathematical tool with potential edge cases, this lack of behavioral detail is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence directly states the tool's purpose, followed by domain and category in parentheses. Every word contributes essential information without redundancy, making it highly efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical calculation tool with no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on behavior, output format, error conditions, and usage context. While concise, it does not provide enough information for reliable tool invocation in varied scenarios.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds minimal semantic context by specifying 'nth' and 'L_n', implying 'n' is an index. However, it does not explain valid ranges, constraints, or examples. Given the low schema coverage, the description partially compensates but remains insufficient for full parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Lucas number L_n.' It specifies the verb ('Calculate'), resource ('nth Lucas number'), and mathematical notation ('L_n'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'lucas_sequence' or 'lucas_u_v', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), which hints at context, but does not specify scenarios, prerequisites, or comparisons to siblings like 'fibonacci' or 'lucas_sequence'. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool generates numbers but doesn't disclose behavioral traits: it doesn't mention what 'n' represents (e.g., non-negative integer, maximum value), whether it returns a list or single value, error handling for invalid inputs, or performance characteristics. The description is minimal and lacks critical operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence states the core purpose clearly. The second sentence adds domain/category context efficiently. There's no wasted text, and it's appropriately sized for a simple tool. However, it could be slightly more structured by separating usage notes.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., a list of integers), handle edge cases, or provide examples. For a tool with one parameter but undefined behavior and output, more detail is needed to ensure correct agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'the first n Lucas numbers', implying 'n' is the count of numbers to generate, which adds meaning beyond the schema's bare 'integer' type. However, it doesn't specify constraints (e.g., n >= 0), format, or examples, leaving gaps. With one parameter and low coverage, this provides basic but incomplete semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n Lucas numbers' with a specific verb ('Generate') and resource ('Lucas numbers'). It distinguishes from siblings like 'lucas_number' (singular) and 'lucas_u_v' by specifying it generates a sequence of the first n numbers. However, it doesn't explicitly contrast with 'fibonacci_sequence' which is a closely related recursive sequence.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), but gives no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools like 'fibonacci_sequence' or 'lucas_number'. Usage is implied by the name and purpose alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks critical behavioral details: it doesn't specify the output format (e.g., list of numbers, JSON structure), performance characteristics (e.g., computational limits for large exponents), error handling (e.g., for invalid limits), or whether the limit is inclusive/exclusive. For a tool with no annotations, this leaves significant gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a single sentence that directly states the tool's purpose. The parenthetical domain and category add minor context without unnecessary elaboration. There's no wasted verbiage, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical computation with prime exponents), lack of annotations, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., a list of Mersenne numbers, their values, or just exponents), how results are formatted, or any limitations (e.g., performance with large limits). For a tool with no structured support, more descriptive detail is needed to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions the 'limit' parameter implicitly ('for prime exponents up to limit'), but the input schema has 0% description coverage. The description adds some semantic context by clarifying that 'limit' refers to the maximum prime exponent considered, which is useful beyond the bare schema. However, it doesn't detail constraints (e.g., must be positive integer, typical ranges) or examples, leaving room for improvement given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate Mersenne numbers 2^p - 1 for prime exponents up to limit.' It specifies the mathematical operation (generating Mersenne numbers), the formula (2^p - 1), and the constraint (prime exponents up to a limit). However, it doesn't explicitly differentiate from sibling tools like 'mersenne_prime_exponents' or 'is_mersenne_prime', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance on when to use this tool. It mentions the domain (arithmetic) and category (special_primes), but offers no explicit advice on when to choose this over alternatives like 'mersenne_prime_exponents' or 'is_mersenne_prime'. There's no mention of prerequisites, typical use cases, or scenarios where this tool is preferred.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the method ('using sieve') but doesn't disclose computational complexity, performance characteristics, error handling, or output format. For a mathematical computation tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence states the core purpose clearly. The parenthetical domain/category adds context without verbosity. No unnecessary words, though it could be slightly more informative given the lack of annotations.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't explain what the output looks like (e.g., integer result), error conditions, or practical usage notes. For a computational tool, this leaves the agent with insufficient context to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It defines n as the upper limit in the summation (k=1 to n), which adds essential meaning beyond the schema's type declaration. However, it doesn't specify constraints (e.g., n must be positive integer) or provide examples, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Mertens function M(n) = Σμ(k) for k=1 to n using sieve.' It specifies the mathematical function, the method (sieve), and the parameter n. However, it doesn't explicitly differentiate from sibling tools like 'mobius_function' or 'mobius_function_range' which might be related.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain (arithmetic) and category (sieve_algorithms), but offers no explicit advice on when to use this tool versus alternatives like 'mobius_function_range' or other number theory tools. No prerequisites, limitations, or comparison to siblings are included.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions 'standard rounding rules' which hints at behavior, but doesn't specify what those rules are (e.g., ties to even, away from zero), nor does it cover error handling, input constraints, or output format. For a tool with zero annotation coverage, this is insufficient behavioral disclosure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with two sentences: one stating the purpose and one providing domain/category context. Every word earns its place, and the core functionality is front-loaded. No wasted verbiage or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on rounding rules, parameter constraints, error cases, and return values. For a mathematical tool with two parameters, this leaves significant gaps in understanding how to use it effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It explains that 'number' is rounded and 'significance' is the multiple, adding meaning beyond the bare schema. However, it doesn't detail parameter constraints (e.g., significance must be positive), formats, or examples, leaving gaps. Baseline 3 is appropriate as it adds some value but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Round') and resource ('a number') with the specific mechanism ('to the nearest multiple of significance'). It distinguishes from siblings like 'round_number' by specifying the multiple-based rounding. However, it doesn't explicitly contrast with 'ceil' or 'floor' tools, keeping it at 4 instead of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'round_number', 'ceil', 'floor', or 'ceiling_multiple'. It mentions the domain and category but offers no explicit when/when-not instructions or named alternatives, leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It only mentions the multiplication action without details on error handling (e.g., overflow, non-numeric inputs), performance, or output format. This leaves significant gaps in understanding how the tool behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's function, followed by domain and category tags. There is no wasted verbiage, making it efficient and easy to parse for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (two numeric parameters, no output schema, no annotations), the description is incomplete. It lacks information on return values, error conditions, and behavioral nuances, which are essential even for basic operations. The domain/category tags add some context but do not fill these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds minimal semantics by specifying 'two numbers' as inputs, aligning with parameters 'a' and 'b'. However, it does not explain data types, constraints, or examples, providing only basic context without compensating fully for the schema's lack of detail.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('multiply') and resource ('two numbers'), making it immediately understandable. However, it does not distinguish itself from sibling tools like 'product' or 'element_wise_multiply', which might serve similar arithmetic functions, leaving room for ambiguity in selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives, such as 'product' for multiplying multiple numbers or 'element_wise_multiply' for vector operations. It only states the basic action without context, prerequisites, or exclusions, offering minimal help in tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the formula but doesn't disclose behavioral traits like input constraints (e.g., n>0, 1≤k≤n), error handling, computational complexity, or output format. The 'FIXED' note is unclear and adds no meaningful context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose. The parenthetical domain/category note adds context without verbosity. However, the 'FIXED' note is cryptic and doesn't earn its place, slightly reducing clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema coverage, the description is incomplete. It provides the formula but lacks essential context: input constraints, error conditions, return value explanation, and usage examples. For a mathematical tool with two parameters, this leaves significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions parameters n and k in the formula N(n,k), giving them semantic meaning as inputs to the Narayana number calculation. However, it doesn't explain what n and k represent (e.g., n total items, k something), their valid ranges, or units, leaving gaps beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool calculates the Narayana number N(n,k) using a specific formula, with the verb 'Calculate' and resource 'Narayana number' explicitly mentioned. It distinguishes from siblings by specifying the combinatorial numbers category, though it doesn't explicitly differentiate from similar tools like 'catalan_number' or 'bell_number' beyond the formula.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (arithmetic) and category (combinatorial_numbers), but gives no explicit when/when-not instructions or references to sibling tools for different combinatorial calculations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds numbers 'up to a limit' but does not describe output format (e.g., list, array), performance characteristics (e.g., computational complexity for large limits), or error handling. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category tags ('Domain: arithmetic, Category: iterative_sequences') are brief and relevant, adding context without unnecessary verbosity. However, the structure could be improved by integrating usage hints more seamlessly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (involves mathematical computation), lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It fails to explain the return values, error conditions, or behavioral nuances, leaving the agent with insufficient information for reliable invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('limit') with 0% description coverage, so the schema provides no semantic information. The description adds meaning by indicating 'limit' defines the upper bound for searching narcissistic numbers, but it does not specify constraints (e.g., positive integer, range) or units. This partial compensation aligns with the baseline for low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all narcissistic numbers up to a limit.' It specifies the verb ('Find'), resource ('narcissistic numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_narcissistic_number' or 'armstrong_numbers' (which may be related), so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context on prerequisites, exclusions, or comparisons to sibling tools such as 'is_narcissistic_number' (which checks a single number) or 'armstrong_numbers' (which might be similar). This omission leaves the agent without clear usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states that the tool generates numbers in a range, but does not specify whether the range is inclusive or exclusive, what happens with invalid inputs (e.g., negative numbers), or if there are any limits on range size. For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Generate natural numbers (positive integers) in a given range.' It efficiently conveys the core functionality without unnecessary words. The parenthetical note about domain and category is brief and adds context without detracting from clarity. Every sentence earns its place, making it highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a simple generation tool), no annotations, no output schema, and low schema description coverage, the description is incomplete. It lacks details on behavior (e.g., inclusivity of range, error handling), parameter usage, and output format. For a tool with 2 parameters and no structured guidance, more context is needed to ensure the agent can use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, so the description must compensate. It mentions 'a given range', which implies the 'start' and 'end' parameters, but does not explain their semantics (e.g., that 'start' and 'end' define the bounds, default values, or that they are integers). This adds minimal meaning beyond the schema, resulting in a baseline score due to the lack of detailed parameter information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate natural numbers (positive integers) in a given range.' It specifies the verb ('generate'), resource ('natural numbers'), and scope ('in a given range'), making it easy to understand. However, it does not explicitly differentiate from sibling tools like 'integers_in_range' or 'whole_numbers', which could offer similar functionality, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('number_systems'), but this is too vague to help an agent choose between this and sibling tools like 'integers_in_range' or 'range_value'. There are no explicit instructions on when to prefer this tool or what scenarios it is best suited for.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool calculates, without mentioning computational details (e.g., precision, handling of edge cases like extreme values), performance characteristics, or error handling. For a mathematical tool with no annotation coverage, this lack of behavioral context is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single, direct sentence that states the core functionality. There is no wasted verbiage or redundant information, making it efficient for quick understanding by an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical function with 3 parameters), lack of annotations, no output schema, and low schema description coverage, the description is incomplete. It does not cover parameter semantics, return values, error conditions, or usage examples. For a tool that performs calculations, more context is needed to ensure reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, meaning the schema provides no semantic information. The description does not explain the parameters (x, mean, std), their roles, or typical values. However, since the tool's name and description imply a standard statistical function, an agent might infer parameter meanings from common knowledge, but this is not explicitly stated. The baseline score reflects this partial compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the cumulative distribution function (CDF) of the normal distribution.' It specifies the verb ('calculate'), resource ('CDF'), and distribution type ('normal'), making the intent unambiguous. However, it does not explicitly differentiate this tool from other statistical or distribution-related siblings (e.g., 'normal_pdf', 'exponential_cdf'), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('probability') and category ('general'), which implies context but does not specify when to use this tool versus alternatives (e.g., 'normal_pdf' for probability density or other CDF tools). There is no explicit advice on prerequisites, limitations, or typical scenarios, leaving the agent with insufficient direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'Get[s] the nth perfect square' but does not elaborate on behavior such as input validation (e.g., handling negative 'n'), output format (e.g., integer result), error handling, or computational limits. The description is minimal and lacks critical behavioral details needed for safe and effective use.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Get the nth perfect square (0-indexed).' It wastes no words and directly states the core functionality. The additional context ('Domain: arithmetic, Category: basic_sequences') is brief and relevant, making every sentence earn its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is incomplete. It lacks details on behavioral aspects (e.g., how 'n' is interpreted, what happens with invalid inputs), output specifics, and differentiation from siblings. While concise, it does not provide enough context for an AI agent to use the tool confidently without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with type 'integer' and 0% schema description coverage. The description adds minimal semantics by implying 'n' is an index (0-indexed) for perfect squares, which provides some context beyond the bare schema. However, it does not explain constraints (e.g., non-negative integers) or provide examples, leaving gaps in understanding. With low schema coverage, the description compensates slightly but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the nth perfect square (0-indexed).' It specifies the verb ('Get'), resource ('nth perfect square'), and indexing method ('0-indexed'), which is specific and unambiguous. However, it does not explicitly distinguish this tool from sibling tools like 'perfect_squares' or 'square_numbers', which might list or generate perfect squares differently.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('basic_sequences'), but this is too generic to help differentiate among the many sibling tools (e.g., 'perfect_squares', 'square_numbers', 'nth_power_of_two'). There are no explicit instructions on when or when not to use it, or what alternatives exist.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a value, implying a read-only operation, but does not mention potential errors (e.g., for negative inputs), performance characteristics, or output format. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted verbiage, and every part of the description adds value (e.g., the domain/category provides context).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low schema description coverage, the description is incomplete. It lacks details on output format, error handling, or mathematical definition of octahedral numbers. While concise, it does not provide enough context for reliable use without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description does not add any parameter-specific semantics (e.g., explaining that 'n' is a non-negative integer or indexing position). However, since the tool name and description imply a simple mathematical function, the baseline score of 3 is appropriate, as the schema alone might suffice for basic use.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth octahedral number.' It specifies the verb ('Calculate') and the resource ('octahedral number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'tetrahedral_number' or 'icosahedral_number', which are similar figurate number calculations, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), but does not specify use cases, prerequisites, or comparisons to sibling tools (e.g., other polyhedral number calculators). This lack of explicit when-to-use information limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the mathematical concept but doesn't disclose behavioral traits such as error handling (e.g., what happens if a and n aren't coprime), computational complexity, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—just one sentence plus domain/category tags. It's front-loaded with the core purpose and wastes no words. Every part earns its place by defining the tool's function and context efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of modular arithmetic, no annotations, no output schema, and low schema description coverage, the description is incomplete. It doesn't explain what the multiplicative order is, how it's computed, what the output looks like, or edge cases. For a mathematical tool with no structured support, more explanatory context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It names the parameters ('a' and 'n') implicitly in the phrase 'a modulo n' and clarifies they are integers, but doesn't explain their mathematical roles (e.g., that 'a' is the base and 'n' is the modulus) or constraints (e.g., n > 1, a and n coprime). This adds some meaning but falls short of fully documenting the parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the multiplicative order of a modulo n.' It specifies the verb ('Find') and the mathematical operation ('multiplicative order'), and provides domain/category context. However, it doesn't differentiate from sibling tools like 'primitive_root' or 'discrete_log_naive' that also involve modular arithmetic concepts.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided about when to use this tool versus alternatives. The description only states what it does, with no mention of prerequisites, constraints (e.g., that a and n must be coprime), or related tools for similar tasks like computing primitive roots or solving discrete logarithms.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a Padovan number, implying a read-only operation, but does not disclose behavioral traits such as input constraints (e.g., valid range for 'n'), performance characteristics, error handling, or output format. This leaves significant gaps for an agent to understand how to invoke it correctly.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Calculate the nth Padovan number P_n.' The additional domain/category information is brief and relevant. There is no wasted text, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is minimal. It states the purpose but lacks context on usage, behavioral details, parameter constraints, or output format. For a tool with no structured support, this leaves the agent with insufficient information to use it effectively beyond the basic calculation intent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description adds meaning by specifying it calculates the 'nth Padovan number', clarifying that 'n' is an index. However, it does not provide details like valid ranges (e.g., non-negative integers) or examples, which would be helpful given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Padovan number P_n.' It specifies the verb ('calculate'), the resource ('Padovan number'), and the parameter ('nth'), which is straightforward. However, it does not explicitly differentiate from siblings like 'fibonacci' or 'lucas_number', though the domain/category hints at specialization.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), which might imply usage in mathematical contexts, but offers no explicit when-to-use, when-not-to-use, or sibling tool comparisons (e.g., vs. 'fibonacci' or 'lucas_number').
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. It only states what the tool calculates, not how it behaves: no information on input validation (e.g., n must be non-negative integer), computational characteristics (recursive vs. formula-based), error handling, or output format. For a mathematical computation tool, this is insufficient behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose with domain/category tags. Every word earns its place with zero redundancy or unnecessary elaboration, making it efficient for agent comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what a Pell-Lucas number is mathematically, how it's computed, what the output looks like, or any edge cases. For a tool with one parameter but no structured documentation, this leaves significant gaps in understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, leaving parameter 'n' undocumented. The description adds minimal semantics by implying 'n' represents the index in the sequence ('nth Pell-Lucas number'), which is better than nothing. However, it doesn't specify constraints (e.g., n ≥ 0) or provide examples, so it only partially compensates for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Pell-Lucas number (companion to Pell numbers).' It specifies the action (calculate), the mathematical object (Pell-Lucas number), and provides domain context. However, it doesn't explicitly differentiate from sibling tools like 'pell_number' or 'lucas_number', which would require a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'companion to Pell numbers' which hints at relationship but doesn't specify use cases, prerequisites, or comparisons with similar tools like 'pell_number' or 'lucas_sequence'. This leaves the agent without practical usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. It only states what the tool does without mentioning any constraints (e.g., valid ranges for n, performance characteristics, error handling). For a computational tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose. Every word earns its place, with no redundant information. The domain/category tags are efficiently appended without disrupting readability.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, and no output schema, the description is insufficient. It doesn't explain what Pell numbers are, the format of the output (e.g., list of integers), or any edge cases. For a tool with one parameter but zero schema description coverage, more context is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions 'first n Pell numbers', which implies the parameter 'n' controls the count of numbers generated. Since schema description coverage is 0%, the description adds basic meaning beyond the bare schema. However, it doesn't specify constraints like n being positive or integer-only (though the schema indicates integer type), keeping it at the baseline.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n Pell numbers.' It specifies the verb ('Generate'), resource ('Pell numbers'), and scope ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'pell_number' or 'pell_lucas_number', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags ('arithmetic, recursive_sequences') give some context, there's no explicit mention of when to choose this over similar sequence generators like 'fibonacci_sequence' or 'lucas_sequence' among the siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates, without mentioning any behavioral traits such as input validation (e.g., whether 'n' must be positive), performance characteristics, error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by a brief domain/category note. Every word earns its place with no redundancy or unnecessary elaboration, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low schema coverage, the description is insufficient. It doesn't explain what a pentagonal pyramidal number is, the formula or method used, valid input ranges, or what the output represents (e.g., integer result). For a tool with these contextual gaps, more detail is needed to be complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds minimal semantics by implying 'n' is an index ('nth'), but does not clarify its meaning (e.g., that it represents position in the sequence) or constraints (e.g., non-negative). This provides some value over the bare schema, but doesn't fully compensate for the low coverage, aligning with the baseline for partial compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth pentagonal pyramidal number.' It specifies the verb ('calculate'), resource ('pentagonal pyramidal number'), and parameter ('nth'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'pentagonal_number' or 'square_pyramidal_number' beyond the domain/category note, which limits full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), but this is generic context that doesn't help an agent choose between similar tools like 'pentagonal_number' or other pyramidal number calculators. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('Euclid-Euler theorem'), which hints at computational characteristics, but does not describe performance aspects (e.g., time complexity for large limits), output format (e.g., list of integers), or error handling (e.g., behavior for negative limits). For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and method. The additional domain/category information is minimal and does not detract from clarity. Every word earns its place, with no redundant or verbose phrasing.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with a specific theorem), lack of annotations, and no output schema, the description is incomplete. It does not explain the return values (e.g., list of perfect numbers), performance considerations, or error cases. While concise, it fails to provide sufficient context for safe and effective use by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It adds meaning by specifying that 'limit' defines the upper bound for finding perfect numbers, which clarifies the parameter's role beyond the schema's type information. However, it does not detail constraints (e.g., must be positive integer) or examples, providing only basic semantic context.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all perfect numbers up to limit using Euclid-Euler theorem.' It specifies the verb ('find'), resource ('perfect numbers'), and method ('Euclid-Euler theorem'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'is_perfect_number' or 'pluperfect_numbers,' which is why it doesn't reach a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the method ('Euclid-Euler theorem') but does not specify scenarios where this tool is preferred over other perfect-number-related tools (e.g., 'is_perfect_number' for checking a single number). There are no exclusions or prerequisites stated, leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'high-precision arithmetic', which hints at computational complexity or accuracy, but doesn't specify performance characteristics, error handling, output format, or limitations (e.g., maximum precision). For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated in the first sentence. The additional domain and category information in parentheses is brief and doesn't detract from clarity. There's no wasted text, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with precision), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't explain what the output looks like (e.g., string of digits, truncation/rounding), error conditions, or performance implications. For a tool that could have nuanced behavior, this leaves too much unspecified.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('precision') with 0% description coverage, so the description must compensate. It adds meaning by specifying that 'precision' refers to 'pi digits' generation, but doesn't clarify units (e.g., decimal places), valid ranges, or default values. This provides some context but falls short of fully documenting the parameter's semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate pi digits to specified precision using high-precision arithmetic.' It specifies the verb ('Generate'), resource ('pi digits'), and method ('high-precision arithmetic'), making it easy to understand what the tool does. However, it doesn't explicitly differentiate from sibling tools like 'pi' or 'compute_pi_chudnovsky', which likely serve similar mathematical constant purposes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('mathematical_constants'), but this is too vague to help an agent choose between many sibling tools (e.g., 'pi', 'compute_pi_chudnovsky', 'e_digits'). There are no explicit instructions on use cases, prerequisites, or comparisons to other tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions handling integer and fractional exponents, which is useful, but fails to disclose critical behavioral traits such as error handling (e.g., for negative bases with fractional exponents), performance characteristics, or output format. The description is too minimal for a mutation tool (raising to a power implies computation).
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core purpose, and the second adds relevant context. There is no wasted verbiage, and every sentence earns its place by providing essential information efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical operation with potential edge cases), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not address error conditions, return values, or limitations, making it inadequate for reliable tool invocation in varied contexts.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It implicitly clarifies that 'base' and 'exponent' are numbers and can be integer or fractional, adding some semantic value. However, it does not explain parameter constraints (e.g., domain restrictions) or provide examples, leaving gaps in understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Raise a number to a power.' It specifies the verb ('raise') and resource ('a number'), and adds useful context about handling integer and fractional exponents. However, it does not explicitly differentiate from sibling tools like 'exp' (exponential function) or 'power_series', which could cause confusion in selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('core'), but does not specify use cases, prerequisites, or comparisons to sibling tools like 'exp' or 'mod_power'. This leaves the agent without clear decision criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool calculates but doesn't describe behavioral traits such as error handling, computational limits, assumptions (e.g., normality for t-test), or output format. For a statistical tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, with a single sentence that directly states the tool's function and domain. Every word earns its place, and there's no unnecessary information or redundancy, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical power calculation tool with 4 parameters (2 required), 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain parameter details, behavioral assumptions, or what the output looks like, leaving the agent with insufficient context to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters are undocumented in the schema. The description mentions 'sample size and effect size,' which maps to two of the four parameters (n, effect_size), but doesn't cover the optional alpha and alternative parameters. It adds some meaning for the required parameters but doesn't fully compensate for the coverage gap, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate statistical power (probability of detecting effect) for t-test given sample size and effect size.' It specifies the statistical method (t-test), the calculation (power), and the required inputs (sample size, effect size). However, it doesn't explicitly differentiate from sibling tools, many of which are unrelated statistical functions, so it doesn't reach the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance on when to use this tool. It mentions the domain (statistics) and category (inference), which implies usage in statistical hypothesis testing contexts, but it doesn't specify when to choose this over alternatives (e.g., other power analysis tools or statistical tests in the sibling list). No explicit when-not-to-use or prerequisite information is given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates a sequence but does not specify output format (e.g., list, array), handling of edge cases (e.g., negative or zero n), performance considerations, or error behavior. For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a single sentence that directly states the tool's purpose. The domain and category tags are efficiently appended. There is no wasted verbiage, making it easy to parse, though it could benefit from slightly more detail without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, output schema, and low schema description coverage, the description is incomplete. It does not address behavioral aspects like output format, error handling, or usage constraints. For a tool with one parameter but no structured context, the description should provide more operational guidance to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds minimal semantics by implying 'n' represents the count of powers to generate ('the first n powers'), but does not clarify valid ranges, units, or examples. Since schema coverage is low, the description partially compensates but remains inadequate for full parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n powers of two.' It specifies the verb ('generate') and resource ('powers of two'), and the domain/category tags provide additional context. However, it does not explicitly differentiate from sibling tools like 'nth_power_of_two' or 'is_power_of_two', which reduces clarity in distinguishing its specific use case.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, constraints (e.g., valid ranges for n), or comparisons to sibling tools such as 'nth_power_of_two' (which might return a single power) or 'is_power_of_two' (which checks a property). This omission leaves the agent without context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks details on behavioral traits such as performance characteristics (e.g., computational complexity for large limits), error handling, or output format. For a tool with no annotations, this is a significant gap, as the agent cannot infer these critical aspects from the description alone.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Find all prime quadruplets up to limit.' The additional context ('Domain: arithmetic, Category: prime_patterns') is brief and relevant. There is no wasted verbiage, and every sentence earns its place by providing essential information efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of prime number calculations and the lack of annotations and output schema, the description is incomplete. It does not explain what a prime quadruplet is, the expected output format, or any limitations (e.g., performance for large limits). For a tool with no structured metadata, the description should provide more context to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the schema provides no semantic information. The description mentions 'limit' but does not explain its meaning, constraints (e.g., must be positive integer), or units. It adds minimal value beyond the schema, but since there is only one parameter, the baseline is higher than for tools with many undocumented parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all prime quadruplets up to limit.' It specifies the verb ('Find'), resource ('prime quadruplets'), and scope ('up to limit'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'prime_triplets' or 'cousin_primes', which is why it doesn't reach a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('prime_patterns'), but this is too vague to help an agent choose between similar tools like 'prime_triplets' or 'cousin_primes'. There are no explicit instructions on when or when not to use it, or what alternatives exist.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does but doesn't disclose behavioral traits like computational complexity, memory usage, performance characteristics for large limits, or what format the results are returned in. For a mathematical computation tool with no output schema, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with zero wasted words. The single sentence efficiently communicates the core functionality, and the parenthetical domain/category information is appropriately placed. It's front-loaded with the essential action and resource, making it immediately understandable.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has no annotations, no output schema, and minimal parameter documentation, the description is insufficiently complete. It doesn't explain what constitutes a 'prime triplet' (e.g., patterns like p, p+2, p+6), what format results are returned in, performance considerations, or error handling. For a computational tool with mathematical output, more context is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions 'limit' as the parameter scope, which aligns with the single required parameter in the schema. However, with 0% schema description coverage, the schema provides no documentation about what 'limit' represents. The description adds minimal semantic context by implying it's an upper bound, but doesn't specify whether it's inclusive/exclusive, valid ranges, or units. This partially compensates for the schema gap but remains basic.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Find') and resource ('prime triplets'), and specifies the scope ('up to limit'). It distinguishes from siblings by focusing on prime triplets rather than other prime patterns like twin primes or prime quadruplets. However, it doesn't explicitly differentiate from tools like 'prime_constellations' which might overlap in functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like 'prime_constellations', 'twin_prime_pairs', or 'cousin_primes' that handle related prime patterns. There's no indication of prerequisites, limitations, or typical use cases beyond the basic arithmetic domain context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation (range) but does not describe error handling (e.g., for empty lists or non-numeric strings), performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence directly states the tool's purpose, and the second adds domain/category context without redundancy. Every sentence earns its place, and there is no wasted verbiage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is incomplete. It lacks details on parameter semantics (string handling), behavioral traits (error cases), and output expectations. While concise, it does not provide enough context for reliable agent use without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description implies the parameter is a 'list of numbers', which aligns with the input schema's 'numbers' array of strings. However, with 0% schema description coverage, the description does not clarify that the array items are strings (not numbers) or provide any formatting details (e.g., numeric parsing, delimiter usage). It adds minimal value beyond what the schema structure indicates.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the range (difference between maximum and minimum) of a list of numbers.' It specifies the verb ('calculate'), resource ('range'), and input type ('list of numbers'). However, it does not explicitly differentiate from sibling tools like 'max_list' or 'min_list', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but this is too vague to help an agent choose between this and sibling tools like 'max_list', 'min_list', or 'comprehensive_stats'. There are no explicit when-to-use or when-not-to-use instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates a sequence, but does not describe output format (e.g., list of integers), error handling (e.g., for negative n), performance characteristics, or any side effects. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no wasted text, and every part adds value (e.g., the domain/category provides additional context without redundancy).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (generating a mathematical sequence), lack of annotations, no output schema, and low schema coverage, the description is insufficient. It does not explain what the Recamán sequence is, the output format, or any behavioral details. While conciseness is good, the description fails to provide enough context for an agent to use the tool effectively without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, so the schema provides no semantic information. The description adds meaning by specifying 'n terms', clarifying that 'n' is the number of terms to generate. However, it does not detail constraints (e.g., n must be positive) or provide examples, leaving some ambiguity. Given the low schema coverage, the description compensates partially but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the Recamán sequence up to n terms.' It specifies the verb ('Generate'), resource ('Recamán sequence'), and scope ('up to n terms'), making it easy to understand. However, it does not explicitly differentiate from sibling tools, which include many other sequence generators (e.g., fibonacci_sequence, collatz_sequence), so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('iterative_sequences'), but this is too vague to help an agent choose between similar tools like fibonacci_sequence or collatz_sequence. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'IEEE remainder operation,' which implies adherence to a specific floating-point standard, but doesn't describe key behaviors: error handling (e.g., division by zero), precision limitations, return format, or edge cases (e.g., NaN/infinity inputs). For a mathematical tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence: 'Calculate floating-point remainder of division (IEEE remainder operation). (Domain: arithmetic, Category: core).' It's front-loaded with the core purpose and avoids redundancy. The parenthetical domain/category could be omitted but doesn't detract significantly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain the return value (e.g., remainder as a number), error conditions, or how it differs from similar sibling tools. For a core arithmetic operation, more context on behavior and usage is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters (x, y) with 0% description coverage, so the schema provides no semantic information. The description doesn't add any parameter details—it doesn't explain what x and y represent (e.g., dividend and divisor) or their constraints. However, for a simple arithmetic operation with only two numeric inputs, the baseline is 3 as the purpose is clear enough to infer parameter roles.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate floating-point remainder of division (IEEE remainder operation).' It specifies the verb ('calculate'), resource ('floating-point remainder'), and operation type ('IEEE remainder operation'), which distinguishes it from basic modulo operations. However, it doesn't explicitly differentiate from sibling tools like 'modulo' or 'fmod', which might have similar mathematical purposes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions 'IEEE remainder operation' (which hints at a specific mathematical standard), it doesn't explain when this is preferable over other remainder/modulo tools in the sibling list (e.g., 'modulo', 'fmod'). There are no explicit when/when-not statements or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the basic operation but lacks behavioral details such as rounding rules (e.g., ties to even, away from zero), handling of negative numbers or decimals, error conditions, or output format. For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with a single, front-loaded sentence that directly states the tool's function. The parenthetical domain and category add minimal but relevant context without waste, making it efficiently structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (2 parameters, no output schema, no annotations), the description is incomplete. It lacks behavioral details (rounding rules, error handling), parameter specifics, and output information, making it inadequate for reliable agent use without additional inference or trial.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate. It mentions 'a number' and 'specified number of decimal places', which maps to parameters 'x' and 'decimals', adding basic meaning. However, it does not detail constraints (e.g., 'decimals' must be non-negative), defaults (schema shows 'decimals' defaults to 0), or examples, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Round') and resource ('a number'), and specifies the operation ('to a specified number of decimal places'). However, it does not explicitly differentiate from sibling tools like 'ceil', 'floor', 'truncate', or 'mround' which also perform rounding-related operations, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('core'), but offers no explicit when-to-use, when-not-to-use, or comparison with sibling tools like 'ceil' or 'floor', leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks critical behavioral details: it does not specify the output format (e.g., list of pairs, count), performance characteristics (e.g., computational complexity for large limits), or any constraints (e.g., limit range, memory usage). For a tool with no annotations, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated in the first sentence. The additional context ('Domain: arithmetic, Category: special_primes') is brief and potentially useful for categorization. There is no wasted verbiage, and the structure is clear, though it could be slightly more informative without losing efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of generating prime pairs, no annotations, no output schema, and low schema description coverage, the description is incomplete. It does not explain what the tool returns (e.g., pairs of numbers, a count, or a structured list), any limitations (e.g., performance for large limits), or error handling. For a tool with these contextual gaps, the description should provide more comprehensive guidance to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It mentions 'up to limit', which clarifies that 'limit' is an upper bound for the search, adding meaning beyond the schema's type information. However, it does not specify the parameter's semantics in detail (e.g., that 'limit' must be a positive integer, or typical usage ranges). This provides some value but is incomplete, aligning with the baseline for moderate schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find Sophie Germain and safe prime pairs up to limit.' It specifies the verb ('Find'), the resource ('Sophie Germain and safe prime pairs'), and the scope ('up to limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_safe_prime' or 'is_sophie_germain_prime', which are predicates rather than pair generators, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_primes'), but this is generic and does not help an agent decide between this tool and siblings like 'twin_prime_pairs' or 'cousin_primes'. There are no explicit when-to-use, when-not-to-use, or alternative tool recommendations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the calculation but doesn't describe error handling (e.g., for invalid inputs), performance characteristics, or output format. For a mathematical tool with zero annotation coverage, this is a significant gap in transparency about how the tool behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: 'Calculate hyperbolic secant (1/cosh).' This efficiently states the core purpose. The additional context '(Domain: trigonometry, Category: hyperbolic)' is brief but relevant. There's no wasted text, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (mathematical function), no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on return values, error conditions, and mathematical assumptions (e.g., input units). For a tool in a server with many siblings, more context is needed to ensure correct usage without trial and error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'x' with 0% description coverage, and the tool description doesn't add any parameter-specific information. It doesn't explain what 'x' represents (e.g., a real number, angle in radians/degrees) or constraints. With low schema coverage, the description fails to compensate, but since there's only one parameter, the baseline is adjusted to 3 as it's minimally adequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate hyperbolic secant (1/cosh).' It specifies the mathematical operation (calculate), the function (hyperbolic secant), and provides the formula (1/cosh). However, it doesn't differentiate from sibling tools like 'sech' vs 'asech' or other hyperbolic functions, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage context with 'Domain: trigonometry, Category: hyperbolic,' which implies when to use it (trigonometry/hyperbolic contexts). However, it doesn't offer explicit guidance on when to choose this tool over alternatives like 'cosh' or 'asech,' nor does it mention prerequisites or exclusions. This lack of comparative guidance limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'memory efficiency,' which hints at performance characteristics, but fails to describe critical behaviors: what the tool returns (e.g., a list of primes, a count), any limitations (e.g., range size constraints, computational complexity), error handling, or side effects. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and key feature ('memory efficiency'). Every word earns its place, with no redundant information or fluff. The domain and category annotations are efficiently appended in parentheses, maintaining clarity without verbosity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a computational algorithm with 2 parameters), lack of annotations, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., a list of primes, a count, or an error for invalid inputs), performance implications, or usage context. For a tool with no structured data to rely on, this leaves significant gaps in understanding how to effectively use it.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It adds meaning by specifying that parameters define a range '[low, high]' for finding primes, which clarifies the purpose of 'low' and 'high' beyond their schema types. However, it doesn't detail constraints (e.g., that 'low' and 'high' must be non-negative integers, or that 'low' <= 'high'), leaving some semantics incomplete. This partial compensation justifies a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Segmented sieve for finding primes in a range [low, high] with memory efficiency.' It specifies the verb ('finding primes'), resource ('range [low, high]'), and a key characteristic ('memory efficiency'), distinguishing it from simpler prime-finding tools like 'sieve_of_eratosthenes' or 'incremental_sieve' in the sibling list. However, it doesn't explicitly differentiate from all siblings (e.g., 'prime_counting_sieve'), keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'memory efficiency' but doesn't specify scenarios where this is advantageous (e.g., large ranges) or when other tools like 'sieve_of_eratosthenes' might be preferable. There are no explicit when/when-not statements or named alternatives, leaving usage unclear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe any behavioral traits such as error handling, performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and parameters, followed by domain and category in parentheses. Every word earns its place, with no wasted information, making it highly efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a mathematical calculation with 3 parameters), no annotations, and no output schema, the description is incomplete. It lacks information on the output format, error conditions, or any contextual details needed for reliable use. The description does not compensate for the absence of structured data, leaving the agent with insufficient guidance.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description lists the parameters ('first term, last term, and number of terms'), which adds meaning beyond the input schema that has 0% description coverage. However, it does not provide details on parameter constraints, units, or examples. With low schema coverage, the description compensates partially but not fully, warranting an average score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the sum of an arithmetic series based on first term, last term, and number of terms.' It specifies the verb ('calculate'), resource ('sum of an arithmetic series'), and parameters. However, it does not explicitly differentiate from sibling tools like 'arithmetic_series' or 'arithmetic_sum', which appear related, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but this does not help an agent choose between this and sibling tools such as 'arithmetic_series' or 'arithmetic_sum'. No explicit when-to-use or when-not-to-use instructions are included.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the algorithm type but does not cover critical traits such as computational complexity, memory usage, output format, error handling, or limitations (e.g., performance with large inputs). This leaves significant gaps for a tool that performs a non-trivial computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category tags. Every word earns its place without redundancy, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, lack of annotations, no output schema, and minimal parameter documentation, the description is insufficient. It does not explain what the output looks like (e.g., a list of primes), performance considerations, or edge cases, leaving the agent under-informed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'limit' of type integer. The description adds minimal semantics by implying 'n' corresponds to 'limit' and that primes are found 'up to n', but does not clarify constraints (e.g., must be positive, typical range). This partial compensation aligns with the baseline for low schema coverage, though more detail would improve utility.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'the classical algorithm for finding all primes up to n.' It specifies the verb ('finding'), resource ('all primes'), and scope ('up to n'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'first_n_primes' or 'prime_counting_sieve', which serve related but distinct purposes, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('sieve_algorithms'), but does not specify scenarios, prerequisites, or comparisons to siblings like 'incremental_sieve' or 'sieve_of_atkin'. Without explicit usage instructions, the agent must infer context independently.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the algorithm's purpose but doesn't describe key behaviors: what the output looks like (e.g., list of primes up to limit), performance characteristics, error handling, or limitations. For a computational tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category metadata. Every word earns its place with zero waste, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain the return value (e.g., list of odd primes), error conditions, or algorithmic specifics. For a sieve algorithm that likely outputs structured data, this leaves the agent with insufficient context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('limit') with 0% description coverage, so the schema provides no semantic information. The description doesn't mention parameters at all, failing to compensate for the schema gap. However, with only one parameter and a common mathematical context, the baseline is 3 as the agent might infer 'limit' refers to the upper bound for prime generation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'finds odd primes by eliminating specific composite patterns.' It specifies the verb ('finds'), resource ('odd primes'), and method ('eliminating specific composite patterns'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'sieve_of_eratosthenes' or 'sieve_of_atkin', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the algorithm's domain and category but offers no explicit when/when-not instructions or comparisons to sibling tools like other sieve algorithms. The agent must infer usage from the name and description alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the calculation behavior but lacks critical details: it does not mention input validation (e.g., handling of non-numeric inputs or special values like NaN/infinity), error handling, output format, or precision/rounding behavior. For a mathematical tool with no annotation coverage, this is a significant gap in behavioral disclosure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the tool's purpose. The additional domain/category information is brief and relevant. There is no redundant or verbose language, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on output (e.g., returns a number, error cases), behavioral traits (e.g., periodicity, special angles), and does not reference sibling tools for context. For a basic function tool in a large set, more guidance is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'angle_degrees' of type 'number'. The description adds minimal semantics by specifying the parameter is 'an angle in degrees,' but does not elaborate on allowed ranges (e.g., any real number, periodic behavior), units, or examples. With low schema coverage, the description provides basic context but does not fully compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate sine of an angle in degrees.' It specifies the mathematical function (sine), the input unit (degrees), and includes domain/category context. However, it does not explicitly differentiate from its sibling 'sin' (which likely calculates sine in radians), leaving room for ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives. The description mentions 'Domain: trigonometry, Category: basic_functions,' which implies a general context but does not specify when to prefer this over 'sin' (radians) or other trigonometric tools. There are no usage prerequisites, exclusions, or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool solves for integer solutions, implying a computational or analytical operation, but does not describe output format, error handling, performance characteristics, or any side effects. For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The parenthetical domain/category adds minor context without redundancy. It is appropriately sized for a straightforward mathematical tool, with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (solving Diophantine equations), lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It fails to explain what the output looks like (e.g., solution set format), handling of edge cases (e.g., no solutions), or computational behavior. For a 3-parameter tool with no structured support, more descriptive detail is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters (a, b, c) with 0% description coverage, meaning no parameter details are documented in the schema. The description only mentions 'ax + by = c', which maps to the parameters but adds minimal semantic context (e.g., no explanation of coefficient roles, integer constraints, or typical value ranges). With low schema coverage, the description does not adequately compensate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Solve linear Diophantine equation ax + by = c for integer solutions.' It specifies the verb ('solve'), the resource ('linear Diophantine equation'), and the domain/category, clearly distinguishing it from sibling tools like 'solve_quadratic_diophantine' or 'diophantine_analysis'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('diophantine_equations'), but does not specify scenarios, prerequisites, or exclusions. Without explicit usage instructions, the agent lacks context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does but lacks behavioral details: it doesn't specify what algorithm is used, computational complexity, precision/accuracy considerations, error handling for invalid inputs, or output format. For a mathematical solver with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence plus domain/category) with zero wasted words. It's front-loaded with the core purpose, and the parenthetical adds useful context without redundancy. Every element earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for a mathematical solver with 3 parameters, the description is incomplete. It doesn't explain what the tool returns (e.g., nth term, closed form, sequence up to n), error conditions, or mathematical assumptions. For this complexity level, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'coefficients and initial values' and 'n', which maps to the three parameters (coeffs, initial, n), providing basic semantic meaning. However, it doesn't explain parameter constraints (e.g., length relationships between coeffs and initial arrays, n's role as term index), leaving gaps that the schema alone doesn't address.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve general linear recurrence relation with given coefficients and initial values.' It specifies the verb ('solve') and the resource ('linear recurrence relation'), and includes domain/category context. However, it doesn't differentiate from potential siblings like 'fibonacci_sequence' or 'lucas_sequence' that might solve specific recurrences.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('recursive_sequences'), it doesn't specify when this general solver is preferable over specialized tools for specific recurrence types (like Fibonacci or Lucas) that exist among the sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool solves the equation but does not disclose behavioral traits such as output format (e.g., integer solutions, existence check), computational complexity, or error handling for invalid inputs (e.g., n values with no solution). This is inadequate for a tool with mathematical operations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in one sentence with additional domain/category context. There is no wasted text, though it could be more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on behavior, output, and usage context, which are critical for a mathematical solving tool. The domain/category hints are insufficient for full understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% description coverage, so the description must compensate. It mentions 'n' in the equation but does not explain its semantics (e.g., integer constraints, typical range). This adds minimal value beyond the schema, meeting the baseline for low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: solving the negative Pell's equation x² - ny² = -1. It specifies the mathematical domain (arithmetic) and category (diophantine_equations), making the verb+resource explicit. However, it does not differentiate from sibling tools like 'solve_pell_equation' (which likely solves x² - ny² = 1), missing full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. The description mentions the equation but does not specify prerequisites, constraints (e.g., valid n values), or refer to sibling tools like 'solve_pell_equation' for comparison. This leaves the agent without usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the basic behavior (sorting numbers) but lacks details on error handling (e.g., invalid inputs like non-numeric strings), performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding its operational traits.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted verbiage, and every word contributes to understanding the purpose. It efficiently communicates the core action and parameters.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (2 parameters, no output schema, no annotations), the description is insufficient. It lacks details on input format (e.g., string array handling), output expectations, error conditions, and differentiation from siblings. For a sorting tool in a crowded namespace, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate. It mentions 'ascending or descending order', which clarifies the 'descending' parameter, and implies a 'list of numbers' for the 'numbers' parameter. However, it does not specify that 'numbers' is an array of strings (per schema) or provide examples, leaving some ambiguity. Given the low schema coverage, this adds moderate but incomplete value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Sort a list of numbers in ascending or descending order.' It specifies the verb ('sort'), resource ('list of numbers'), and direction options. However, it does not explicitly differentiate from sibling tools like 'digit_sort' or 'rank_numbers', which may have overlapping functionality, so it misses the highest score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('comparison'), but this is too vague to help an agent choose between similar tools like 'digit_sort' or 'rank_numbers'. No explicit when/when-not or alternative recommendations are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates the square root but does not mention error handling (e.g., for negative inputs), performance characteristics, or output format. This leaves significant gaps in understanding how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Calculate the square root of a number.' The parenthetical adds minimal context without redundancy. Every word serves a purpose, making it efficient and easy to parse, with no wasted sentences.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is incomplete. It lacks details on error conditions, output format, and behavioral traits. While the purpose is clear, the overall context for safe and effective use is insufficient, especially without annotations to fill in gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'x' with 0% description coverage, so the schema provides no semantic information. The description adds meaning by specifying that 'x' is a 'number' for which the square root is calculated, but it does not detail constraints (e.g., non-negative) or units. This partially compensates for the low schema coverage but is not comprehensive.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the square root of a number.' It specifies the verb ('calculate') and resource ('square root'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'sqrt2', 'sqrt3', or 'sqrt5', which are specific square root functions, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance with the parenthetical '(Domain: arithmetic, Category: core)', which implies context but does not specify when to use this tool versus alternatives like 'sqrt2' or 'cbrt2'. There is no explicit mention of when or when not to use it, or any prerequisites, leaving the agent with little direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates, without mentioning computational characteristics (e.g., performance with large n, error handling, or output format). For a mathematical function with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first. The domain/category annotation is brief and doesn't add unnecessary length. However, the lack of usage or parameter details means it's under-specified rather than optimally concise, slightly reducing the score.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low parameter coverage, the description is incomplete. It doesn't explain the return value (e.g., integer result), error conditions, or mathematical definition of square pyramidal numbers. For a tool with minimal structured data, more descriptive context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, documenting only the parameter type (integer n). The description adds no parameter semantics beyond the name 'n' implying an index. It doesn't explain valid ranges (e.g., n ≥ 1), units, or examples. With low schema coverage, the description fails to compensate adequately, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth square pyramidal number.' It specifies the verb ('calculate') and resource ('square pyramidal number'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'triangular_pyramidal_number' or 'pentagonal_pyramidal_number' beyond the name, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'triangular_number' or 'polygonal_number'. This leaves the agent with insufficient context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a value, implying a read-only operation, but does not mention error handling (e.g., for invalid inputs), performance characteristics, or output format. For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Calculate the nth star number (6-pointed star). (Domain: arithmetic, Category: figurate_numbers)'. Every word contributes essential information without redundancy, making it efficient and well-structured for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on output format, error conditions, and behavioral context. While concise, it does not provide enough information for reliable tool invocation in a broader context, especially compared to sibling tools with similar functions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one required integer parameter 'n'. The description adds no parameter-specific information beyond implying 'n' is the index for the star number. It does not explain constraints (e.g., n must be positive) or provide examples. Given the low schema coverage, the description compensates minimally, meeting the baseline for adequate but incomplete parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth star number (6-pointed star).' It specifies the verb ('calculate'), resource ('star number'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools (e.g., other figurate number calculators like 'hexagram_number'), which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), but does not specify scenarios, prerequisites, or comparisons to sibling tools (e.g., 'hexagram_number' or 'polygonal_number'). This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not describe any behavioral traits such as input constraints (e.g., n and k must be non-negative integers, k ≤ n), computational complexity, error handling, or output format. For a mathematical function with two parameters, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category information is efficiently appended. Every word earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (a combinatorial function with two parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is insufficient. It does not explain the mathematical definition, typical use cases, input constraints, or what the output represents (e.g., an integer count). For effective agent use, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'S(n,k)' which implies n and k are parameters, but does not explain their meanings (e.g., n is the number of elements, k is the number of non-empty subsets). This adds minimal semantic value beyond the schema's parameter names, resulting in a baseline score for inadequate compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Stirling number of the second kind S(n,k).' It specifies the verb ('Calculate'), resource ('Stirling number of the second kind'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'stirling_first' or 'stirling_second_row', which are closely related combinatorial functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('combinatorial_numbers'), but does not specify typical use cases, prerequisites, or comparisons with sibling tools like 'stirling_first' (which calculates the first kind) or 'stirling_second_row' (which might compute a row of these numbers).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It states what the tool does (representation as sum of two squares) but doesn't describe how it behaves: whether it returns all representations or just one, what happens with non-representable integers, whether there are computational limits, or what the output format looks like. This leaves significant gaps for a tool that solves a mathematical problem.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the core purpose is stated in the first phrase, followed by domain/category tags. There is zero wasted verbiage, and every element (mathematical operation, input type, categorization) serves a clear purpose. This is a model of efficiency for a simple mathematical tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical complexity (solving a diophantine equation) and the absence of both annotations and an output schema, the description is inadequate. It doesn't explain what the tool returns (e.g., pairs of integers, existence boolean, error handling), behavioral constraints, or usage examples. For a tool that could have multiple behavioral interpretations, this leaves too much ambiguity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds some semantic context by specifying this represents 'integer as sum of two squares,' clarifying that 'n' is the integer to be represented. However, it doesn't provide details about valid ranges, constraints (e.g., non-negative integers), or examples, which would be needed for full compensation of the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Represent integer as sum of two squares x² + y².' It specifies the mathematical operation (representation as sum of two squares) and the resource (integer input). However, it doesn't explicitly distinguish this from sibling tools like 'sum_of_two_squares' or other diophantine equation tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance through the domain/category tags ('Domain: arithmetic, Category: diophantine_equations'), which implies when this mathematical tool might be applicable. However, it offers no explicit guidance on when to use this tool versus alternatives like 'sum_of_two_squares' or other representation tools, nor does it mention any prerequisites or constraints.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details: it does not specify output format (e.g., list of integers), handling of large n (e.g., performance or overflow issues), or error conditions (e.g., invalid n). For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's purpose and includes domain/category tags. It is front-loaded with the core functionality and has no redundant or verbose elements, making it highly concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on behavior, output, error handling, and usage context. For a mathematical sequence generator, more information (e.g., output format, sequence definition) would help the agent use it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% description coverage. The description does not add any parameter-specific information beyond implying n is an integer for generating terms. It does not explain n's meaning (e.g., number of terms, starting index), constraints (e.g., n > 0), or examples. With low schema coverage, the description compensates minimally, meeting the baseline.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n terms of Sylvester's sequence.' It specifies the verb ('Generate'), resource ('first n terms of Sylvester's sequence'), and domain context ('Domain: arithmetic, Category: egyptian_fractions'). However, it does not explicitly differentiate from sibling tools (e.g., other sequence generators like fibonacci_sequence or lucas_sequence), though the specific sequence name helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify use cases, prerequisites, or comparisons to sibling tools (e.g., when to choose this over other mathematical sequences). The agent must infer usage from the tool name and context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation action but does not describe potential behaviors like handling undefined angles (e.g., 90 degrees), numerical precision, error conditions, or output format. For a mathematical function with no annotation coverage, this leaves significant gaps in understanding how the tool behaves beyond basic computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single, clear sentence followed by domain/category tags. Every word serves a purpose, with no redundant information, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is incomplete. It lacks information on output behavior, error handling, and usage context relative to siblings. While concise, it does not provide enough detail for an agent to fully understand how to invoke and interpret results, especially without annotations to fill gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'angle_degrees' of type 'number'. The description adds minimal semantics by specifying the parameter is in 'degrees', which clarifies the unit beyond the schema. However, it does not provide details on valid ranges, special cases, or examples, leaving the parameter meaning partially documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate tangent of an angle in degrees.' It specifies the verb ('calculate'), resource ('tangent'), and input unit ('degrees'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'tan' (which likely uses radians) or 'atan_degrees', though the domain/category hints at context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('trigonometry') and category ('basic_functions'), which implies context but does not specify when to use this tool versus alternatives like 'tan' (radians) or other trigonometric functions. No explicit when/when-not instructions or sibling comparisons are included.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not mention performance characteristics (e.g., computational complexity for large n), error handling (e.g., for negative inputs), or output format. For a mathematical tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: a single sentence that directly states the tool's purpose and includes domain/category in parentheses. There is no wasted verbiage, and every part of the sentence adds value, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on output format (e.g., integer result), error conditions, and practical usage examples. While concise, it does not provide enough context for reliable agent invocation without additional assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (n) with 0% description coverage. The description adds meaning by explaining that n is the index for the tetrahedral number calculation, but does not specify constraints (e.g., n must be non-negative integer) or examples. Since schema coverage is low, the description partially compensates but not fully, warranting a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth tetrahedral number (sum of first n triangular numbers).' It specifies the verb ('calculate'), resource ('tetrahedral number'), and mathematical definition. However, it does not explicitly differentiate from sibling tools like 'triangular_number' or 'triangular_sequence', which are related but distinct.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('basic_sequences'), but does not specify use cases, prerequisites, or comparisons to sibling tools such as 'triangular_number' or 'triangular_sequence'. This leaves the agent without clear direction on tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not describe key behavioral traits such as input constraints (e.g., valid range for 'n'), performance characteristics (e.g., recursion depth limits), error handling, or output format. For a computational tool with no annotations, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first. The additional domain and category information is brief and relevant. There is no wasted verbiage, making it efficient for an agent to parse, though it could be slightly more structured (e.g., separating usage notes).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on input validation, output format, error conditions, and performance limits. While it states the purpose, it does not provide enough context for reliable agent invocation without assumptions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds minimal semantic context by implying 'n' is the index in the Tetranacci sequence, but it does not specify meaning (e.g., zero-based vs. one-based), constraints, or examples. Since schema coverage is low, the description partially compensates but not sufficiently for a higher score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Tetranacci number (4th order Fibonacci).' It specifies the verb ('Calculate'), resource ('Tetranacci number'), and mathematical context. However, it does not explicitly differentiate from sibling tools like 'fibonacci' or 'tribonacci_number', which would be needed for a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category ('Domain: arithmetic, Category: recursive_sequences'), but this is generic and does not help an agent choose between similar tools like 'fibonacci', 'tribonacci_number', or other sequence calculators. No explicit when-to-use or when-not-to-use instructions are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool calculates without mentioning any behavioral traits such as input validation, error handling, performance characteristics, or output format. For a mathematical function with no annotation coverage, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with zero wasted words. The single sentence efficiently conveys the core purpose, and the parenthetical domain/category information is appropriately brief. It's front-loaded with the main functionality and doesn't contain any redundant or unnecessary information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. While the tool is mathematically simple, the description doesn't address what the tool returns, how it handles edge cases (negative n, large n), or any mathematical properties of triangular pyramidal numbers. For a tool with no structured documentation, more context would be helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions 'nth' which corresponds to the single parameter 'n' in the schema, but provides no additional semantic context beyond what's implied by the tool name. With 0% schema description coverage and only one parameter, the description doesn't compensate by explaining what 'n' represents (e.g., that it should be a non-negative integer, or its mathematical meaning). The baseline is appropriate given the single parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool calculates the nth triangular pyramidal number (tetrahedral), providing a specific verb ('calculate') and resource ('triangular pyramidal number'). It distinguishes from siblings by specifying the mathematical domain (arithmetic) and category (figurate_numbers), though it doesn't explicitly differentiate from similar figurate number tools like 'tetrahedral_number' or 'square_pyramidal_number' in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain and category, it doesn't indicate scenarios where this specific figurate number calculation is appropriate or suggest alternative tools for related calculations. There's no mention of prerequisites, constraints, or comparison with sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates numbers but doesn't describe output format (e.g., list, array, JSON), error handling (e.g., for negative n), performance characteristics, or side effects. The description is minimal and lacks behavioral details beyond the basic action.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the tool's purpose. The domain/category in parentheses adds context without redundancy. It's appropriately sized for a simple tool, with no wasted words, though it could be slightly more informative without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is incomplete. It doesn't explain the output format, handle edge cases (e.g., what if n=0?), or differentiate from similar tools. For a basic sequence generator, more context on behavior and usage would improve completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description adds meaning by specifying 'first n triangular numbers,' clarifying that 'n' controls the count of numbers generated. However, it doesn't explain constraints (e.g., n must be positive integer) or provide examples. With low schema coverage, the description partially compensates but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate the first n triangular numbers.' It specifies the verb ('generate') and resource ('triangular numbers'), and the domain/category context helps differentiate it from siblings like 'triangular_number' (likely checks if a number is triangular) or 'triangular_numbers' (might list triangular numbers up to a limit). However, it doesn't explicitly contrast with these similar-named tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('basic_sequences'), but this is too vague to help an agent choose between this and sibling tools like 'triangular_numbers' or 'triangular_number' without further context. No explicit when/when-not instructions or named alternatives are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a statistical test but lacks details on output format (e.g., returns p-value, test statistic), error handling (e.g., invalid input), or computational behavior (e.g., handling of large datasets). For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a single sentence that directly states the tool's function. It avoids unnecessary words, though it could be more structured (e.g., separating purpose from context). The parenthetical additions (Domain, Category) are brief and relevant, contributing to efficiency without clutter.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (statistical inference with 4 parameters), no annotations, and no output schema, the description is incomplete. It lacks details on output (e.g., what statistical values are returned), assumptions (e.g., normality, independence), and error conditions. For a tool with moderate complexity and no structured support, the description should provide more comprehensive guidance to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'two-sample t-test (independent samples)', which implicitly relates to 'data1' and 'data2' parameters, and 'test whether two sample means differ significantly', hinting at the 'alpha' parameter for significance level. However, it doesn't explain parameter roles (e.g., 'equal_variance' for Welch's test) or data requirements (e.g., numeric arrays). The description adds some meaning but doesn't fully cover the 4 parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform two-sample t-test (independent samples) to test whether two sample means differ significantly.' It specifies the statistical test type, sample independence, and the goal of comparing means. However, it doesn't explicitly differentiate from sibling tools like 'paired_t_test' or 't_test_one_sample', which are related statistical tests.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain (statistics) and category (inference), which implies context, but offers no explicit advice on when to use this tool versus alternatives like 'paired_t_test' or 'mann_whitney_u' (a non-parametric alternative). There's no mention of prerequisites, assumptions (e.g., normality), or scenarios where this test is appropriate.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds twin prime pairs but does not describe output format (e.g., list of pairs, count), performance characteristics (e.g., computational complexity for large limits), or error handling (e.g., invalid limit values). This is a significant gap for a tool with no structured behavioral hints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: 'Find twin prime pairs up to limit.' It wastes no words and directly states the core functionality. The additional domain/category note is brief and informative. Every sentence earns its place, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation), lack of annotations, no output schema, and low parameter schema coverage, the description is insufficient. It does not explain what twin prime pairs are, the return format, performance considerations, or error cases. For a tool with no structured support, more contextual information is needed to be complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description mentions 'limit' but adds minimal semantics beyond the schema. It implies the parameter is an integer upper bound but does not specify constraints (e.g., positive, maximum value) or meaning (e.g., inclusive/exclusive). With low schema coverage, the description partially compensates but lacks detail, aligning with the baseline for incomplete coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find twin prime pairs up to limit.' It specifies the verb ('find'), resource ('twin prime pairs'), and scope ('up to limit'), which is straightforward. However, it does not explicitly differentiate from sibling tools like 'cousin_primes' or 'sexy_primes', which also find prime pairs with different gaps, so it misses full sibling distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks context such as prerequisites, limitations (e.g., performance for large limits), or comparisons to similar tools like 'cousin_primes' or 'sexy_primes' that find other types of prime pairs. This leaves the agent without clear usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds numbers 'up to limit,' implying a search operation, but does not describe output format (e.g., list structure), performance characteristics (e.g., computational complexity for large limits), or error handling. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first: 'Find all vampire numbers up to limit.' The additional domain/category tags are brief and relevant. There is no unnecessary verbosity, and every sentence contributes to understanding, though the structure could be slightly improved by integrating the tags more seamlessly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (finding special numbers), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not explain what vampire numbers are, how they are returned, or any algorithmic details. While the domain/category tags help, they are insufficient for an agent to fully understand the tool's operation and results without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('limit') with 0% description coverage, so the schema provides no semantic context. The description adds value by clarifying that 'limit' defines the upper bound for finding vampire numbers, but it does not specify constraints (e.g., must be positive integer) or units. This partial compensation aligns with the baseline for low schema coverage, but more detail would improve usability.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all vampire numbers up to limit.' It specifies the verb ('Find'), resource ('vampire numbers'), and scope ('up to limit'), making the action unambiguous. However, it does not differentiate from sibling tools like 'is_vampire_number' (which tests individual numbers) or other number-finding tools (e.g., 'armstrong_numbers'), so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It includes domain/category tags ('Domain: arithmetic, Category: special_numbers'), which imply context but do not explicitly state when to use this tool versus alternatives like 'is_vampire_number' or other number generators. There is no mention of prerequisites, limitations, or comparisons to sibling tools, leaving the agent with insufficient direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the output is in radians by default, with an optional 'degrees' parameter, which is useful. However, it lacks details on error handling (e.g., invalid vectors, dimension mismatches), performance, or mathematical assumptions (e.g., Euclidean space). For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that efficiently conveys the core purpose and key details (radians default, domain). There is no wasted text, and it is front-loaded with the essential action. Every word earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for 3 parameters, the description is incomplete. It covers the basic purpose and output units but misses critical context: vector format, error conditions, mathematical context (e.g., dot product formula), and how results are returned. For a mathematical tool with multiple inputs, this leaves too much undefined.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description adds minimal semantics: it implies 'vector_a' and 'vector_b' are the vectors to compare, and 'degrees' controls output units. However, it doesn't explain vector format (e.g., arrays of strings representing numbers), dimensionality requirements, or default behavior. With 3 parameters and 0% coverage, the description partially compensates but remains inadequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the angle between two vectors in radians.' It specifies the verb ('calculate'), resource ('angle between two vectors'), and domain/context ('linear_algebra.vectors'). However, it doesn't explicitly differentiate from sibling tools like 'angle_difference' or 'convert_angle', which might handle similar angle-related operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('linear_algebra.vectors') and category ('general'), but offers no explicit advice on when to use this tool versus alternatives like 'angle_difference' or 'convert_angle'. There are no prerequisites, exclusions, or comparisons to sibling tools listed.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates, without describing how it behaves: no information on input validation (e.g., n must be positive integer), computational characteristics (e.g., efficiency for large n), error handling, or output format. For a mathematical function tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with domain/category tags. It's front-loaded with the core purpose and wastes no words. Every part earns its place, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a specialized mathematical function), lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It doesn't explain the function's definition, typical use cases, output values (e.g., log(p) for prime powers, 0 otherwise), or mathematical context. For users unfamiliar with the von Mangoldt function, this description is insufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description doesn't add any parameter semantics beyond the schema—it doesn't explain what 'n' represents (e.g., a positive integer, the input to the von Mangoldt function) or any constraints. With no schema descriptions, the baseline is low, but the description fails to compensate, leaving the parameter meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the von Mangoldt function Λ(n).' It specifies the verb ('calculate') and the mathematical function, and provides domain/category context ('Domain: arithmetic, Category: arithmetic_functions'). However, it doesn't explicitly differentiate from sibling tools like 'liouville_function' or 'mobius_function', which are also arithmetic functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but doesn't explain what the von Mangoldt function is used for (e.g., prime number theory, analytic number theory) or when it's appropriate compared to other arithmetic functions in the sibling list. There's no mention of prerequisites, typical use cases, or limitations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden for behavioral disclosure. While it states what the tool does mathematically, it doesn't describe important behavioral aspects: what input range is valid (e.g., does it handle negative numbers, zero, or very large integers?), what happens with invalid inputs, whether there are computational limitations, or what the output format will be. The description is mathematically correct but operationally incomplete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence that states the theorem and includes domain/category metadata. Every element serves a purpose: the mathematical statement defines the operation, while the parenthetical metadata provides categorization. There's no wasted verbiage, though it could benefit from slightly more operational context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical verification tool with no annotations, no output schema, and minimal parameter documentation, the description is insufficient. It provides the mathematical theorem but lacks crucial operational details: expected input behavior, output format, computational characteristics, and guidance on when this specific primality test is appropriate versus alternatives. The mathematical correctness doesn't compensate for these practical gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, providing only that parameter 'n' is an integer. The description adds no information about what 'n' represents (presumably the number to test for primality), valid ranges, or special cases. For a mathematical tool where parameter semantics are crucial, this represents a significant gap in documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check Wilson's theorem: p is prime iff (p-1)! ≡ -1 (mod p).' It specifies the exact mathematical operation (checking primality using Wilson's theorem) and distinguishes itself from sibling tools like 'is_prime' or other primality tests by focusing specifically on Wilson's theorem verification.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain (arithmetic) and category (primality_tests), but offers no explicit advice on when to use this tool versus alternatives like 'is_prime', 'fermat_primality_test', or 'miller_rabin_test'. There's no mention of performance characteristics, accuracy considerations, or typical use cases for Wilson's theorem versus other primality tests.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses 'domain validation' as a behavioral trait, which is useful beyond basic calculation. However, it lacks details on error handling, input constraints (e.g., valid ranges for 'x'), output format, or performance characteristics. This leaves gaps in understanding how the tool behaves in edge cases.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's function and key feature ('domain validation'). There is no wasted text, and it efficiently communicates the core purpose without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (a mathematical function with domain validation), no annotations, no output schema, and low parameter coverage, the description is incomplete. It hints at behavior but lacks details on inputs, outputs, errors, or usage context. For a tool that likely has specific mathematical constraints, more information is needed to ensure correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description does not add any semantic information about the parameter 'x'. It does not explain what 'x' represents (e.g., a real number, domain restrictions), its units, or how domain validation applies. This fails to compensate for the low schema coverage, leaving the parameter poorly documented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate inverse hyperbolic cosecant with domain validation.' It specifies the verb ('calculate'), resource ('inverse hyperbolic cosecant'), and an important behavioral aspect ('domain validation'). However, it does not explicitly differentiate from sibling tools like 'acsch' (which might be similar) or other inverse hyperbolic functions, though the domain/category hints at context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions domain validation and categorizes the tool under 'trigonometry' and 'inverse_hyperbolic', which implies usage in mathematical contexts. However, it does not specify when to use this tool versus alternatives (e.g., other inverse hyperbolic functions like 'asinh' or 'acosh'), nor does it provide explicit when-not-to-use instructions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation and output format but does not cover critical behavioral aspects such as error handling (e.g., for x=0, y=0), input constraints (e.g., domain of valid numbers), or performance characteristics. For a mathematical function tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's function and output. The domain and category tags are appended efficiently without redundancy. Every word earns its place, making it highly readable and to-the-point.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical function with two parameters, no annotations, and no output schema, the description is incomplete. It lacks details on parameter meanings, behavioral traits (e.g., edge cases), and output format beyond 'degrees'. For a tool in a server with many siblings, more context is needed to ensure correct usage without ambiguity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has two parameters (y and x) with 0% description coverage, meaning the schema provides no semantic information. The description does not explain what y and x represent (e.g., Cartesian coordinates, vector components) or their roles in the calculation (e.g., atan2(y, x) convention). It adds no parameter semantics beyond the bare schema, failing to compensate for the low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate two-argument arctangent with result in degrees.' It specifies the verb ('calculate'), resource ('two-argument arctangent'), and output unit ('degrees'), which is specific and unambiguous. However, it does not explicitly differentiate from sibling tools like 'atan' or 'atan2', which likely produce results in radians or have different parameter conventions, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain and category tags ('trigonometry', 'inverse_functions'), suggesting it should be used for trigonometric calculations involving inverse functions. However, it does not provide explicit guidance on when to use this tool versus alternatives like 'atan' (single-argument arctangent) or 'atan2' (likely in radians), nor does it mention any prerequisites or exclusions. The guidance is implied but not detailed.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool is 'useful for floating-point comparisons', which hints at its application but does not detail behavioral traits such as return format (e.g., boolean or numeric), error handling, performance characteristics, or specific floating-point considerations. The description lacks depth for a tool with parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of two sentences that directly state the tool's purpose and utility. There is no wasted verbiage, and the structure efficiently conveys essential information without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 2 parameters with 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It does not explain the return value, error conditions, or detailed usage context. For a comparison tool with floating-point implications, more information on behavior and parameters is needed to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'tolerance' but does not explain its role, default value, or units. The parameter 'x' is not described at all. The description adds minimal semantic value beyond the schema, failing to clarify how parameters interact or what 'close to zero' means operationally.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is close to zero within a tolerance.' It specifies the verb ('check'), resource ('a number'), and context ('floating-point comparisons'), but does not explicitly differentiate it from sibling tools like 'approximately_equal' or 'is_close', which likely serve similar comparison functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides implied usage guidance by mentioning 'Useful for floating-point comparisons' and categorizing it under 'arithmetic' and 'comparison'. However, it does not explicitly state when to use this tool versus alternatives like 'approximately_equal' or 'is_close' (which are siblings), nor does it outline any exclusions or prerequisites for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'faster convergence', which hints at performance, but fails to disclose critical behavioral traits such as what the tool returns (e.g., optimized parameters, convergence status), error handling, computational requirements, or side effects. For a complex optimization tool with 7 parameters, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted text, and the structure efficiently conveys the core information without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (optimization algorithm with 7 parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits essential details such as return values, error conditions, performance characteristics, and parameter explanations. For a tool of this nature, the description should provide more context to guide effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning none of the 7 parameters have descriptions in the schema. The tool description adds no information about parameters like 'f', 'grad_f', or 'x0', leaving their semantics (e.g., function definitions, initial point format) completely undocumented. This fails to compensate for the lack of schema coverage, making parameter understanding difficult.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform gradient descent with momentum for faster convergence'. It specifies the verb ('perform'), resource ('gradient descent'), and a key feature ('with momentum'), distinguishing it from basic gradient descent. However, it doesn't explicitly differentiate from sibling tools like 'gradient_descent' or 'adam_optimizer' beyond the mention of momentum.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage in optimization contexts ('Domain: numerical, Category: optimization') and suggests momentum aids 'faster convergence', but it lacks explicit guidance on when to use this tool versus alternatives like 'gradient_descent' or 'adam_optimizer'. No prerequisites, exclusions, or specific scenarios are mentioned, leaving usage somewhat vague.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds the minimum value but does not describe how it handles edge cases (e.g., empty lists, non-numeric strings in the array), performance characteristics, or error behavior. For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Find the minimum value in a list of numbers.' The additional domain and category tags are brief and relevant. There is no wasted verbiage, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is minimal. It states the purpose but lacks details on parameter handling, return values, error conditions, or behavioral nuances. For a tool with zero schema description coverage and no annotations, this description is insufficient to fully guide an agent without additional context or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'numbers' of type array with string items, and schema description coverage is 0%, meaning the schema provides no descriptions. The description mentions 'a list of numbers' but does not clarify that the numbers are expected as strings in the array, nor does it explain format, constraints, or examples. It adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the minimum value in a list of numbers.' It specifies the verb ('Find'), resource ('minimum value'), and input type ('list of numbers'), making it easy to understand. However, it does not explicitly distinguish this tool from sibling tools like 'minimum' or 'min_float', which might have similar purposes, so it doesn't achieve a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category tags ('Domain: arithmetic, Category: comparison'), which imply usage in arithmetic contexts for comparison tasks. However, it does not provide explicit guidance on when to use this tool versus alternatives like 'minimum' or 'min_float', nor does it mention any prerequisites or exclusions. The guidance is implied but not detailed.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool performs a statistical test but doesn't disclose behavioral traits such as what the output includes (e.g., t-statistic, p-value, confidence interval), assumptions (e.g., normality of differences), or error handling (e.g., for unequal array lengths). The description is minimal and lacks operational details needed for effective use.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with no wasted words. It front-loads the core action ('Perform paired t-test') and includes essential qualifiers ('dependent samples,' 'test whether paired observations differ significantly') and domain context. Every part earns its place, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on parameters, output format, assumptions, and usage compared to siblings. While concise, it doesn't provide enough context for reliable tool invocation, especially for an AI agent needing to interpret results or handle errors.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It doesn't mention any parameters, leaving 'before', 'after', and 'alpha' undocumented. The description hints at 'paired observations' which relates to 'before' and 'after' arrays, but doesn't explain their required format (e.g., equal length, numeric) or 'alpha' as the significance level. This is inadequate given the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform paired t-test (dependent samples) to test whether paired observations differ significantly.' It specifies the statistical test (paired t-test), the sample type (dependent/paired), and the goal (test for significant differences). However, it doesn't explicitly differentiate from sibling tools like 't_test_one_sample' or 't_test_two_sample' beyond mentioning 'paired' and 'dependent samples'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through 'paired observations' and 'dependent samples,' suggesting this tool is for before-after or matched-pairs data. However, it doesn't provide explicit guidance on when to use this versus alternatives like 't_test_two_sample' (for independent samples) or 'wilcoxon_signed_rank' (non-parametric alternative). No exclusions or prerequisites are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses key behavioral traits: it handles ties appropriately and uses 1-based indexing. However, it lacks details on error handling (e.g., for non-numeric strings in the input array), performance characteristics, or output format. For a tool with no annotations, this is a moderate but incomplete disclosure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's function, followed by parenthetical domain/category notes. Every word earns its place, with no redundancy or fluff. It efficiently communicates the core purpose without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (ranking with tie-handling), no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on the output format (e.g., whether it returns an array of ranks), error conditions, and examples. The agent would struggle to use this tool correctly without additional context or trial-and-error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'numbers' of type array of strings. The description adds minimal semantics: it implies the list contains numbers (though the schema uses strings) and that they will be sorted. It does not explain the expected format of the strings (e.g., numeric strings), handling of invalid inputs, or any constraints. With low schema coverage, the description fails to compensate adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the rank (1-based position) of each number in a list when sorted. Handles ties appropriately.' It specifies the verb ('Get the rank'), resource ('each number in a list'), and scope ('when sorted'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'sort_numbers' or 'percentile', which perform related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('comparison'), but these are too broad to help an agent choose between this and siblings like 'sort_numbers' (which sorts but doesn't rank) or 'percentile' (which calculates percentiles). There are no explicit when-to-use or when-not-to-use instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions that the method is 'fast but requires derivative', which gives some insight into performance and prerequisites. However, it doesn't describe convergence behavior, error handling, output format, or what happens when max_iter is reached. For a numerical method tool with 5 parameters, this leaves significant gaps in understanding how the tool behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence with parenthetical clarifications. It front-loads the core purpose ('Find root of a function using Newton's method') and efficiently adds key characteristics and domain context. Every word earns its place with no redundancy or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (numerical root-finding with 5 parameters), no annotations, and no output schema, the description is insufficient. It doesn't explain what the tool returns (e.g., root approximation, iterations, convergence status), doesn't detail parameter semantics, and omits behavioral aspects like convergence criteria or error conditions. For a tool in this context, more completeness is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'requires derivative', which hints at the 'fprime' parameter, but doesn't explain any parameters explicitly. It doesn't clarify what 'func' and 'fprime' should contain (e.g., mathematical expressions), what 'x0' represents (initial guess), or the roles of 'tol' and 'max_iter'. This leaves most parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find root of a function using Newton's method'. It specifies the method (Newton's), mentions key characteristics (fast but requires derivative), and provides domain/category context (calculus, general). However, it doesn't explicitly differentiate from sibling root-finding tools like 'root_find_bisection' and 'root_find_secant', which is why it doesn't achieve a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context by noting Newton's method is 'fast but requires derivative', suggesting it's suitable when derivatives are available and speed is prioritized. However, it doesn't explicitly state when to use this tool versus alternatives like bisection or secant methods, nor does it mention prerequisites or limitations beyond the derivative requirement.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the SMA computation method but lacks critical behavioral details: it doesn't specify what happens with insufficient data (e.g., if window > data length), whether it returns an array of same length or truncated, error handling, or performance characteristics. This is inadequate for a tool with parameters and no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence defines the tool's purpose, followed by domain/category tags. There is no wasted verbiage; every element serves a clear purpose, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits essential details: parameter semantics, behavioral traits (e.g., handling edge cases), and expected output format. This leaves significant gaps for an AI agent to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It only partially explains parameters: 'window' is described as the number of last values, but 'data' is not explained at all (e.g., expected format, numeric constraints). The description adds minimal meaning beyond the bare schema, failing to address the coverage gap adequately.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Compute Simple Moving Average (SMA) - average of last 'window' values at each point.' It specifies the verb ('compute'), resource ('Simple Moving Average'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'moving_average' or 'exponential_moving_average', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context with 'Domain: timeseries, Category: analysis', suggesting it's for time series analysis. However, it provides no explicit guidance on when to use this tool versus alternatives like 'moving_average' or 'exponential_moving_average', nor does it mention prerequisites or exclusions, leaving usage somewhat vague.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the test is non-parametric and for paired samples, but doesn't disclose behavioral traits like what the output contains (e.g., test statistic, p-value), assumptions (e.g., symmetric differences), or limitations (e.g., sample size requirements). This leaves significant gaps for a statistical inference tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the key information: the test name, type, and purpose. There's no wasted text, and it's appropriately sized for a tool with a clear statistical function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, no output schema, and a statistical test with behavioral complexity, the description is incomplete. It lacks details on parameters, output format, assumptions, and usage nuances, making it inadequate for reliable tool invocation without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It doesn't explain the parameters at all—'before' and 'after' arrays or 'alpha' significance level—leaving their meaning and format undocumented. The description adds no parameter semantics beyond what's inferred from the test name.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs a Wilcoxon signed-rank test, specifying it's a non-parametric paired test for determining significant differences between paired samples. It distinguishes itself from other statistical tests by naming the specific test, though it doesn't explicitly differentiate from sibling tools like 'paired_t_test' or 't_test_two_sample' beyond mentioning it's non-parametric.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context by stating it's for 'paired samples' and 'non-parametric' testing, which suggests when to use it versus parametric alternatives. However, it doesn't provide explicit guidance on when to choose this over other non-parametric tests or when not to use it, and doesn't mention alternatives by name.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool calculates arctangent in degrees, which implies a mathematical computation with no side effects. However, it doesn't mention any behavioral aspects like error handling (e.g., for invalid inputs), performance characteristics, or whether the input 'value' represents a ratio (y/x) for single-argument arctangent. The domain/category tags add some context but don't fully describe behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence directly states the tool's core functionality. The parenthetical domain/category information is brief and relevant. There's no wasted verbiage or unnecessary elaboration, making it efficient for an AI agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single mathematical function), no annotations, no output schema, and minimal parameters, the description is somewhat complete but has gaps. It specifies what the tool does and the output unit, but doesn't explain parameter meaning, error conditions, or differentiation from similar tools. For a basic mathematical function, this might be minimally adequate, but more context would improve agent understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The tool description doesn't explain what the 'value' parameter represents (e.g., that it's the tangent ratio y/x for single-argument arctangent). Since schema coverage is 0%, the description should compensate but only adds minimal context through the domain/category. This meets the baseline for a single-parameter tool but lacks detailed semantic clarification.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate arctangent with result in degrees.' It specifies both the mathematical function (arctangent) and the output unit (degrees), which is more specific than just the tool name. However, it doesn't explicitly differentiate from its sibling 'atan' (which likely returns radians) or 'atan2_degrees', leaving some ambiguity about when to choose this exact tool.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions 'Domain: trigonometry, Category: inverse_functions' which gives high-level context but doesn't specify when to use this tool versus alternatives like 'atan' (radians output) or 'atan2_degrees' (two-argument version). No explicit when-to-use or when-not-to-use instructions are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'domain validation,' which implies input constraints (e.g., x must be in (-1, 1) for real-valued results), but doesn't detail what happens on invalid input (e.g., error handling, return values). It also omits other behavioral traits like performance, precision, or output format, making it insufficient for a mutation-free but constraint-sensitive tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: the first part states the core functionality, and the parenthetical adds domain and category context. Every sentence earns its place with no redundant information, making it efficient and easy to parse for an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no annotations, no output schema), the description is minimally adequate. It covers the basic purpose and hints at constraints but lacks details on domain specifics, error handling, or output values. For a mathematical function with potential input restrictions, more completeness would be beneficial, but it's not entirely inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It adds context by implying 'x' is the input for the inverse hyperbolic tangent function and mentions 'domain validation,' suggesting constraints on 'x.' However, it doesn't specify the exact domain (e.g., |x| < 1) or validation behavior, leaving gaps. This provides some meaning beyond the schema but not fully compensatory.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate inverse hyperbolic tangent with domain validation.' It specifies the verb ('calculate'), resource ('inverse hyperbolic tangent'), and constraint ('domain validation'), distinguishing it from generic math tools. However, it doesn't explicitly differentiate from sibling tools like 'atan' or 'atan2', which are related but not identical.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('trigonometry') and category ('inverse_hyperbolic'), but doesn't specify scenarios, prerequisites, or exclusions. For example, it doesn't clarify when to choose 'atanh' over 'atan' or other inverse hyperbolic functions, leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool computes (Bézout coefficients) but doesn't disclose behavioral traits like input constraints (e.g., handling of negative integers, zero values), computational characteristics (e.g., performance with large numbers), error conditions, or output format. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences. The first sentence clearly states the purpose, and the second provides domain/category context. There's no wasted text, and the key information is front-loaded. The parenthetical domain/category could be considered slightly extraneous but doesn't significantly detract from efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical computation tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It states what is computed but doesn't cover important aspects like input validation, error handling, output format (e.g., how coefficients are returned), or performance considerations. For a tool that solves a non-trivial mathematical problem, more context is needed for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description doesn't explicitly mention parameters, but it implicitly defines 'a' and 'b' through the equation 'ax + by = gcd(a, b)'. With 0% schema description coverage (no parameter descriptions in the schema), the description adds some semantic meaning by indicating these are integers in a Bézout identity context. However, it doesn't provide details like valid ranges, special cases (e.g., zero or negative values), or examples, so it only partially compensates for the schema gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find Bézout coefficients: integers x, y such that ax + by = gcd(a, b).' It specifies the verb ('Find'), the resource ('Bézout coefficients'), and the mathematical relationship. It distinguishes from siblings like 'extended_gcd' and 'extended_gcd_bezout' by explicitly naming the Bézout identity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: bezout_identity' which gives some context but doesn't specify when to choose this over similar tools like 'extended_gcd' or 'extended_gcd_bezout' that likely compute related values. No explicit when/when-not statements or alternatives are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a conversion, which implies a read-only, non-destructive operation, but does not specify any behavioral traits such as error handling (e.g., invalid units), precision, or output format. For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose with relevant examples. There is no wasted text, and it efficiently communicates the core functionality without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (3 parameters, no output schema, no annotations), the description is minimally adequate. It covers the basic purpose and hints at parameter semantics but lacks details on behavioral traits, full unit support, or error handling. Without annotations or output schema, it should do more to be complete, but it meets the minimum viable threshold.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It lists example units (square meters, square feet, acres, hectares, etc.), which adds meaning to the 'from_unit' and 'to_unit' parameters beyond the schema's string type. However, it does not detail the 'value' parameter or provide a full list of supported units, leaving some semantics incomplete. This partial compensation justifies a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: converting area between different units, with examples of units (square meters, square feet, acres, hectares). It specifies the verb ('convert') and resource ('area'), but does not explicitly differentiate from sibling tools like convert_length or convert_volume, which handle different types of conversions. This makes it clear but not fully sibling-distinctive.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (conversions) and category (general), but offers no explicit when/when-not instructions or references to sibling tools (e.g., convert_length for length conversions). This leaves usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates 'with high precision,' which hints at accuracy but lacks specifics on numerical stability, error handling, or performance. It does not address potential issues like input validation (e.g., handling of non-numeric inputs) or output format, leaving behavioral traits largely undefined.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured, consisting of a single sentence that front-loads the core functionality ('Calculate cosine of an angle in radians with high precision') followed by brief domain and category tags. There is no redundant or verbose language, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no annotations, no output schema), the description is minimally adequate. It covers the basic purpose and parameter unit, but lacks details on behavior, error handling, and usage compared to siblings. For a simple mathematical function, this might suffice, but it misses opportunities to fully guide an agent, such as explaining output format or common pitfalls.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('angle') with 0% description coverage, so the schema provides no semantic information. The description adds value by specifying that the angle is 'in radians,' clarifying the unit beyond the schema's type definition. However, it does not explain acceptable ranges (e.g., any real number), special cases (e.g., large values), or default behaviors, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate cosine of an angle in radians with high precision.' It specifies the verb ('calculate'), resource ('cosine'), and domain context ('trigonometry, basic_functions'). However, it does not explicitly differentiate from sibling tools like 'cos_degrees' or 'cos_series', which are closely related trigonometric functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('trigonometry') and category ('basic_functions'), which implies context, but offers no explicit instructions on when to use this tool versus alternatives like 'cos_degrees' (which handles degrees) or 'cos_series' (which might compute series approximations). There is no mention of prerequisites, limitations, or typical scenarios for application.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the input ('angle in radians') and the mathematical operation, but does not cover potential edge cases (e.g., behavior at angles where tan is zero, leading to undefined results), error handling, or output format. This leaves significant gaps for a tool performing a mathematical function with potential domain restrictions.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it directly states the tool's function in the first phrase, followed by domain and category in parentheses. Every sentence (effectively one main clause) earns its place by providing essential information without redundancy or fluff, making it highly efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no annotations, no output schema), the description is minimally adequate. It covers the basic operation and input semantics but lacks details on behavior, error cases, and output. For a mathematical function with potential domain issues, more context would be beneficial, making it just sufficient but with clear gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It adds meaning by specifying that the parameter is an 'angle in radians', which clarifies the unit and type beyond the schema's generic 'number'. However, it does not provide further details like valid ranges or constraints, resulting in a baseline score of 3 as it partially compensates for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate cotangent (1/tan) of an angle in radians.' It specifies the verb ('calculate'), resource ('cotangent'), and clarifies the mathematical relationship (1/tan). However, it does not explicitly differentiate from sibling tools like 'coth' (hyperbolic cotangent) or 'acot' (inverse cotangent), which are present in the sibling list, preventing a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance: it mentions the domain ('trigonometry') and category ('basic_functions'), which implies context but does not specify when to use this tool versus alternatives like 'tan' or 'coth'. No explicit when-to-use, when-not-to-use, or alternative tool references are included, leaving usage unclear beyond basic categorization.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It only states what the tool calculates without disclosing behavioral traits like error handling for negative inputs, performance characteristics, or output format. For a computational tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately concise with two sentences that efficiently define the operation and categorize it. Every element earns its place, though it could be slightly more front-loaded by leading with the core calculation. No wasted words or redundancy are present.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and 0% schema description coverage for a 2-parameter tool, the description is incomplete. It doesn't explain return values, error conditions, or parameter details. For a computational tool in a server with many mathematical siblings, more context is needed to ensure correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'digital root' and 'base' implicitly through the mathematical concept, but doesn't explicitly explain the 'n' parameter (the input number) or 'base' parameter's role. The description adds minimal semantic value beyond what's inferable from the tool name and schema structure.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('digital root'), including the mathematical definition ('single digit obtained by repeatedly summing digits'). It distinguishes from siblings by specifying its unique arithmetic domain and digital operations category, unlike tools like 'digit_sum' or 'digital_sum_sequence'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'digital_sum_sequence' or 'digit_sum' that might handle similar operations. This leaves the agent without contextual usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a mathematical function, implying it is a read-only, deterministic operation, but does not explicitly confirm this or mention any limitations (e.g., input constraints, performance considerations, or error handling). For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and includes domain/category tags. There is no wasted verbiage, and every element (function definition, domain) serves a clear purpose, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, no output schema, no annotations), the description is minimally adequate. It explains what the tool computes but lacks details on input validation, output format, or error cases. For a straightforward arithmetic function, this might suffice, but it does not provide a complete picture for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description adds some semantic context by defining φ(n) as 'count of integers ≤ n coprime to n,' which clarifies the parameter's role. However, it does not specify constraints (e.g., n must be positive integer) or provide examples. Given the low schema coverage, the description partially compensates but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate Euler's totient function φ(n) - count of integers ≤ n coprime to n.' It specifies the verb ('calculate'), the mathematical function, and its definition. However, it does not explicitly differentiate from sibling tools like 'euler_totient_inversion' or other arithmetic functions, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance: it mentions the domain ('arithmetic') and category ('arithmetic_functions'), but does not specify when to use this tool versus alternatives (e.g., 'euler_totient_inversion' or other number theory tools). No explicit when/when-not instructions or prerequisites are given, leaving the agent with little contextual direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates and returns e^x, but lacks details on error handling (e.g., for large inputs), precision, or computational behavior. The domain/category hint adds some context but is vague.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the tool's function, followed by clarifying details. Every sentence adds value without redundancy, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is adequate but incomplete. It covers the basic purpose but lacks details on usage, behavioral traits, and parameter semantics, leaving gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions 'x' as the input but doesn't elaborate beyond what the schema provides (type: number). With 0% schema description coverage, the description partially compensates by naming the parameter, but doesn't explain its meaning (e.g., exponent value) or constraints.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate e raised to the power of x. Returns e^x, the exponential function.' It specifies the verb ('calculate'), resource ('e^x'), and output, though it doesn't explicitly differentiate from sibling tools like 'exp_series' or 'exponential_pdf' beyond the domain/category note.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with 'Domain: arithmetic, Category: general', which implies context but doesn't specify when to use this tool versus alternatives like 'exp_series' or 'exponential_pdf'. No explicit when/when-not instructions or prerequisites are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates harmonic mean for 'positive numbers', which is a constraint not in the schema. However, it lacks details on behavior such as error handling for non-positive inputs, return format, or performance characteristics. More behavioral context would be helpful given the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and constraints, followed by domain/category tags. There is no wasted verbiage, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is somewhat complete but has gaps. It covers the basic purpose and a key constraint (positive numbers), but lacks details on return values, error cases, and usage compared to siblings. For a simple arithmetic tool, it's minimally adequate but could be more informative.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds some semantic context: it clarifies that 'numbers' should be 'positive'. This compensates partially for the schema gap. However, it does not explain the array structure, expected length, or numeric types beyond positivity, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate harmonic mean of a list of positive numbers.' It specifies the verb ('calculate'), resource ('harmonic mean'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'mean' or 'harmonic_number', which could provide similar statistical calculations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('harmonic_series'), but does not specify when to use this tool versus alternatives like 'mean' or 'harmonic_number' (which are siblings). No explicit when-to-use or when-not-to-use instructions are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates a value, implying a read-only operation, but doesn't disclose any behavioral traits such as input validation (e.g., handling negative 'n'), performance characteristics, error conditions, or output format. For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core purpose, and the second adds domain/category context. There is no wasted text, and every sentence contributes directly to understanding the tool's function. It efficiently communicates the essential information without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is minimally complete. It states what the tool does but lacks details on usage, behavior, and parameter semantics. For a simple calculator, this might suffice, but the absence of output information and behavioral context leaves room for improvement in helping an agent invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('n') with 0% description coverage. The description adds no parameter-specific information beyond implying 'n' is an integer for the calculation. It doesn't explain what 'n' represents (e.g., index, order) or any constraints (e.g., non-negative). Given the low schema coverage, the description compensates minimally, meeting the baseline for adequate but incomplete documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth icosahedral number.' It specifies the verb ('calculate') and resource ('icosahedral number'), and the domain/category context helps distinguish it from general arithmetic tools. However, it doesn't explicitly differentiate it from other figurate number tools like 'tetrahedral_number' or 'dodecahedral_number' in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), which implies context, but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'polygonal_number' or other figurate number calculators. The agent must infer usage from the category alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does (checks automorphicity) but does not describe any behavioral traits such as input constraints (e.g., handling of negative numbers, large integers), performance characteristics, error handling, or output format. This leaves significant gaps for an agent to understand how to invoke it correctly.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated in the first sentence. The additional domain and category information is brief and relevant. There is no wasted verbiage, making it efficient for quick understanding, though it could be slightly more structured with explicit parameter or usage notes.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (mathematical check with one parameter), no annotations, no output schema, and low schema description coverage, the description is incomplete. It lacks details on behavioral traits, parameter semantics, and output expectations, which are crucial for an agent to use the tool effectively. The domain/category tags do not compensate for these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It implies the parameter 'n' is the number to check, but does not specify any semantics beyond that (e.g., valid ranges, integer type). The description adds minimal value over the schema, as it does not explain parameter meaning or usage, resulting in a baseline score due to the lack of detailed parameter information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('if a number is automorphic'), and includes a precise mathematical definition ('its square ends with the number itself'). It also distinguishes from sibling tools by specifying a unique arithmetic domain and category, unlike generic tools like 'is_prime' or 'is_even'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention any prerequisites, constraints, or sibling tools that might be relevant (e.g., 'automorphic_numbers' for generating such numbers). The domain and category tags are generic and do not offer specific usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does (checking coprimality) but doesn't disclose behavioral traits like input constraints (e.g., handling of negative numbers, zero, or large integers), performance characteristics, error handling, or output format. The description is purely functional without operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence with parenthetical clarification and domain/category tags. It's front-loaded with the core purpose and avoids unnecessary verbiage. The domain/category could be considered slightly extraneous but adds useful context without significant bloat.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (2 parameters, no annotations, no output schema), the description is minimally adequate but lacks completeness. It doesn't explain what the output will be (e.g., boolean true/false, or a structured result), doesn't cover edge cases, and provides no examples. For a mathematical tool, more operational context would be helpful despite the straightforward function.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'two numbers' which aligns with parameters 'a' and 'b', but doesn't add meaning beyond what's obvious from the schema (two integers). No details about parameter interpretation (e.g., order matters, valid ranges) are provided. With 0% coverage and minimal parameter clarification, this meets the baseline for adequate but incomplete documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('if two numbers are coprime'), and provides the mathematical definition ('their greatest common divisor is 1'). It also includes domain/category context ('Domain: arithmetic, Category: number_theory') that helps distinguish it from sibling tools, though not by direct comparison.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category hints at context, it doesn't explicitly state when this tool is appropriate or when other tools (like 'gcd' or 'is_prime') might be better choices. No usage boundaries or prerequisites are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the mathematical operation but doesn't disclose behavioral traits like input validation (e.g., handling of non-positive integers), performance characteristics, error conditions, or return format. The description is purely functional without operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in a single sentence that states the purpose and mathematical definition, with no wasted words. The domain/category in parentheses is slightly extraneous but not disruptive. It's appropriately front-loaded with the core functionality.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and minimal schema coverage, the description is incomplete. It doesn't explain what the tool returns (e.g., boolean, detailed analysis), error handling, or edge cases. For a mathematical function with potential input constraints, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage and only one parameter, the description adds value by implying 'n' should be an integer to check for deficiency. However, it doesn't specify constraints (e.g., positive integers only) or provide examples. The baseline is 3 since the schema covers the parameter type minimally.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific verb ('Check if') and resource ('a number'), and defines the mathematical condition ('sum of proper divisors < n'). It distinguishes from siblings like 'is_abundant_number' and 'is_perfect_number' by specifying the deficiency condition.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'is_abundant_number' or 'is_perfect_number', nor does it mention prerequisites or typical use cases. The domain/category tags are generic and don't offer practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe how it behaves: e.g., whether it handles non-numeric inputs gracefully, returns a boolean, or throws errors. For a simple comparison tool, this is a moderate gap, as the agent lacks operational details beyond the basic check.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence stating the tool's purpose, followed by a brief parenthetical for context. Every word earns its place with no redundancy or fluff, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, simple boolean output), no annotations, no output schema, and 0% schema description coverage, the description is minimally adequate. It states the core purpose but lacks details on behavior, error handling, or output format. For such a simple tool, this is borderline acceptable but leaves gaps an agent might need to infer.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (x) with 0% description coverage, so the schema only indicates it's a number. The description doesn't add any parameter semantics beyond implying 'x' is the number to check. This meets the baseline of 3 since the schema provides the type, but the description doesn't compensate for the lack of schema descriptions (e.g., explaining NaN semantics for 'x').
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is NaN (Not a Number).' It includes a specific verb ('Check') and resource ('a number'), and the parenthetical adds domain/category context. However, it doesn't explicitly distinguish this from sibling tools like 'is_finite' or 'is_infinite' that also check number properties, though the NaN focus is inherently distinct.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('comparison'), but doesn't specify scenarios (e.g., validating input after division by zero) or contrast it with similar sibling tools like 'is_finite' or 'is_infinite'. Without such context, an agent must infer usage from the name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool performs a comparison check but doesn't disclose behavioral traits like error handling (e.g., for non-numeric inputs), performance characteristics, or output format. The description is basic and lacks details needed for full transparency in the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category tags in parentheses. Every word earns its place with zero waste, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (simple comparison), two parameters with basic schema, no annotations, and no output schema, the description is minimally adequate. It covers the core purpose but lacks details on output (e.g., boolean result) and error cases. For such a simple tool, it's passable but could be more informative.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaningful semantics: it clarifies that parameter 'a' is 'the first number' and 'b' is 'the second number', and that the tool checks if 'a' is less than 'b'. This compensates somewhat for the lack of schema descriptions. However, it doesn't specify numeric types (e.g., integer vs. float) or constraints beyond what the schema implies.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if the first number is less than the second number.' It specifies the verb ('check') and resource ('numbers'), and distinguishes it from other arithmetic tools by focusing on comparison. However, it doesn't explicitly differentiate from its closest sibling 'greater_than' beyond the domain/category tags.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It includes domain and category tags ('Domain: arithmetic, Category: comparison'), which imply context but don't explicitly state when to use this tool versus alternatives like 'greater_than', 'equal', or 'less_than_or_equal'. No specific scenarios, prerequisites, or exclusions are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the test's purpose and domain but lacks details on what the tool returns (e.g., U statistic, p-value, effect size), error handling, assumptions (e.g., independence of samples), or performance characteristics. For a statistical inference tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that packs key information: the tool name, its statistical purpose, and context. It's front-loaded with the main action and avoids redundancy. However, it could be more structured by separating usage notes or parameter hints, but given its brevity, it earns a high score for conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a statistical test, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the tool returns, assumptions, or how to interpret results. For a tool with three parameters and inference purposes, more detail is needed to ensure proper use by an AI agent, making this inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema only defines parameter types without descriptions. The description adds no information about parameters like 'data1', 'data2', or 'alpha' (e.g., that 'alpha' is the significance level). It partially compensates by implying two independent samples are needed, but doesn't explain parameter meanings or constraints, leaving them undocumented. Baseline is 3 due to the schema's basic coverage, but the description adds minimal value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Perform Mann-Whitney U test' with the explanation that it's a 'non-parametric alternative to t-test' to 'test whether two independent samples come from same distribution.' It specifies the domain (statistics) and category (inference), making the verb+resource relationship explicit. However, it doesn't differentiate from sibling tools like 't_test_two_sample' or 'wilcoxon_signed_rank', which are related statistical tests.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context by mentioning it's a 'non-parametric alternative to t-test' and for 'two independent samples,' suggesting when it might be preferred over parametric tests. However, it doesn't explicitly state when to use this tool versus alternatives like 't_test_two_sample' or other non-parametric tests in the sibling list, nor does it provide exclusions or prerequisites. The guidance is present but not comprehensive.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool retrieves 'known' exponents, implying a read-only operation, but does not specify whether this is a lookup from a fixed database, a computational process, or if it has any limitations (e.g., performance, data freshness). For a tool with no annotations, this leaves significant gaps in understanding its behavior and constraints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by optional metadata in parentheses. Every word earns its place, with no redundancy or fluff. It efficiently communicates the core functionality without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is minimally adequate. It covers the basic purpose and parameter intent, but lacks details on behavioral traits, usage context, or output format. For a read-only lookup tool, this might suffice, but the absence of annotations and output schema means the agent must infer more from limited information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('limit') with 0% description coverage, meaning the schema provides no semantic context. The description adds value by explaining that 'limit' bounds the exponents retrieved ('up to a limit'), which clarifies its purpose. However, it does not specify units (e.g., integer values), valid ranges, or default behavior, leaving some ambiguity. Given the low schema coverage, the description partially compensates but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get known Mersenne prime exponents up to a limit.' It specifies the verb ('Get'), resource ('Mersenne prime exponents'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'mersenne_numbers' or 'is_mersenne_prime', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a 'Domain' and 'Category' (arithmetic, special_primes), but this is generic metadata that does not help an agent choose between sibling tools like 'mersenne_numbers' (which might compute Mersenne numbers) or 'is_mersenne_prime' (which tests primality). No explicit when-to-use, when-not-to-use, or alternative tools are indicated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool finds the smaller number but doesn't disclose behavioral traits like error handling (e.g., for non-numeric inputs), performance characteristics, or whether it returns a single value or additional metadata. For a simple comparison tool, this is minimal but adequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: one clear sentence stating the tool's purpose, followed by domain/category in parentheses. Every word earns its place with zero redundancy, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple 2-parameter comparison tool with no annotations or output schema, the description is minimally complete. It explains what the tool does but lacks details on return values, error conditions, or usage context. Given the tool's simplicity, this is adequate but leaves gaps an agent might need to infer.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaningful context: it clarifies that parameters 'a' and 'b' are numbers to compare. However, it doesn't specify numeric types (integer vs float), ranges, or special cases (e.g., NaN, infinity). Given the simple schema, this provides basic compensation but lacks depth.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the smaller of two numbers.' It specifies the verb ('find'), resource ('two numbers'), and domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'minimum' vs 'min_list' or 'clamp', which have similar comparison purposes but different scopes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions domain (arithmetic) and category (comparison), it doesn't specify use cases, prerequisites, or when to choose this over similar sibling tools like 'minimum' vs 'min_list' (which handles lists) or 'clamp' (which bounds values).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the basic behavior (finding the mode and returning all most frequent values), but lacks critical details such as how it handles empty lists, ties, non-numeric inputs (since the schema expects strings), error conditions, or performance characteristics. For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with two sentences that directly state the purpose and return behavior. Every word earns its place, and there is no redundancy or unnecessary information. The parenthetical domain/category note is brief and relevant.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (statistical operation with one parameter), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on input handling, error cases, output format (beyond a high-level description), and practical usage context. The absence of structured support makes the description insufficient for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'a list of numbers' for the 'numbers' parameter, but does not explain that the schema expects strings (not numbers), clarify formatting (e.g., comma-separated, numeric strings), or detail constraints (e.g., minimum list length, allowed numeric formats). This adds minimal semantic value beyond the schema's type definition.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Find') and resource ('mode in a list of numbers'), specifies the exact mathematical operation, and distinguishes it from siblings by focusing on statistical mode calculation rather than other mathematical functions like mean, median, or trigonometric operations. It explicitly mentions the return behavior ('Returns all values that appear most frequently'), which is precise.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but does not specify scenarios where mode is preferred over other central tendency measures (e.g., mean or median), nor does it reference sibling tools for related operations. Usage is implied only by the tool's name and purpose.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the tool is for forecasting but doesn't describe key behaviors: what the output looks like (e.g., single value or array), error handling (e.g., for invalid inputs), computational characteristics, or any limitations (e.g., window size constraints). This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in one sentence followed by domain/category tags. There's no wasted text, and it efficiently communicates the essential idea without redundancy, though it could be slightly more informative without losing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 3 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain parameter details, output format, or behavioral traits, making it inadequate for an agent to use the tool effectively. The domain/category hints help but don't compensate for the lack of critical information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning parameters are undocumented in the schema. The description adds no specific information about parameters like 'data', 'window', or 'forecast_periods' beyond implying they relate to 'recent observations' and 'predict next value.' It doesn't explain data format, window meaning, or forecast_periods usage, so it provides minimal semantic value, aligning with the baseline for low coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'predict next value using average of recent observations.' It specifies the verb ('predict'), resource ('next value'), and method ('average of recent observations'). However, it doesn't explicitly differentiate from sibling tools like 'simple_moving_average' or 'exponential_moving_average' that might also involve moving averages, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context with 'Domain: timeseries, Category: analysis,' suggesting it's for time series analysis. However, it provides no explicit guidance on when to use this tool versus alternatives (e.g., 'holt_winters_forecast' or other forecasting methods), nor does it mention prerequisites or exclusions, leaving usage somewhat vague.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. The description states that the tool 'Get NaN,' implying it returns a value, but does not specify what type of value (e.g., a float constant), any side effects, or error conditions. It lacks details on how NaN is represented or any limitations, which is insufficient for a tool with no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and well-structured in a single sentence: 'Get NaN (Not a Number). Represents undefined or invalid mathematical operations. (Domain: arithmetic, Category: general).' It front-loads the core purpose and efficiently adds context without unnecessary details. However, the parenthetical domain and category could be integrated more smoothly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no output schema, no annotations), the description is adequate but has gaps. It explains what NaN is and its domain, but does not cover behavioral aspects like return format or usage context relative to siblings. For a tool in a server with many mathematical functions, more guidance on when to use it would improve completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so no parameter information is needed. The description does not mention parameters, which is appropriate. It adds value by explaining what NaN represents, but since there are no parameters, a baseline score of 4 is applied as it meets the requirement without redundancy.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get NaN (Not a Number).' It specifies the verb ('Get') and the resource ('NaN'), and explains what NaN represents ('undefined or invalid mathematical operations'). However, it does not explicitly differentiate this tool from sibling tools like 'is_nan', which likely checks if a value is NaN rather than retrieving NaN itself.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance on when to use this tool. It mentions the domain ('arithmetic') and category ('general'), but does not specify scenarios or alternatives. For example, it does not clarify when to use this tool versus a constant like 'infinity' or other mathematical operations, nor does it explain its role among sibling tools such as 'is_nan'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden but only states the basic operation without behavioral details. It doesn't cover error handling (e.g., for non-numeric inputs), performance, or output format, leaving gaps for a tool with undocumented parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with the core purpose stated in the first clause and additional context (domain/category) efficiently appended. Every word serves a purpose without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema), the description is minimal but incomplete. It lacks details on parameter semantics and behavioral traits, which are essential even for basic tools to ensure correct usage by an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description doesn't explain the parameter 'x' beyond implying it's a number. No details on valid ranges, special cases (e.g., zero, infinity), or examples are provided, failing to compensate for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('negate a number') and the outcome ('return its additive inverse'), distinguishing it from sibling tools like 'abs_value' or 'sign' by focusing on mathematical negation rather than absolute value or sign extraction. The domain/category tags further contextualize it within arithmetic operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives. While the description implies it's for arithmetic negation, it doesn't mention scenarios where other tools (e.g., 'multiply' with -1) might be preferable or any prerequisites for use.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'Get[s] the nth power of two,' implying a read-only operation, but does not address potential errors (e.g., negative or large 'n' values), performance characteristics, or output format. For a tool with no annotations, this leaves significant behavioral gaps, though it at least implies a safe read operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: a single sentence that directly states the tool's purpose with no wasted words. The additional domain and category information is brief and relevant, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one integer parameter) and lack of annotations or output schema, the description is minimally adequate. It covers the basic purpose and parameter semantics but lacks details on usage guidelines, behavioral traits, and error handling. For such a simple tool, it meets the minimum viable threshold but has clear gaps in completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, so the description must compensate. It adds that 'n' is '0-indexed,' which clarifies the indexing semantics beyond the schema's type ('integer'). However, it does not explain valid ranges, constraints, or examples, leaving some ambiguity. Given the low schema coverage, this partial compensation justifies a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the nth power of two (0-indexed).' It specifies the verb ('Get'), resource ('nth power of two'), and clarifies indexing ('0-indexed'), which is helpful. However, it does not explicitly differentiate from sibling tools like 'powers_of_two' or 'is_power_of_two', which are related but distinct operations, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('basic_sequences'), but this is too vague to inform usage decisions. There is no mention of prerequisites, constraints, or comparison to sibling tools like 'powers_of_two' or 'is_power_of_two', leaving the agent without clear direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the conversion action but lacks behavioral details such as input validation (e.g., handling invalid octal strings), error handling, or output format. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is brief and front-loaded with the core purpose in the first sentence. The domain/category tags are efficient but could be integrated more seamlessly. No wasted words, though slightly terse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low parameter coverage, the description is incomplete. It doesn't explain what the tool returns (e.g., integer, string), error conditions, or usage nuances, leaving significant gaps for a conversion tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It implies the parameter is an octal string but doesn't specify format constraints (e.g., valid characters, leading zeros). The description adds minimal meaning beyond the schema's basic type definition.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Convert') and resource ('octal (base-8) to decimal number'), and distinguishes it from siblings by specifying the exact conversion type. The domain and category tags further clarify its mathematical context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like 'base_to_decimal' or 'decimal_to_octal' among the many sibling tools. The description only states what it does, without context or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('dynamic programming'), which hints at computational behavior, but does not describe performance characteristics (e.g., time complexity for large n), error handling, or output format. This is a significant gap for a tool with no annotations, as the agent lacks insight into its operational traits.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with a single sentence stating the core functionality followed by domain/category tags. Every part earns its place, but the domain/category tags are somewhat redundant given the sibling context. It could be slightly more efficient by integrating the tags into the main sentence.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with one parameter), no annotations, and no output schema, the description is minimally adequate. It covers the purpose and method but lacks details on behavior, output format, and usage context. For a tool in a server with many siblings, more guidance is needed to ensure the agent can use it correctly without trial and error.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, so the description must compensate. It adds meaning by specifying that 'n' is the integer whose partitions are counted, which is crucial semantic context not in the schema. However, it does not detail constraints (e.g., n must be non-negative) or examples, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Count the number of integer partitions of n using dynamic programming.' It specifies the verb ('Count'), resource ('integer partitions of n'), and method ('dynamic programming'), distinguishing it from siblings like 'distinct_partitions' or 'partitions_into_k_parts'. However, it does not explicitly differentiate from all siblings, such as 'generate_partitions', which might generate partitions rather than count them.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('partitions'), but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if this is for counting all partitions or distinct ones, or when to choose it over other partition-related tools in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a Pell number, implying a read-only operation, but does not address potential constraints like input range (e.g., n must be non-negative), performance considerations (e.g., recursion depth for large n), or error handling. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose. Every word earns its place, with no redundant information. The parenthetical domain and category are brief and add context without verbosity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer parameter) and lack of annotations or output schema, the description is minimally adequate. It explains what the tool does but lacks details on usage, behavioral traits, or parameter constraints. For a simple arithmetic tool, this might suffice, but it leaves gaps that could hinder an agent's ability to use it correctly in all scenarios.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds minimal semantics by specifying 'nth' in 'Calculate the nth Pell number P_n', indicating 'n' is an index. However, it does not explain valid ranges (e.g., n >= 0) or the meaning of 'P_n', which is insufficient to fully compensate for the low schema coverage. The baseline is 3 due to the single parameter, but the description adds only marginal value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Pell number P_n.' It specifies the verb ('Calculate'), resource ('Pell number'), and parameter ('nth'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'pell_sequence' or 'pell_lucas_number', which is why it scores 4 instead of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), but this is too vague to help an agent choose between similar tools like 'pell_sequence' or 'pell_lucas_number'. There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe important behavioral aspects: what 'n' represents (e.g., maximum value constraints, whether it must be positive), the output format (e.g., list of integers), performance characteristics, or error handling. For a tool with zero annotation coverage, this is insufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded with the core purpose in the first sentence. The domain/category information in parentheses adds useful context without verbosity. Every word serves a clear purpose with zero wasted text.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no annotations), the description is incomplete. It doesn't explain the parameter semantics adequately, doesn't describe the output format, and provides no behavioral context. While the tool is mathematically straightforward, the description leaves too much for the agent to infer.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for the undocumented parameter 'n'. The description mentions 'n' in context ('the first n perfect squares') but doesn't explain its meaning, constraints (e.g., must be positive integer, range limits), or provide examples. This leaves significant ambiguity about parameter usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Generate') and resource ('the first n perfect squares'), and distinguishes it from siblings by specifying the exact sequence type. It also provides domain/category context ('Domain: arithmetic, Category: basic_sequences') which helps differentiate it from other mathematical tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain/category, it doesn't specify use cases, prerequisites, or compare it to similar tools like 'square_numbers' or 'nth_perfect_square' that appear in the sibling list. The agent must infer usage from the purpose alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool returns 'the prime factorization as a list', which is useful behavioral information. However, it doesn't disclose important traits like input constraints (e.g., n must be positive, handling of large numbers, error behavior for non-integer inputs), performance characteristics, or whether duplicates are included for repeated prime factors. For a mathematical tool with no annotation coverage, this leaves significant gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core purpose, the second adds return format, and the parenthetical provides domain context. Every sentence earns its place with zero waste, making it easy for an agent to parse quickly. The structure is logical and efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, list output) and no annotations or output schema, the description is minimally complete. It covers the basic operation and return type but lacks details on input constraints, error handling, and output formatting (e.g., sorted order, multiplicity representation). For a simple mathematical function, this is adequate but leaves room for improvement in guiding an agent fully.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds no parameter-specific semantics beyond implying 'n' is the number to factorize. It doesn't clarify valid ranges (e.g., n > 0), special cases (n=0,1,negative), or formatting expectations. Since schema coverage is low, the description compensates minimally, meeting the baseline but not adding meaningful detail.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all prime factors of a number' with the verb 'find' and resource 'prime factors', and specifies the return format 'as a list'. It distinguishes from siblings like 'is_prime' or 'prime_count' by focusing on factorization rather than primality testing or counting. However, it doesn't explicitly differentiate from potential factorization alternatives (though none are listed among siblings).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: number_theory', which gives broad context but doesn't help an agent choose between this and siblings like 'divisors' or 'prime_gap'. There are no explicit when/when-not instructions or named alternatives, leaving usage decisions to inference.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'high precision,' which adds some context about output quality, but fails to describe other critical behaviors such as error handling (e.g., for invalid inputs), performance characteristics, or the format of the result. For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence directly states the tool's purpose, and the second provides domain/category tags without unnecessary elaboration. Every word serves a clear purpose, making it efficient and easy to parse for an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one input, no output schema, no annotations), the description is minimally adequate. It covers the basic purpose and domain but lacks details on output format, error conditions, or precision specifics. While the simplicity of the tool means extensive documentation isn't critical, the absence of any behavioral or output information keeps the completeness at a baseline level.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the tool has only one parameter ('radians'), which is self-explanatory given the tool's name and purpose. The description does not add any parameter-specific details beyond what is implied by the context, such as expected units or valid ranges. With a single, straightforward parameter, the baseline score of 3 is appropriate, as the schema's lack of description is mitigated by the parameter's simplicity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert radians to degrees with high precision.' It specifies the verb ('Convert'), resource ('radians to degrees'), and quality ('high precision'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'degrees_to_radians' or 'convert_angle', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal guidance with the domain and category tags ('Domain: trigonometry, Category: angle_conversion'), which imply usage in trigonometric contexts. However, it lacks explicit instructions on when to use this tool versus alternatives like 'degrees_to_radians' or 'convert_angle', and offers no exclusions or prerequisites. This leaves the agent with insufficient direction for optimal tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the conversion action without detailing output format, precision, error handling (e.g., invalid inputs), or any side effects. For a tool with no annotations, this leaves significant gaps in understanding how it behaves beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Convert radians to gradians.' The additional domain/category tag is brief and does not detract. Every word serves a purpose, with no redundant or verbose language, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no annotations, no output schema), the description is minimally complete. It states what the tool does but lacks details on behavior, output, or usage context. For a simple conversion tool, this might be sufficient, but it does not fully compensate for the absence of annotations or output schema, leaving some operational questions unanswered.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter ('radians') with 0% description coverage, so the schema provides no semantic context. The description does not add any parameter-specific information beyond implying the input is in radians. It does not explain units, valid ranges, or examples. However, with only one parameter and a straightforward conversion, the baseline is adequate but minimal.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Convert radians to gradians.' It specifies both the verb ('Convert') and the resource/transformation ('radians to gradians'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'degrees_to_gradians' or 'radians_to_degrees', which perform similar angle conversions but with different units.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it includes a domain/category tag ('Domain: trigonometry, Category: angle_conversion'), this is generic and does not specify scenarios, prerequisites, or comparisons to sibling tools such as 'degrees_to_gradians' or 'convert_angle'. There is no explicit when-to-use or when-not-to-use information.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates a random integer within an inclusive range, which implies a read-only, non-destructive operation. However, it lacks details on randomness quality (e.g., pseudorandom vs. cryptographic), distribution (uniform), side effects, rate limits, or error handling (e.g., if min_val > max_val). For a tool with no annotations, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core functionality ('Generate a random integer...') and includes essential details (range, inclusiveness) without waste. The parenthetical domain/category note is brief and relevant. It's appropriately sized for a simple tool with two parameters.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (two integer parameters, no output schema, no annotations), the description is minimally complete. It covers the basic operation and parameter roles but lacks depth in behavioral transparency and usage guidelines. For a random number generator, additional context on randomness properties or error cases would enhance completeness, but it's adequate for the simple schema.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter descriptions. The description adds meaning by explaining that min_val and max_val define an inclusive range for the random integer. However, it doesn't specify constraints (e.g., valid integer ranges, handling of negative values, or what happens if min_val equals max_val). It compensates partially but not fully for the lack of schema documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Generate') and resource ('a random integer') with specific boundaries ('between min_val and max_val (inclusive)'). It distinguishes from siblings by specifying the random integer generation domain, though it doesn't explicitly differentiate from other random tools (like random_float or random_array) that might exist in the sibling list. The purpose is unambiguous but could be more distinct regarding sibling tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('general'), but this is too vague to inform selection among the many arithmetic/general sibling tools (e.g., random_float, uniform_sample). There are no explicit when/when-not statements or named alternatives, leaving the agent without practical usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it states the mathematical operation and input format, it doesn't describe important behavioral aspects like error handling (e.g., what happens when cos(angle)=0), output format, precision, or computational characteristics. The description is mathematically correct but operationally incomplete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and well-structured. The first sentence directly states the tool's function and input requirements, while the parenthetical adds useful categorization without redundancy. Every word earns its place, and the information is front-loaded effectively.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical simplicity (single input, no output schema, no annotations), the description is adequate but has clear gaps. It covers the basic operation and input format but lacks information about output format, error conditions, and practical usage context. For a basic mathematical function, this is minimally viable but could be more complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate. It specifies that the parameter 'angle' should be in radians, which adds meaningful context beyond the schema's type declaration. However, it doesn't provide additional details like valid ranges, special values, or units beyond radians. With one parameter and partial semantic information, this meets the baseline expectation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate secant (1/cos) of an angle in radians.' It specifies the mathematical operation (calculate secant), the input (angle in radians), and provides domain/category context. However, it doesn't explicitly differentiate from sibling trigonometric tools like 'csc' (cosecant) or 'cos' (cosine), which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions the domain (trigonometry) and category (basic_functions), but offers no explicit advice on when to use this tool versus alternatives like 'cos' or other trigonometric functions. There's no mention of typical use cases, edge cases, or comparisons with sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool finds prime pairs but does not describe output format, performance characteristics (e.g., computational limits), error handling, or whether it's read-only or mutative. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. Every element earns its place with no redundant information, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is minimally adequate. It explains what the tool does but lacks details on behavior, output format, and usage context. While it meets basic requirements, it does not fully compensate for the absence of structured data like annotations or output schema.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'limit' of type integer. The description adds context by specifying 'up to limit', implying an upper bound for the search. However, it does not detail constraints (e.g., minimum value, handling of invalid inputs) or examples, providing only basic semantic clarification beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find all sexy prime pairs (primes differing by 6) up to limit.' It specifies the verb ('Find'), resource ('sexy prime pairs'), and scope ('up to limit'), making it easy to understand what the tool does. However, it does not explicitly differentiate from sibling tools like 'cousin_primes' or 'twin_prime_pairs', which also find prime pairs with specific differences.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('prime_patterns'), but does not specify scenarios, prerequisites, or comparisons to sibling tools such as 'cousin_primes' or 'twin_prime_pairs'. This leaves the agent without explicit usage instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a Tribonacci number, implying a deterministic mathematical function, but does not describe potential behaviors such as handling of negative or large integer inputs, performance characteristics, or error conditions. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and includes domain/category tags. There is no wasted verbiage, and every element (calculation, parameter, context) earns its place efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is minimally adequate. It covers the basic purpose but lacks details on usage, behavior, and parameter semantics that would enhance completeness. For a simple mathematical function, it meets a baseline but could be more informative to fully guide an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds minimal semantics by specifying 'nth' in the context of Tribonacci numbers, implying 'n' is an index. However, it does not elaborate on valid ranges, default values, or examples, leaving the schema to define the parameter fully. Given the low schema coverage, the description provides some but insufficient compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Tribonacci number T_n.' It specifies the verb ('Calculate'), resource ('Tribonacci number'), and parameter ('nth'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'fibonacci' or 'tetranacci_number', which are similar recursive sequence tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), which implies context but does not specify use cases, prerequisites, or comparisons to siblings like 'fibonacci' or 'tetranacci_number'. This lack of explicit guidance limits its utility for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It only states what the tool calculates without disclosing behavioral traits such as input validation (e.g., handling of non-positive integers), performance characteristics, error handling, or output format. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted verbiage, making it efficient and easy to parse for an AI agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, no output schema, and low schema coverage, the description is incomplete. It fails to address key contextual elements such as return values, error conditions, or practical usage examples, leaving significant gaps for a tool that performs a mathematical calculation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description implies the parameter 'n' is an integer for which Ω(n) is computed. However, it does not add details like valid ranges (e.g., n > 0), examples, or edge cases. With low schema coverage, the description provides minimal compensation, meeting the baseline for partial parameter context.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Calculate Ω(n) - total number of prime factors (with multiplicity).' It specifies the verb ('Calculate'), the mathematical function (Ω(n)), and clarifies the domain and category, distinguishing it from siblings like 'little_omega' or 'prime_factors' by focusing on total count with multiplicity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify scenarios, prerequisites, or comparisons to sibling tools like 'prime_factors' or 'divisor_count', leaving the agent without usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'ensures the value stays within specified limits,' which implies a deterministic, non-destructive operation, but lacks details on error handling (e.g., invalid inputs), performance, or output format. Without annotations, this is a significant gap for a tool that modifies numeric values, warranting a low score.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded and highly efficient: two sentences that directly state the tool's function and outcome, with no wasted words. The parenthetical domain and category add minimal but relevant context without redundancy. Every sentence earns its place, making it appropriately sized for a simple tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (3 parameters, no nested objects, no output schema) and lack of annotations, the description is minimally adequate. It explains the basic operation but misses behavioral details like error handling or output specifics. Without annotations or output schema, it should provide more context for safe use, but it meets the baseline for a simple arithmetic tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates by explaining the parameters' roles: 'value' to clamp, and 'min_val' and 'max_val' as bounds. It adds meaning beyond the schema's type definitions, clarifying the clamping logic. However, it does not detail constraints (e.g., min_val <= max_val) or examples, preventing a perfect score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Clamp a value between a minimum and maximum bound. Ensures the value stays within specified limits.' It specifies the verb ('clamp'), resource ('value'), and outcome ('within specified limits'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'between' or 'in_range', which might have similar numeric range-checking functions, so it falls short of a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('comparison'), but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if it handles edge cases like min_val > max_val or compare to siblings like 'between' or 'in_range', leaving usage context implied at best.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool generates the sequence until reaching 1, which implies iterative computation, but lacks details on behavior such as error handling for invalid inputs, computational limits, or output format. This leaves significant gaps in understanding how the tool operates beyond the basic algorithm.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted language, and it efficiently communicates the core purpose without unnecessary elaboration, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical sequence generator with no annotations, no output schema, and low parameter coverage, the description is incomplete. It fails to address key aspects such as the output format (e.g., list of integers), error conditions, or performance implications, leaving the agent with insufficient context for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage. The description adds minimal semantics by indicating 'n' is the starting point for the sequence, but does not specify constraints (e.g., must be a positive integer) or provide examples. Given the low schema coverage, the description compensates slightly but not fully, meeting the baseline for partial value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Generate') and resource ('Collatz sequence'), and distinguishes it from siblings by specifying the mathematical problem (3n+1). It explicitly mentions the domain and category, which helps differentiate it from other arithmetic or iterative sequence tools in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain and category, it does not specify scenarios, prerequisites, or exclusions. For example, it doesn't indicate if 'n' must be positive or if there are performance considerations for large inputs.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses 'numerical stability' as a key behavioral trait, which is valuable for understanding performance with large/small inputs. However, it doesn't cover other aspects like error handling, input constraints (e.g., domain limits), or output format. The description adds some context but is incomplete for a computational tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that states the core purpose and key trait, followed by domain/category tags. Every word earns its place with no redundancy or fluff. It's appropriately sized for a simple mathematical function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low parameter coverage, the description is incomplete. It covers the basic purpose and a stability trait but misses parameter explanations, usage context, and behavioral details like error handling. For a computational tool with one parameter, more guidance is needed to be fully helpful to an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It doesn't mention the parameter 'x' at all, nor explain its meaning (e.g., input angle in radians). The description adds no parameter semantics beyond what the bare schema provides, leaving the parameter undocumented. Baseline is 3 due to low schema coverage but lack of compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate hyperbolic cosine with numerical stability.' It specifies the verb ('calculate'), resource ('hyperbolic cosine'), and a key behavioral trait ('numerical stability'). However, it doesn't explicitly distinguish it from sibling hyperbolic tools like 'cosh' (implied) or 'acosh', though the domain/category tags help.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: trigonometry, Category: hyperbolic' which gives general context, but doesn't specify scenarios, prerequisites, or comparisons to siblings like 'cosh' (if present) or other hyperbolic functions. No explicit when/when-not instructions are included.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the input ('angle in radians') but does not disclose behavioral traits such as error handling (e.g., for angles where sin=0), output format, or computational limits. The description is minimal and lacks essential operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's function. There is no wasted language, and it efficiently communicates the core purpose without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks information on output values, error conditions, and practical usage examples, making it insufficient for an AI agent to reliably invoke the tool without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, but the description adds meaning by specifying that the parameter is an 'angle in radians'. However, it does not provide further details like valid ranges, units, or examples. With one parameter and low schema coverage, the description offers basic but incomplete semantic context.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Calculate'), resource ('cosecant'), and mathematical definition ('1/sin of an angle in radians'). It distinguishes itself from sibling tools like 'sin', 'csc', and 'acsc' by specifying it's a trigonometric function for cosecant calculation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain (trigonometry) and category (basic_functions), it does not specify use cases, prerequisites, or comparisons to related tools like 'sin' or 'acsc' for inverse cosecant.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the mathematical function but doesn't disclose behavioral traits like input constraints (e.g., negative numbers, zero, large integers), performance characteristics, or what happens with invalid inputs. The description is mathematically accurate but operationally incomplete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with a single sentence that directly states the tool's purpose and mathematical context. Every word earns its place, and there's no redundant information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the return value (e.g., integer count), error handling, or practical usage details. For a tool with minimal structured data, the description should provide more operational context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It explains that parameter 'n' represents 'a number' for which divisors are counted, adding semantic meaning beyond the schema's type declaration. However, it doesn't specify constraints (e.g., positive integers only) or examples, leaving gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Count') and resource ('positive divisors of a number'), and distinguishes it from siblings by specifying the mathematical function (divisor function τ(n)). It also provides domain and category context, making it highly specific.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain (arithmetic) and category (number_theory), it doesn't specify when this tool is appropriate compared to other divisor-related tools like 'divisors' or 'divisor_sum' in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'Get[s]' the constant, implying a read-only operation, but does not clarify if it requires computation, has performance characteristics, or returns a specific format. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior beyond the basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured: it states the purpose upfront ('Get the Euler-Mascheroni constant γ ≈ 0.57722.'), adds context with the mathematical definition, and includes domain/category tags efficiently. Every sentence earns its place without redundancy, making it easy for an AI agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is adequate but has gaps. It explains what the tool does and provides mathematical context, but without annotations or output schema, it lacks details on behavioral traits (e.g., computation method, error handling) and return format. This is the minimum viable for such a tool, but more completeness would be beneficial.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has 0 parameters, and the input schema has 100% description coverage (though empty). The description does not need to explain parameters, so it appropriately focuses on the constant itself. It adds value by providing the constant's approximate value and mathematical definition, which compensates for the lack of parameters. A baseline of 4 is suitable for zero-parameter tools.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the Euler-Mascheroni constant γ ≈ 0.57722.' It specifies the exact mathematical constant being retrieved and provides its approximate value. However, it does not explicitly differentiate from sibling tools like 'compute_euler_gamma_harmonic' or 'constant_relationships', which might offer related functionality, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the constant's mathematical definition ('Limit of harmonic series minus natural logarithm') and domain/category tags, but these do not help an AI agent choose between this and sibling tools like 'compute_euler_gamma_harmonic' or 'constant_relationships'. There is no explicit when-to-use or when-not-to-use advice.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While it mentions the operation is 'similar to % but for floats', it doesn't describe edge cases (e.g., division by zero, NaN handling), precision considerations, or what the output looks like. For a mathematical operation tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with just two sentences that directly state the purpose and provide a helpful analogy. Every word earns its place, and the information is front-loaded with no unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical operation tool with 2 parameters, 0% schema description coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain parameter roles, edge case behavior, return format, or how it differs from similar sibling tools. The domain/category tags help somewhat, but don't compensate for the missing operational details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage for its two parameters (x and y), and the description doesn't explain what these parameters represent. However, given the tool's name 'fmod' (common for floating-point modulo) and the description's reference to similarity with '%', an experienced user might infer x is the dividend and y is the divisor. This provides minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate floating-point modulo operation' with the specific verb 'calculate' and resource 'floating-point modulo operation'. It distinguishes from the standard modulo operator by specifying 'Similar to % but for floats', though it doesn't explicitly differentiate from sibling tools like 'modulo' or 'remainder' which might handle different numeric types.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides implied usage guidance through the phrase 'Similar to % but for floats', suggesting this tool should be used for floating-point modulo calculations rather than integer modulo. However, it doesn't explicitly state when to use this versus alternatives like 'modulo' or 'remainder' tools in the sibling list, nor does it mention any prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the mathematical operation but lacks critical behavioral details: it doesn't specify error handling (e.g., for invalid inputs like r=1 with large n), performance characteristics, or output format. The domain/category tags add minimal context, leaving significant gaps for a computational tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the core formula is stated immediately, followed by brief domain/category tags. Every word earns its place, with no redundant or verbose phrasing. The structure efficiently communicates the essential information in a single, compact sentence.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's computational nature, 3 parameters, no annotations, and no output schema, the description is incomplete. It lacks details on output format (e.g., returns a number), error conditions, mathematical limitations (e.g., convergence issues), or usage examples. The domain/category tags are too vague to compensate, making it inadequate for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 3 parameters with 0% description coverage, so the description must compensate. It implicitly defines parameters via the formula (a=first term, r=common ratio, n=number of terms), which adds essential meaning beyond the bare schema. However, it doesn't clarify constraints (e.g., n must be positive integer, r can be any number) or examples, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific mathematical formula: 'Compute geometric series sum a + ar + ar^2 + ... + ar^(n-1)'. It clearly distinguishes this from sibling tools like 'geometric_sequence' (which likely generates terms) and 'geometric_sum' (which might be a different formulation), making the verb+resource distinction precise.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: numerical, Category: series', but this is generic and doesn't help differentiate from other series tools (e.g., 'arithmetic_series', 'harmonic_series'). There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool 'checks' a condition, implying a read-only operation that returns a boolean, but does not disclose any behavioral traits such as error handling (e.g., for non-numeric inputs), performance characteristics, or side effects. The description is minimal and lacks context beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and every part contributes essential information. The structure is clear and efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (simple comparison), no annotations, no output schema, and 2 parameters with 0% schema coverage, the description is minimally adequate. It explains what the tool does and parameter roles, but lacks details on return values (e.g., boolean result), error cases, or usage context. For such a simple tool, it meets basic needs but could be more informative.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaningful context for the parameters: it clarifies that 'a' is 'the first number' and 'b' is 'the second number', and specifies the comparison order ('first number is greater than the second number'). Since the schema description coverage is 0% (no parameter descriptions in schema), this compensates well by explaining the semantic roles, though it does not detail data types or constraints beyond 'number'.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if the first number is greater than the second number.' It specifies the verb ('check'), resource ('numbers'), and domain/category. However, it does not explicitly differentiate from sibling tools like 'greater_than_or_equal', 'less_than', or 'equal', which are closely related comparison operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (arithmetic) and category (comparison), but does not specify scenarios where this exact comparison is appropriate over other comparison tools (e.g., 'greater_than_or_equal' for inclusive checks). There is no mention of prerequisites, exclusions, or typical use cases.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the calculation but does not disclose behavioral traits such as input validation (e.g., n must be positive), performance characteristics, error handling, or output format. This leaves gaps in understanding how the tool behaves beyond the basic formula.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded with the core formula in one clear sentence, followed by domain/category tags. It is appropriately sized with no redundant information, though the tags could be integrated more seamlessly. Every sentence earns its place by defining the tool's purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is adequate but incomplete. It defines the calculation but lacks details on input validation, output type, and error conditions. For a mathematical tool, this is minimally viable but leaves room for improvement in guiding usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not add any parameter-specific information beyond the formula's use of 'n'. It implies 'n' is an integer in the harmonic sum but does not explain constraints (e.g., n > 0) or semantics. With one parameter and no schema descriptions, the baseline is 3 as it minimally covers the parameter's role.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the mathematical operation: 'Calculate the nth harmonic number H_n = 1 + 1/2 + 1/3 + ... + 1/n.' It provides the specific formula and distinguishes this tool from siblings by specifying the domain (arithmetic) and category (harmonic_series), making its purpose unambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category tags, which imply usage in arithmetic and harmonic series contexts, but it does not explicitly state when to use this tool versus alternatives like 'harmonic_series' or 'harmonic_partial_sum' from the sibling list. No guidance on prerequisites, limitations, or specific scenarios is provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does but doesn't disclose behavioral traits like input constraints (e.g., valid integer ranges), performance characteristics, error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—one sentence plus domain/category tags—with zero wasted words. It front-loads the core purpose and efficiently includes additional context without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage, the description is incomplete. It explains the mathematical concept but lacks details on input validation, output format, error cases, and practical usage. For a tool with these contextual gaps, the description should provide more operational information.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds some semantic context by explaining that 'n' is the number being checked for abundance. However, it doesn't specify constraints (e.g., positive integers only) or provide examples. With one parameter and low schema coverage, the description offers basic but incomplete parameter semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('a number'), and defines the mathematical condition ('sum of proper divisors > n'). It also includes domain/category tags that help distinguish it from sibling tools like 'is_deficient_number' or 'is_perfect_number'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives. While the description mentions the domain/category, it doesn't specify use cases, prerequisites, or compare it to related tools like 'is_deficient_number' or 'is_perfect_number' that check similar number properties.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool's function but does not cover critical behavioral aspects: it doesn't mention error handling (e.g., division by zero), performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding how the tool behaves in edge cases.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category tags. Every word earns its place with no redundancy or fluff, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (2 simple integer parameters) and lack of annotations or output schema, the description is minimally adequate. It explains what the tool does but misses key contextual details: no output schema means the return value (likely a boolean) is unspecified, and behavioral aspects like error handling are omitted. It's complete enough for basic understanding but lacks depth for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaningful context beyond the input schema. The schema only defines 'a' and 'b' as integers with 0% description coverage. The description clarifies that 'a' is 'the first number' and 'b' is 'the second number', and specifies their relationship ('divisible by' with 'remainder is zero'). This compensates well for the low schema coverage, though it doesn't detail constraints like non-zero 'b'.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if the first number is divisible by the second number (remainder is zero).' It specifies the verb ('check'), resource ('first number' and 'second number'), and the exact condition ('remainder is zero'). However, it does not explicitly differentiate from siblings like 'modulo' or 'remainder', which are related but distinct operations, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('number_theory'), but this is too generic given the many sibling tools (e.g., 'modulo', 'remainder', 'is_even', 'is_odd') that handle similar concepts. There are no explicit when/when-not instructions or named alternatives, leaving usage ambiguous.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool's function but does not disclose behavioral traits such as performance characteristics, error handling, input constraints (e.g., valid ranges for 'n'), or output format. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose without unnecessary words. The parenthetical domain and category add useful metadata without clutter, making it highly concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low parameter coverage, the description is incomplete. It explains what the tool does but lacks details on behavior, input constraints, and output format, which are essential for a mathematical verification tool. The domain/category hint helps but does not fill these gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds some semantic context by implying 'n' is used in the formula 2^(2^n) + 1, but it does not specify valid ranges, units, or examples. This partial compensation aligns with the baseline for low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a number is a Fermat prime (prime of form 2^(2^n) + 1).' It includes a specific verb ('Check'), resource ('number'), and mathematical definition, clearly distinguishing it from siblings like 'is_prime' or 'fermat_primality_test' by focusing on the special Fermat prime form.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools like 'fermat_primality_test' or 'is_prime', leaving the agent without context for selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the tool checks oddness but doesn't disclose behavioral traits like error handling (e.g., for non-integer inputs), performance, or return format. This leaves gaps for a tool with no structured safety hints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded with the core purpose in a single, efficient sentence. The parenthetical domain/category adds minor context without verbosity, making it appropriately concise for a simple tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one integer parameter) and lack of annotations or output schema, the description is minimally adequate. It covers the basic operation but misses details like return type or edge cases, which could be helpful for completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaning by specifying that the input 'n' is a 'number' to check for oddness. However, it doesn't detail constraints beyond what the schema implies (integer type), so it partially compensates but remains basic.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('a number'), and distinguishes it from its sibling 'is_even' by explicitly defining oddness as 'not divisible by 2'. This is precise and unambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'is_even' or other number-checking tools. It only defines what the tool does, without context or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'checks' a number, implying a read-only operation that returns a boolean, but doesn't specify the return type, error handling (e.g., for negative inputs), or performance characteristics. For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core purpose, and the second provides domain/category context without redundancy. Every word earns its place, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, boolean output implied), no annotations, and no output schema, the description is minimally adequate. It covers the basic purpose and parameter intent but lacks details on return values, error cases, or behavioral nuances. For a simple predicate tool, this is acceptable but not comprehensive.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, but the description compensates by clarifying the parameter's purpose: 'a number' to check. It adds semantic meaning beyond the schema's bare 'integer' type, though it doesn't detail constraints like non-negative requirements. With 0% schema coverage, the description does well to explain the parameter's role.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a perfect square.' It specifies the verb ('Check') and resource ('a number'), and the domain/category context ('Domain: arithmetic, Category: basic_sequences') adds useful classification. However, it doesn't explicitly differentiate from sibling tools like 'sqrt' or 'square_numbers', which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, context for application, or comparison to sibling tools like 'sqrt' (which returns the square root) or 'square_numbers' (which lists perfect squares). This leaves the agent without usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does (checking for repdigits) but does not describe how it behaves: e.g., whether it handles negative numbers, zero, non-integer inputs, or what the return value looks like (e.g., boolean or detailed output). For a tool with zero annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence clearly states the tool's purpose. The second sentence adds domain/category context, which is somewhat redundant but not wasteful. It uses only two sentences with no fluff, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (simple check), no annotations, no output schema, and low schema coverage, the description is minimally adequate. It states what the tool does but lacks details on behavior, parameters, and output. For a straightforward tool, this might suffice, but it leaves gaps that could confuse an agent about edge cases or return format.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the schema provides no parameter semantics. The description does not mention any parameters (n, base) or explain their roles. However, since there are only 2 parameters and the tool's purpose is straightforward (checking if all digits are identical), the lack of parameter explanation is partially mitigated by the tool's simplicity, but it still leaves the base parameter's purpose unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a number has all identical digits (repdigit).' It uses a specific verb ('Check') and resource ('a number'), and distinguishes itself from siblings by focusing on a unique digital property (repdigit detection) rather than general arithmetic operations like 'add' or 'divide'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions 'Domain: arithmetic, Category: digital_operations,' this is too vague to help an agent choose between this and other digital operation tools like 'is_palindromic_number' or 'digit_frequency.' There are no explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool retrieves the five known Fermat primes, implying a read-only operation that returns a fixed set of data. However, it does not disclose any behavioral traits such as whether the output is static, if there are any rate limits, error conditions, or the format of the return value. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Get the five known Fermat primes. (Domain: arithmetic, Category: special_primes)'. Every sentence earns its place by stating the core purpose and providing contextual metadata without unnecessary elaboration. It is appropriately sized for a simple, parameter-less tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is minimally adequate. It explains what the tool does but lacks details on output format, behavioral constraints, or usage context. While the absence of an output schema means the description should ideally clarify return values, the tool's straightforward nature (returning a known set of primes) makes the description passable but not fully complete for an agent needing precise execution guidance.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has no parameters (parameter count: 0), and schema description coverage is 100%, meaning the schema fully documents the lack of inputs. The description does not add any parameter information, which is appropriate since no parameters exist. In such cases, a baseline score of 4 is warranted as the description need not compensate for missing parameter details.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the five known Fermat primes.' It specifies the verb ('Get') and resource ('five known Fermat primes'), making the action and target explicit. However, it does not distinguish this tool from potential siblings like 'fermat_numbers' or 'is_fermat_prime', which are listed among the sibling tools, so it lacks sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It includes a domain and category ('Domain: arithmetic, Category: special_primes'), but this does not specify usage context, exclusions, or comparisons to sibling tools like 'fermat_numbers' or 'fermat_primality_check'. Without explicit when-to-use instructions, the agent must infer usage from the name and description alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool's function but doesn't disclose behavioral traits like error handling (e.g., for non-numeric inputs), performance characteristics, or what happens with special values like NaN or infinity. For a comparison tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose, followed by domain/category metadata. There is zero waste, and the core functionality is front-loaded, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (2 parameters, no output schema, no annotations), the description is incomplete. It doesn't explain the return value (presumably a boolean), error conditions, or how it compares to similar tools. While concise, it lacks the context needed for reliable agent invocation in a crowded namespace of comparison tools.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds minimal semantic context by naming the parameters as 'first number' and 'second number', which aligns with the schema's 'a' and 'b'. However, with 0% schema description coverage, the schema provides no parameter descriptions. The description doesn't compensate by explaining parameter roles, constraints, or examples beyond the basic naming.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Check if') and the specific operation ('first number is less than or equal to the second number'), making the purpose unambiguous. It also distinguishes this tool from its sibling 'less_than' and 'greater_than_or_equal' by specifying the exact comparison operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'less_than', 'greater_than_or_equal', or 'between'. It mentions the domain (arithmetic) and category (comparison), but this is too generic to help an agent choose between sibling comparison tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the return value ('Returns log_base(x)') but lacks behavioral details such as error handling for invalid inputs (e.g., non-positive numbers), precision, or performance characteristics. The description is minimal and does not compensate for the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with two sentences that directly state the tool's function and return value. There is no wasted text, and the domain/category note is brief and relevant.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical function with two parameters), no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks information on output format, error conditions, and usage context, making it inadequate for full understanding without external knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds meaning by naming the parameters ('x' and 'base') and explaining their roles in 'log_base(x)'. However, it does not provide details on constraints (e.g., base > 0, base ≠ 1, x > 0) or examples, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with specific verb ('Calculate') and resource ('logarithm of a number to a specified base'), and distinguishes it from siblings by specifying the mathematical operation (logarithm) rather than other arithmetic functions like 'abs_value' or 'add'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but does not specify use cases, prerequisites, or compare it to sibling tools like 'ln' or 'log10' for natural or base-10 logarithms.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions the return value ('Returns log₂(x)') but does not cover error handling (e.g., for non-positive inputs), performance characteristics, or other behavioral traits. The domain/category hint is minimal and not actionable.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with every word contributing essential information: the action, the mathematical function, and the return value. There is no wasted text, making it efficient for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (1 parameter, no output schema, no annotations), the description is minimal but adequate for basic understanding. However, it lacks details on error conditions, input constraints, and output format, which are important for a mathematical function tool, making it incomplete for robust use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaning by naming the parameter 'x' and specifying it as 'a number' for which the base-2 logarithm is calculated. However, it does not elaborate on constraints (e.g., x > 0) or provide examples, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Calculate') and resource ('base-2 logarithm of a number'), and distinguishes it from siblings by specifying 'log₂(x)' and the domain/category. It directly answers what the tool does without ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives like 'log' or 'ln', nor does it mention any prerequisites or exclusions. It only states the function's mathematical operation without contextual usage advice.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. While 'Find the larger' implies a read-only, non-destructive operation, it doesn't specify error handling (e.g., for non-numeric inputs), performance characteristics, or return format details. The description is minimal and lacks behavioral context beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Find the larger of two numbers.' The parenthetical domain/category adds minimal but relevant context without redundancy. Every word earns its place, and there's no wasted verbiage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (two numeric inputs, no annotations, no output schema), the description is incomplete. It doesn't explain what the tool returns (e.g., the larger number, an error for equal inputs), behavioral nuances, or how it differs from sibling tools. For a basic arithmetic tool, more context on usage and output would be helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with two required parameters ('a' and 'b') documented only as numbers. The description adds no parameter-specific semantics beyond implying they are 'two numbers' for comparison. Since schema coverage is low, the description doesn't compensate with additional details about parameter meaning, constraints, or examples.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the larger of two numbers.' It specifies the verb ('Find'), resource ('two numbers'), and domain/category context. However, it doesn't explicitly distinguish from sibling tools like 'max_list' or 'max_float' that might serve similar comparison purposes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides implied usage through the domain/category context ('Domain: arithmetic, Category: comparison'), suggesting this is for numerical comparisons. However, it doesn't explicitly state when to use this versus alternatives like 'max_list' (for lists) or 'greater_than' (for boolean comparisons), nor does it mention any prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It describes the calculation method but does not disclose behavioral traits such as error handling (e.g., empty lists, non-numeric strings), performance characteristics, or output format. The description is functional but lacks operational context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded with the core purpose and includes a brief mathematical explanation and domain tags. It is efficient with no wasted sentences, though the parenthetical domain note could be integrated more smoothly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It explains the calculation but misses critical context: parameter semantics (string array vs. numbers), error conditions, and output details. For a tool with undocumented parameters, this is inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'a list of numbers' but does not clarify that the input schema expects an array of strings, not numbers, nor does it explain formatting (e.g., numeric strings, delimiters). This gap leaves parameter meaning ambiguous beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb ('calculate') and resource ('arithmetic mean (average) of a list of numbers'), with a clear mathematical definition ('sum all values and divide by count'). It distinguishes from siblings by specifying the statistical domain, unlike many other mathematical tools in the list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for statistical averaging but does not explicitly state when to use this tool versus alternatives like 'median' or 'harmonic_mean' (both siblings). It provides domain context ('statistics, Category: general') but lacks explicit guidance on scenarios or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool returns a value ('Get the minimum...'), implying it's a read-only operation, but doesn't clarify if it's deterministic, has side effects, or requires specific inputs. For a tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence directly states the purpose, and the second adds clarifying context ('Smallest positive normal float') and metadata ('Domain: arithmetic, Category: general'). Every sentence earns its place with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (no parameters, no annotations, no output schema), the description is adequate but minimal. It explains what the tool returns but doesn't provide examples, precision details, or comparisons to related constants. For a mathematical constant tool, more context could enhance usability, but it meets the minimum viable threshold.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the input schema has 100% description coverage (though empty). The description does not need to explain parameters, as there are none. It appropriately focuses on the tool's output semantics, so it meets the baseline for a parameterless tool.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the minimum positive normalized floating-point value. Smallest positive normal float.' It specifies the verb ('Get') and resource ('minimum positive normalized floating-point value'), making the action explicit. However, it does not distinguish this tool from its sibling 'max_float' or other floating-point tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('general'), but this is too vague to help an agent choose between this and similar tools like 'max_float' or 'machine_epsilon'. There are no explicit when-to-use or when-not-to-use instructions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool checks inequality but doesn't disclose behavioral traits such as error handling (e.g., for non-numeric inputs), performance characteristics, or return format (e.g., boolean). This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: one sentence states the core purpose, followed by domain/category in parentheses. Every word earns its place with zero waste, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity, no annotations, no output schema, and minimal parameter semantics, the description is incomplete. It lacks details on return values, error conditions, and usage nuances, which are essential for effective tool invocation despite the simple operation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has two parameters (a, b) with 0% description coverage. The description adds minimal semantics by specifying 'two numbers,' but doesn't explain parameter roles, constraints, or examples. With low schema coverage, the description doesn't fully compensate, though the tool's simplicity mitigates this somewhat.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if two numbers are not equal.' It specifies the verb ('check'), resource ('two numbers'), and operation ('not equal'). However, it doesn't explicitly differentiate from its sibling 'equal' tool, which is a close alternative, though the domain/category context helps.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain ('arithmetic') and category ('comparison'), suggesting it's for numerical comparisons. It doesn't provide explicit guidance on when to use this tool versus alternatives like 'equal' or other comparison tools (e.g., 'greater_than'), leaving some ambiguity in sibling differentiation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does but lacks behavioral details such as input constraints (e.g., valid range for n), output format, performance characteristics, or error handling. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence with no wasted words. It front-loads the core functionality and includes domain/category context without redundancy, making it highly concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (combinatorial number generation), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not address output format, error cases, or usage examples, which are essential for effective tool invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'row n' which implies the parameter 'n' is an integer row index, adding some meaning beyond the schema's type declaration. However, it does not explain constraints (e.g., n must be non-negative) or provide examples, leaving gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb ('Generate') and resource ('row n of Stirling numbers of the second kind'), making the purpose clear. It distinguishes from siblings by specifying a particular combinatorial number type, unlike general arithmetic tools in the list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify prerequisites, typical use cases, or compare it to similar tools like 'stirling_first' or 'stirling_second' in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the algorithm (Tonelli-Shanks) but does not disclose behavioral traits such as input constraints (e.g., p must be prime, a must be a quadratic residue), performance characteristics, error handling, or output format. This leaves significant gaps for a tool performing a non-trivial mathematical computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context efficiently. However, it could be slightly more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of the Tonelli-Shanks algorithm, no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks essential details such as input validation, output format (e.g., returns one or both square roots), and mathematical assumptions, making it inadequate for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It does not explain the parameters a and p beyond the equation x² ≡ a (mod p). No details are provided on their roles (e.g., a is the quadratic residue, p is the modulus), valid ranges (e.g., p odd prime), or constraints, leaving parameters largely undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Solve x² ≡ a (mod p) using Tonelli-Shanks algorithm.' It specifies the exact mathematical operation (solving quadratic congruences), the algorithm used, and distinguishes it from siblings by mentioning its domain (arithmetic) and category (modular_arithmetic), which are unique among the listed tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for solving quadratic congruences modulo a prime, but does not explicitly state when to use this tool versus alternatives (e.g., other modular arithmetic tools like 'is_quadratic_residue' or 'legendre_symbol'). It provides domain/category context, but lacks specific guidance on prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden but only states the calculation formula without addressing behavioral aspects like input validation (e.g., handling negative n), performance, error handling, or output format. It lacks context on what the tool does beyond the basic computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's function and context without any unnecessary words or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It does not cover behavioral traits, error cases, or return values, making it inadequate for a tool that performs a mathematical computation where input validation and output details are important.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, but the description adds meaning by defining 'n' as the input for the triangular number formula. However, it does not explain constraints (e.g., n must be non-negative integer) or provide examples, leaving gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific mathematical formula (T_n = n(n+1)/2) and clarifies its domain and category, distinguishing it from sibling tools like 'triangular_numbers' (which likely lists them) and 'is_triangular_number' (which tests membership).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like 'triangular_numbers' or 'triangular_sequence' from the sibling list. The description mentions the domain and category but does not specify practical scenarios or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool generates numbers and gives the formula, but does not disclose behavioral traits such as input validation (e.g., handling of negative n), output format (e.g., list, array), performance characteristics, or error handling. The description is minimal and misses key operational details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in the first sentence. The formula and domain/category tags add value without redundancy. However, it could be slightly more structured by explicitly listing the parameter, but overall it avoids unnecessary verbosity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It explains what the tool does mathematically but lacks details on parameter usage, output format, error conditions, and behavioral context. For a tool with one parameter but no structured documentation, this leaves significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'n' implicitly in the formula and context, but does not explicitly define the parameter, its constraints (e.g., positive integer), or semantics beyond the mathematical relation. This leaves gaps in understanding how to use the parameter effectively.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Generate') and resource ('first n triangular numbers'), provides the mathematical formula for clarity, and distinguishes it from sibling tools like 'triangular_number' (which likely checks if a number is triangular) and 'triangular_sequence' (which might generate sequences differently). The domain/category tags add helpful context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage by specifying what the tool generates, but does not explicitly state when to use it versus alternatives like 'triangular_sequence' or 'triangular_number'. It provides the mathematical context (arithmetic/general) which helps infer applicability, but lacks direct guidance on tool selection among siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the mathematical logic but omits critical behavioral details: computational complexity (factorials grow rapidly), input limitations (e.g., n must be positive integer), error handling, or performance characteristics. For a primality test with no annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context efficiently. No wasted words, though it could benefit from slightly more detail given the lack of annotations.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a primality test, no annotations, no output schema, and low parameter coverage, the description is incomplete. It explains the theorem but misses practical implementation details, return format (e.g., boolean result), error cases, and performance warnings, leaving the agent under-informed for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, with one parameter 'n' undocumented in the schema. The description adds minimal semantics by implying 'n' is the number to test for primality, but doesn't specify constraints (e.g., n > 0, integer type), domain, or examples. It partially compensates for the schema gap but insufficiently for a tool with computational implications.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Test primality using Wilson's theorem' with the specific mathematical condition '(n-1)! ≡ -1 (mod n) iff n is prime.' It distinguishes itself from sibling tools like 'aks_primality_test', 'fermat_primality_test', and 'miller_rabin_test' by specifying the unique theorem-based approach.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through 'Domain: arithmetic, Category: wilson_theorem', suggesting it's for mathematical primality testing. However, it lacks explicit guidance on when to choose this method over alternative primality tests available among siblings, such as efficiency considerations or input constraints.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the operation is 'pure arithmetic addition,' which implies it's a deterministic, side-effect-free computation without external dependencies like network calls or state changes. However, it doesn't mention error handling (e.g., for non-numeric inputs), performance characteristics, or output format (since no output schema exists), leaving gaps in behavioral understanding.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: 'Add two numbers together.' is the core purpose, followed by clarifying phrases ('Pure arithmetic addition operation.') and metadata tags. Every sentence earns its place without redundancy, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (simple arithmetic), no annotations, and no output schema, the description is minimally adequate. It covers the basic operation but lacks details on error cases, numerical precision, or example usage. For a core arithmetic tool, this might suffice, but it doesn't provide full context for robust agent interaction.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It mentions 'two numbers' but doesn't specify parameter names ('a' and 'b') or provide additional context like acceptable ranges (e.g., integers vs. floats) or units. The description adds minimal value beyond the schema's structural definition, resulting in a baseline score due to the schema's lack of descriptive content.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Add two numbers together. Pure arithmetic addition operation.' It specifies the verb ('Add'), resource ('two numbers'), and scope ('Pure arithmetic addition operation'), making the intent unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'add_in_base' or 'element_wise_add', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the phrase 'Pure arithmetic addition operation' and domain/category tags ('Domain: arithmetic, Category: core'), suggesting it's for basic numeric addition. However, it doesn't provide explicit guidance on when to use this tool versus alternatives like 'add_in_base' (for addition in different bases) or 'sum' (for summing multiple numbers), leaving the agent to infer context from the tool name and category alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'domain validation', which hints at input constraints (likely x in (0,1] for asech), but does not detail error handling, output format, or computational behavior. This adds some context but leaves gaps in behavioral understanding for a mathematical function tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: one sentence with no wasted words. It front-loads the core action ('Calculate inverse hyperbolic secant') and adds clarifying context ('with domain validation'). This is efficient and well-structured for a simple mathematical tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single-parameter mathematical function) and no output schema, the description is minimally adequate. It covers the operation and hints at validation, but lacks details on return values, error cases, or examples. With no annotations, it should provide more behavioral context to be fully complete for reliable agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (x) with 0% description coverage. The description does not explain what 'x' represents (e.g., a real number in the domain of asech) or provide examples. Since schema coverage is low, the description should compensate more; it only implies domain validation without parameter specifics, meeting the baseline but not adding significant value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate inverse hyperbolic secant with domain validation.' It specifies the mathematical operation (inverse hyperbolic secant) and adds domain validation as a key feature. However, it does not explicitly differentiate from sibling tools like 'sech' (direct hyperbolic secant) or other inverse hyperbolic functions in the list, which would be needed for a score of 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (trigonometry) and category (inverse_hyperbolic), but does not specify use cases, prerequisites, or compare it to related tools like 'acosh' or 'asec'. Without explicit when-to-use instructions, the agent must infer usage from context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the conversion action without mentioning any behavioral traits such as input validation (e.g., handling negative or large values), precision, error handling, or output format. For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose, followed by domain/category context. There is no wasted verbiage, and the information is front-loaded, making it easy to understand quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no annotations, no output schema), the description is minimally adequate. It states what the tool does but lacks details on behavior, usage context, or output. For a basic conversion tool, this might suffice, but it leaves gaps in understanding how to use it effectively in practice.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not add any parameter-specific information beyond what the input schema provides. With 0% schema description coverage and one parameter ('degrees'), the schema only indicates it's a required number. The description does not explain what 'degrees' represents (e.g., angle measurement), acceptable ranges, or units. However, since the tool's purpose is straightforward and the parameter count is low, the baseline score of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb 'Convert' and the resource 'degrees to gradians', making the purpose clear and specific. It also includes domain and category context ('trigonometry, angle_conversion'), which helps distinguish it from sibling tools like 'degrees_to_radians' or 'gradians_to_degrees'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'degrees_to_radians' or 'convert_angle', nor does it specify any prerequisites, constraints, or typical use cases. The domain/category hint is too vague to serve as practical usage guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates the divisor sum but does not mention any behavioral traits such as input constraints (e.g., handling of negative numbers, large integers), performance characteristics, or error handling. This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, stating the core purpose in a single sentence with additional domain/category context. Every part earns its place, though it could be slightly more informative without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of a mathematical function with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what the tool returns (e.g., integer sum), handle edge cases, or provide usage examples, making it inadequate for full understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the description does not add any parameter-specific information beyond implying 'n' is a number. It does not clarify the meaning of 'n' (e.g., positive integer, natural number) or any constraints. With low schema coverage, the description fails to compensate adequately, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('sum of all positive divisors of a number'), and it distinguishes itself by naming the divisor function σ(n). It also includes domain and category context, which helps differentiate it from sibling tools like 'divisor_count' or 'divisors'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage in arithmetic or number theory contexts but does not explicitly state when to use this tool versus alternatives like 'divisor_count' or 'divisors'. It provides some contextual guidance through the domain and category, but lacks explicit when/when-not instructions or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool performs division and returns two values, but doesn't disclose critical behavioral traits like error handling (e.g., division by zero), input constraints (e.g., integer vs. floating-point), or whether it's a pure mathematical function. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core functionality, the second clarifies the return format, and the third provides domain/category context. Every sentence earns its place with zero wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't explain parameter roles, error conditions, or detailed return format beyond '(quotient, remainder)'. For a mathematical tool with potential edge cases (like division by zero), this leaves significant gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'division' but doesn't explain what parameters 'a' and 'b' represent (dividend and divisor), their expected types beyond the schema's 'number', or any constraints (e.g., b cannot be zero). The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with specific verbs ('perform division') and resources ('return both quotient and remainder'), and distinguishes it from sibling tools like 'divide' (which likely returns only quotient) and 'remainder' (which likely returns only remainder). The explicit mention of returning both values makes the purpose unambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for arithmetic division with both quotient and remainder needed, but doesn't explicitly state when to use this tool versus alternatives like 'divide' or 'remainder' from the sibling list. The domain/category tags provide some context, but no explicit guidance on selection criteria is given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It implies a read-only operation ('Get'), but does not disclose behavioral traits such as whether it's a constant lookup, if there are any side effects, or error conditions. The description adds some context about the golden ratio's applications, but lacks details on how the tool behaves beyond returning a value.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the purpose. The additional context about where the golden ratio appears is relevant but could be more tightly integrated. It avoids unnecessary verbosity, making it efficient for an agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is adequate but could be more complete. It explains what the tool returns but does not specify the format (e.g., numeric value, precision) or any limitations. For a constant-fetching tool, this is minimally viable but leaves room for improvement in clarifying output details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has 0 parameters, and the schema description coverage is 100% (since there are no parameters to describe). The description does not need to add parameter semantics, so it meets the baseline of 4 for tools with no parameters, as it doesn't have to compensate for any gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the golden ratio φ ≈ 1.61803.' It specifies the verb ('Get') and resource ('golden ratio'), and provides the approximate value. However, it does not explicitly differentiate from sibling tools like 'compute_golden_ratio_continued_fraction' or 'compute_golden_ratio_fibonacci', which are also related to the golden ratio but compute it differently.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions that the golden ratio 'Appears in art, nature, and Fibonacci sequence,' which gives context but does not specify usage scenarios, prerequisites, or exclusions. With sibling tools that compute the golden ratio in various ways, this lack of differentiation is a significant gap.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the default inclusivity behavior ('inclusive by default'), which is useful context not inferable from the schema alone. However, it doesn't describe error handling (e.g., what happens if min_val > max_val), return format (boolean? string?), or performance characteristics. The description adds some value but leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core functionality. Every word earns its place: 'Check' (action), 'number' (subject), 'within a specified range' (purpose), and '(inclusive by default)' (key behavioral detail). The domain/category tags are appended concisely without disrupting the main message.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (simple range check), no annotations, 0% schema description coverage, and no output schema, the description is minimally adequate. It covers the basic purpose and default behavior but lacks details on parameter semantics, error conditions, return values, and usage distinctions from siblings. For a 4-parameter tool with no structured documentation, it should provide more guidance to be fully helpful.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the schema provides no parameter documentation. The description mentions 'range (inclusive by default)', which implicitly relates to 'min_val', 'max_val', and 'inclusive' parameters, but doesn't explain 'value' or provide details on parameter interactions, constraints, or examples. It adds marginal semantic context but doesn't fully compensate for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is within a specified range (inclusive by default).' It includes a specific verb ('Check'), resource ('number'), and scope ('range'), though it doesn't explicitly differentiate from sibling tools like 'clamp' or 'between' that might have similar functionality. The domain/category tags provide additional context but aren't part of the core description.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like 'clamp' (which restricts values to a range) or 'between' (which might check range membership), nor does it specify any prerequisites, constraints, or typical use cases. The agent must infer usage from the tool name and parameters alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the mathematical definition but does not disclose behavioral traits such as input validation (e.g., handling of negative numbers, large integers), performance characteristics, or error handling. This leaves gaps for a mutation-free but computationally intensive tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain/category tags. Every word earns its place with zero waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical check with no annotations, 0% schema coverage, no output schema), the description is incomplete. It defines Mersenne primes but omits details on input constraints, output format (e.g., boolean), and computational behavior. While concise, it should provide more context for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaning by implying the parameter 'n' is the number to check. However, it does not specify constraints (e.g., n must be integer, possibly positive), expected format, or examples. With only one parameter, the baseline is 4, but the lack of detail beyond the schema's type reduces it to 3.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('a number'), and distinguishes it from siblings by specifying the mathematical definition of a Mersenne prime (prime of form 2^p - 1 where p is prime). The domain/category tags further clarify its scope.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives (e.g., general primality tests like 'is_prime' or other special prime checks like 'is_fermat_prime'). The description implies usage for checking Mersenne primes but lacks context about prerequisites, limitations, or comparisons to sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool returns a value ('Get the maximum finite floating-point value'), implying it's a read-only operation without side effects. However, it lacks details on potential errors, performance, or return format (e.g., numeric type). The description adds basic context but misses behavioral specifics like precision or limitations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded: the first sentence directly states the purpose, and the second adds domain/category context. Both sentences earn their place by clarifying the tool's scope. It could be slightly more structured by explicitly mentioning sibling tools, but it avoids unnecessary verbosity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is adequate but not fully complete. It explains what the tool does but lacks details on the return value (e.g., that it's a float) and any edge cases (e.g., how it differs from 'infinity'). For a basic tool, this is minimal viable, but more context would improve usability.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so no parameter documentation is needed. The description appropriately does not discuss parameters, focusing on the tool's purpose instead. This meets the baseline for a tool with no parameters, as there is nothing to compensate for.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the maximum finite floating-point value. Largest representable float.' It specifies the verb ('Get') and resource ('maximum finite floating-point value'), making it easy to understand. However, it does not explicitly differentiate from sibling tools like 'infinity' or 'min_float', which slightly reduces clarity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('general'), but this is too vague to help an agent decide between this and similar tools like 'infinity' (for infinite values) or 'min_float' (for minimum values). No explicit when-to-use or when-not-to-use instructions are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'efficient prime generation,' which hints at performance but lacks details on computational limits, error handling, or output format. The domain and category tags ('arithmetic, number_theory') add some context but are not behavioral traits. More specifics on constraints or behavior would improve transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: the first sentence states the core purpose, followed by efficiency note and domain tags. Every sentence adds value without redundancy. It efficiently communicates essential information in a compact form.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical computation with one parameter), no annotations, and no output schema, the description is moderately complete. It covers purpose and indexing but lacks details on performance, error cases, or return values. For a tool without structured output documentation, more behavioral context would enhance completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The description adds meaning by specifying 'n' as '1-indexed,' clarifying the indexing semantics beyond the schema's type. However, it does not detail valid ranges (e.g., positive integers) or potential limitations (e.g., large n values). With low schema coverage, this partially compensates but is insufficient for full clarity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find the nth prime number (1-indexed).' It specifies the verb ('Find') and resource ('nth prime number'), and clarifies indexing. However, it does not explicitly differentiate from sibling tools like 'first_n_primes' or 'next_prime', which are related but distinct operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'efficient prime generation' but does not specify contexts or prerequisites, nor does it refer to sibling tools like 'first_n_primes' for listing primes or 'is_prime' for primality testing. Usage is implied but not explicitly stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It adds 'saturation handling', which hints at numerical behavior for extreme inputs, but doesn't detail error handling, input ranges, or output format. For a mathematical function with no annotations, this is minimal but not entirely absent.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise: one sentence plus domain/category tags. Every word earns its place, with no redundancy or fluff. It's front-loaded with the core purpose and includes supplementary context efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given a simple mathematical function with 1 parameter, no annotations, and no output schema, the description is adequate but minimal. It states what the tool does and adds a behavioral hint ('saturation handling'), but lacks details on input constraints, output format, or error conditions. For this complexity level, it's passable but not thorough.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The description doesn't mention the parameter 'x' or its meaning. However, for a simple hyperbolic tangent function, the parameter is self-explanatory (input number), so the baseline 3 is appropriate despite the lack of explicit parameter semantics in the description.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate hyperbolic tangent with saturation handling.' It specifies the verb ('calculate'), resource ('hyperbolic tangent'), and adds a behavioral detail ('saturation handling'). However, it doesn't explicitly differentiate from sibling tools like 'atanh' or 'sinh', which are also hyperbolic functions, though the domain/category tags help.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: trigonometry, Category: hyperbolic' but doesn't specify use cases, prerequisites, or comparisons with sibling hyperbolic tools like 'atanh' or 'sinh'. The agent must infer usage from the name and category alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion action but does not disclose behavioral traits such as input constraints (e.g., valid number ranges), error handling, or output format. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with a single, direct sentence that states the tool's purpose, followed by domain and category tags. There is no wasted verbiage, and the information is front-loaded effectively.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations and output schema, the description is incomplete. It does not address key contextual elements such as valid input ranges, error conditions, or the structure of the Roman numeral output. For a conversion tool with no structured metadata, this leaves significant gaps for an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, and the description does not add any parameter-specific information beyond the tool's purpose. It mentions 'Arabic number' which aligns with the 'number' parameter, but provides no details on constraints, format, or examples. Baseline 3 is appropriate as the schema defines the parameter type.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Convert') and resource ('Arabic number to Roman numeral representation'), and distinguishes it from its sibling 'roman_to_arabic' by specifying the direction of conversion. The domain and category tags provide additional context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage when conversion from Arabic to Roman numerals is needed, but does not explicitly state when to use this tool versus alternatives (e.g., 'roman_to_arabic' for the reverse operation). It provides basic context but lacks explicit guidance on exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool returns a specific constant value (∛2 ≈ 1.25992) with a geometric interpretation, which gives basic behavioral context. However, it doesn't mention whether this is a computed or cached value, precision characteristics, or any limitations—leaving gaps for a tool with zero annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it immediately states the core value and purpose in the first phrase. The parenthetical domain/category adds minimal but potentially useful metadata without redundancy. Every sentence earns its place with zero waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (no parameters, no output schema, no annotations), the description is reasonably complete for a constant-returning tool. It provides the exact value and a geometric interpretation. However, without annotations or output schema, it could benefit from mentioning precision or computational characteristics to be fully complete for agent use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters (schema coverage 100%), so there are no parameters to document. The description appropriately doesn't discuss parameters, and the baseline for zero parameters is 4. No additional parameter semantics are needed or provided.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get ∛2 ≈ 1.25992. Cube root of 2, edge length of cube with volume 2.' It provides a specific mathematical operation (cube root of 2) with a geometric interpretation. However, it doesn't explicitly differentiate from siblings like 'cbrt3' or 'sqrt2', which would be needed for a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions 'Domain: arithmetic, Category: general', this is too vague to help an agent choose between this and similar mathematical constant tools like 'sqrt2', 'cbrt3', or 'e' in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool generates a representation but does not disclose behavioral traits such as output format, error handling, computational limits, or whether it's deterministic. The description is minimal and lacks details on how the tool behaves beyond its basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded with the core purpose in the first part. The additional domain/category information is relevant but could be more integrated. It avoids unnecessary verbosity, but the structure is slightly fragmented with parentheses.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (mathematical constant generation), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It specifies what is generated but misses details on behavior, parameters, and output. However, it provides enough context to understand the basic function, making it minimally adequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description does not add any parameter semantics beyond the schema. The schema defines a 'depth' parameter as an integer, but the description does not explain what depth means (e.g., number of terms, precision) or provide usage examples. With one parameter and no schema descriptions, the baseline is 3 as it doesn't compensate for the coverage gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Generate continued fraction representation of e' with a specific pattern '[2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, ...]'. It distinguishes from siblings like 'e_continued_fraction' by specifying the exact mathematical constant (e) and its unique pattern, avoiding tautology.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for generating continued fractions of e, but does not explicitly state when to use this tool versus alternatives like 'e_continued_fraction' or 'continued_fraction_expansion'. It provides domain/category context ('arithmetic, mathematical_constants'), which helps infer usage, but lacks explicit guidance on exclusions or comparisons.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the calculation but doesn't disclose behavioral traits like precision limits, handling of large n values, error conditions, or return format. For a computational tool with zero annotation coverage, this leaves significant gaps in understanding its operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is appropriately sized and front-loaded, with the core purpose in the first sentence and domain/category tags efficiently appended. Every sentence earns its place without redundancy or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It covers the basic purpose but lacks details on behavior, parameter constraints, return values, and error handling, which are essential for a computational tool with one parameter.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It mentions 'n' as the parameter in the formula context, adding meaning beyond the schema's type declaration. However, it doesn't specify constraints (e.g., n must be positive integer) or provide examples, leaving some semantic gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('nth partial sum of the harmonic series'), including the mathematical formula. It distinguishes from siblings by specifying the harmonic series partial sum, unlike general arithmetic tools like 'arithmetic_series' or 'harmonic_number'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for calculating harmonic series partial sums, with domain/category tags ('arithmetic', 'general') providing some context. However, it lacks explicit guidance on when to use this versus alternatives like 'harmonic_number' or 'harmonic_analysis', and doesn't mention prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes what the tool returns ('positive infinity') and its mathematical meaning, but doesn't disclose behavioral traits like whether it's deterministic, has side effects, or requires specific inputs (though parameters are none). It adequately explains the output concept but lacks operational details like error conditions or performance characteristics.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first three words ('Get positive infinity') state the core purpose, followed by clarifying context. Every sentence earns its place, with no wasted words. The parenthetical domain/category is brief and informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (no parameters, no annotations, no output schema), the description is reasonably complete for its purpose. It explains what 'positive infinity' means mathematically, but doesn't cover output format (e.g., numeric representation) or potential edge cases. For a basic constant-fetching tool, this is adequate but minimal.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and schema description coverage is 100% (empty schema). The description doesn't need to explain parameters, so it appropriately focuses on the output. No parameter information is missing or needed, making this sufficient for a parameterless tool.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get positive infinity' with additional context about its representation ('unbounded growth or division by zero limit'). It distinguishes from siblings by specifying 'positive infinity' (e.g., vs. 'nan' or 'is_infinite'), though it doesn't explicitly contrast with all siblings. The domain/category tags are helpful but not essential to the core purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but gives no explicit when/when-not instructions, prerequisites, or named alternatives. The agent must infer usage from context alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the core behavior (checking divisibility by digit sum) and mentions an optional 'base' parameter implicitly via the domain hint. However, it lacks details on edge cases (e.g., negative numbers, zero), performance, error handling, or output format, leaving gaps in behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. Every word earns its place, with no redundant or vague phrasing, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (a mathematical check), no annotations, no output schema, and 0% schema coverage, the description is minimally adequate. It covers the core functionality but omits details on parameters, return values, and edge cases. It meets basic needs but lacks depth for full contextual understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates well. It explains the primary parameter 'n' as the number to check and implies 'base' through the mathematical context (Harshad numbers are base-dependent). While not detailing exact usage, it adds meaningful semantics beyond the bare schema, justifying a high score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is a Harshad (Niven) number (divisible by sum of its digits).' It specifies the verb ('check'), resource ('number'), and mathematical definition. However, it does not explicitly differentiate from sibling tools like 'harshad_numbers' (which likely lists them) or other number property checkers, keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('digital_operations'), but does not specify contexts, prerequisites, or compare to similar tools like 'is_perfect_number' or 'is_palindromic_number'. This lack of explicit usage instructions limits its helpfulness.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates LCM but does not describe any behavioral traits such as error handling (e.g., for non-integer inputs, negative numbers, or zero), performance characteristics, or output format. For a tool with no annotation coverage, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that states the tool's purpose and includes domain/category information. It is front-loaded with the core functionality and avoids any unnecessary verbiage, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (2 parameters, no annotations, no output schema), the description is minimal. It covers the basic purpose but lacks details on behavior, output format, error handling, or usage context. For a tool with no structured support, the description should provide more completeness to guide the agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description specifies that the tool calculates LCM for 'two integers', which directly maps to the two parameters (a and b) in the input schema. Since schema description coverage is 0%, the description compensates by clarifying the parameter types and purpose, adding meaningful context beyond the bare schema. However, it does not detail constraints or examples (e.g., range, handling of negatives).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb ('Calculate') and resource ('Least Common Multiple (LCM) of two integers'), making the purpose specific and clear. It distinguishes this tool from sibling tools by focusing on LCM calculation, which is a distinct mathematical operation among the many arithmetic/number theory tools listed.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify scenarios, prerequisites, or comparisons to other tools (e.g., gcd or other arithmetic operations). This lack of usage context leaves the agent without direction on appropriate application.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It describes what the tool returns (machine epsilon) but does not cover important behavioral aspects such as the floating-point type (e.g., single or double precision), platform dependencies, error handling, or performance characteristics. The description is minimal and lacks depth for a tool that could have implementation-specific nuances.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise and front-loaded, with the core purpose stated first ('Get machine epsilon for floating-point precision'), followed by a clarifying definition and domain/category tags. Every sentence adds value, and there is no redundant or verbose language. However, the parentheses around the domain/category could be slightly more integrated for optimal structure.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is adequate but minimal. It explains what the tool does but lacks details on behavioral traits (e.g., precision type) and usage context. For a tool that returns a fundamental numerical constant, more information on applicability and limitations would enhance completeness, though the current description meets the minimum viable threshold.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the input schema has 100% description coverage (though empty). The description does not need to explain parameters, and it appropriately focuses on the tool's output. Since there are no parameters to document, the description's lack of parameter information is not a gap, warranting a score above the baseline.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific verb ('Get') and resource ('machine epsilon for floating-point precision'), and provides a clear mathematical definition ('Smallest value where 1 + ε > 1'). It distinguishes itself from sibling tools by focusing on a specific numerical constant rather than general arithmetic operations or other mathematical functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category tags ('Domain: arithmetic, Category: general'), which provide some contextual framing, but it does not offer explicit guidance on when to use this tool versus alternatives. There is no mention of specific use cases, prerequisites, or comparisons to sibling tools that might handle precision-related calculations differently.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It implies a read-only operation (fetching a constant) and mentions the constant's appearance in 'octagon constructions,' adding some contextual value. However, it lacks details on error handling, performance, or output format, which are important for a tool with no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it immediately states the tool's purpose, provides the constant's value and formula, and adds brief context. Every sentence earns its place, with no wasted words or unnecessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is adequate but not complete. It explains what the tool returns (the silver ratio) and adds mathematical context, but it does not specify the return type (e.g., numeric value, string) or any behavioral constraints, which could be helpful for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the input schema has 100% description coverage (empty schema). The description does not need to explain parameters, so it meets the baseline. It appropriately focuses on the tool's purpose without redundant parameter information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the silver ratio δ ≈ 2.41421.' It specifies the mathematical constant and provides its approximate value and alternative expression (1 + √2). However, it does not explicitly differentiate from sibling tools like 'golden_ratio' or other constant-fetching tools, which prevents a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain/category tags ('Domain: arithmetic, Category: general'), which imply a general arithmetic context, but it provides no explicit guidance on when to use this tool versus alternatives like 'golden_ratio' or other mathematical constant tools. There are no usage examples, prerequisites, or comparisons to sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It implies a read-only operation by using 'Get', but does not disclose any behavioral traits such as performance characteristics, error handling, or output format. The description adds some context about the mathematical meaning of tau, but lacks details on how the tool behaves beyond returning a constant value. This is adequate for a simple tool but leaves gaps in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured: it uses a single sentence to state the tool's purpose, provide the constant value, explain its relation to π, and note its mathematical representation. Every part of the sentence adds value, with no wasted words, making it front-loaded and efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (no parameters, no output schema, no annotations), the description is reasonably complete for a constant-fetching tool. It explains what tau is and its value, which is sufficient for basic use. However, it could be more complete by specifying the output format or precision, especially since there is no output schema. The description covers the essentials but leaves some contextual details implicit.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has no parameters (parameter count: 0), and schema description coverage is 100%. The description does not need to add parameter semantics, as there are none to document. It appropriately focuses on the tool's purpose without unnecessary parameter details, meeting the baseline for zero parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get tau (τ) ≈ 6.28318. Equal to 2π, represents a full turn in radians.' It specifies the verb 'Get' and the resource 'tau', with additional context about its mathematical value and significance. However, it does not explicitly differentiate from sibling tools like 'pi' or 'e', which are also mathematical constants, though the distinction is implied by the different constant values.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance: it mentions the domain ('arithmetic') and category ('general'), but does not specify when to use this tool versus alternatives. For example, it does not explain when to use 'tau' instead of 'pi' or other constants, nor does it provide any exclusions or prerequisites. The guidance is vague and lacks explicit context for tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. It only states what the tool calculates, without mentioning computational characteristics (e.g., performance with large n, precision limits, error handling for invalid inputs, or return format). For a mathematical computation tool with zero annotation coverage, this leaves significant behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first phrase states the core functionality, followed by the mathematical definition in parentheses, and ends with domain/category tags. Every element adds value with zero wasted words, making it easy for an agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a single-parameter mathematical tool with no annotations and no output schema, the description provides adequate basic purpose and parameter semantics. However, it lacks information about return values (what format the Bell number is returned in), error conditions, computational limits, or relationships to sibling tools. The completeness is minimal but acceptable for this simple function.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage for the single parameter 'n', the description compensates by explaining that 'n' represents the index for the Bell number calculation ('the nth Bell number'). This adds essential semantic meaning beyond the schema's type declaration. However, it doesn't specify constraints like valid ranges or integer requirements beyond what's implied.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate the nth Bell number B_n' with the specific mathematical definition 'number of partitions of a set'. It distinguishes this tool from siblings like 'bell_sequence' and 'bell_triangle' by focusing on individual Bell number calculation rather than sequences or triangles. The domain/category tags further clarify the mathematical context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the mathematical domain, it doesn't indicate when to choose this over similar combinatorial tools (like 'partition_count' or 'distinct_partitions'), nor does it specify any prerequisites, limitations, or typical use cases for Bell number calculations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It adds valuable context beyond the basic function by mentioning 'singularity handling,' which informs the agent about potential edge cases (e.g., near zero where sinh(x) approaches zero). However, it doesn't detail error handling, return formats, or performance characteristics, leaving some gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured in a single sentence. It front-loads the core purpose ('Calculate hyperbolic cosecant (1/sinh) with singularity handling') and efficiently adds domain/category context. Every word earns its place without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is reasonably complete for a mathematical function. It covers the core operation and a key behavioral trait (singularity handling). However, it lacks details on return values, error cases, or examples, which could enhance completeness for an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'x' with 0% description coverage. The description doesn't add any parameter-specific semantics beyond implying 'x' is a number for the hyperbolic cosecant calculation. It doesn't explain units, valid ranges, or the effect of singularity handling on input values. With low schema coverage, the description compensates minimally, meeting the baseline.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate hyperbolic cosecant (1/sinh) with singularity handling.' It specifies the mathematical operation (calculate hyperbolic cosecant), the formula (1/sinh), and a key behavioral aspect (singularity handling). However, it doesn't explicitly differentiate from sibling tools like 'csch' (which might be a duplicate or variant) or other hyperbolic functions, keeping it from a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides minimal usage guidance. It mentions 'Domain: trigonometry, Category: hyperbolic,' which gives some context but doesn't specify when to use this tool versus alternatives like 'sinh', 'csch', or other hyperbolic functions in the sibling list. No explicit when-to-use or when-not-to-use instructions are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the output is 'sorted order', which is useful, but does not cover other important aspects such as error handling (e.g., for negative inputs), performance characteristics, or whether it handles large numbers efficiently. The description is minimal and lacks depth for a tool with no annotation support.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with two sentences that directly state the tool's function and domain. Every word earns its place, and it is front-loaded with the core purpose, making it easy to understand quickly without unnecessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is adequate but minimal. It covers the basic purpose and output order, but for a tool with no annotations, it should ideally include more behavioral context (e.g., input validation, performance notes). The lack of output schema means the description doesn't explain return values, which is a gap.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, so the description must compensate. It adds meaning by specifying that the parameter 'n' is a 'number' for which divisors are found, but does not detail constraints (e.g., must be positive integer, range limits) or provide examples. This is a baseline score as the description offers some context but not enough to fully document the parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Find') and resource ('all positive divisors of a number'), and specifies the output order ('sorted order'). It also distinguishes itself from sibling tools like 'divisor_count' or 'divisor_sum' by focusing on listing divisors rather than counting or summing them.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain and category tags ('arithmetic, number_theory'), suggesting it's for mathematical computations. However, it does not explicitly state when to use this tool versus alternatives like 'divisor_count' or 'divisor_sum', nor does it provide any exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the algorithm and output format, but lacks behavioral details such as input constraints (e.g., handling of negative integers, zero values), performance characteristics, error conditions, or whether it's a pure computation without side effects. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: it states the algorithm name, outputs, and mathematical relationship in one sentence, followed by domain/category tags. Every word contributes directly to understanding the tool's purpose, with zero wasted information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, 2 parameters, no annotations, and no output schema, the description is minimally adequate. It covers the core purpose and output format but lacks details on parameter semantics, behavioral traits, and usage context. For a tool in a server with many mathematical siblings, more guidance on differentiation would improve completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, so the description must compensate. It names the parameters (a, b) and implies they are integers for the Euclidean algorithm, but does not specify their meaning beyond being inputs to the algorithm. No details on constraints, default values, or examples are provided. The description adds minimal semantic value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Extended Euclidean algorithm. Returns gcd(a,b) and coefficients x,y such that ax + by = gcd(a,b).' It specifies the exact mathematical operation (Extended Euclidean algorithm), the inputs (a, b), and the outputs (gcd and coefficients). It clearly distinguishes from sibling tools like 'gcd' by including the extended algorithm with coefficient computation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through its mathematical definition (computing gcd and Bézout coefficients), but does not explicitly state when to use this tool versus alternatives like 'gcd' or 'bezout_identity'. The domain/category tags ('arithmetic', 'number_theory') provide some context, but no explicit guidance on prerequisites or comparisons with siblings is given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the mathematical behavior but lacks details on edge cases (e.g., handling of negative numbers, non-integer inputs, or special values like NaN/infinity), error handling, or performance considerations. This is insufficient for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, delivering the core functionality in a single, efficient sentence. The parenthetical domain and category add minimal but relevant metadata without redundancy, making every word earn its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is minimally adequate. It explains the basic operation but lacks details on behavioral traits, edge cases, or output format, which could hinder an agent's correct invocation in non-standard scenarios.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaningful context for the parameter 'x' by defining it as 'a number' and explaining the floor operation in relation to it. With 0% schema description coverage and only one parameter, this adequately compensates by clarifying the parameter's role, though it could specify accepted number types (e.g., integer, float) more precisely.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific mathematical operation: 'Return the floor of a number (largest integer less than or equal to x).' It clearly distinguishes this from sibling tools like 'ceil' or 'round_number' by specifying the exact mathematical function, avoiding tautology or vagueness.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('core'), it does not specify scenarios, prerequisites, or comparisons with similar tools (e.g., 'ceil', 'truncate', 'round_number'), leaving the agent without explicit usage context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks for infinity but does not describe the return value (e.g., boolean true/false), error handling (e.g., for non-numeric inputs), or performance considerations. For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with a clear purpose statement followed by domain/category tags. Every sentence earns its place, and there is no redundant or verbose language. It efficiently communicates the essential information without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is minimally complete. It states what the tool does but lacks details on return values, error cases, or usage context. While adequate for a simple check, it could be more informative to fully guide an AI agent, especially without annotations or output schema.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not explicitly mention parameters, but with only one parameter ('x') and 0% schema description coverage, it implies the input is 'a number'. This adds minimal semantic context beyond the schema's type definition. Since the parameter count is low (1) and the purpose is straightforward, the description adequately compensates for the lack of schema details, though it could specify input constraints (e.g., accepts integers, floats).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose as 'Check if a number is infinite (positive or negative infinity)', which is a specific verb ('Check') and resource ('a number'), clearly distinguishing it from siblings like 'is_finite' or 'is_nan'. It also includes domain/category context ('Domain: arithmetic, Category: comparison'), which further clarifies its role.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'is_finite' or 'is_nan', nor does it specify scenarios where this check is appropriate (e.g., after division by zero or handling special numeric values). Without such context, users must infer usage from the purpose alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It explains what a narcissistic number is, but does not describe the tool's behavior beyond the check—such as input validation (e.g., handling negative numbers or non-integers), performance characteristics, or error handling. This leaves gaps in understanding how the tool operates in practice.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it states the tool's purpose in one clear sentence, followed by domain/category tags. There is no wasted verbiage, and every element (definition and context) earns its place, making it easy for an AI agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no annotations, no output schema), the description is minimally adequate. It defines the narcissistic number concept, but lacks details on behavior, output format, or error cases. For a simple check tool, this might suffice, but it does not fully compensate for the absence of structured data, leaving some contextual gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'n' with 0% description coverage, but the description implicitly defines 'n' as the number to check, adding semantic meaning beyond the schema. Since there is only one parameter, the description adequately clarifies its purpose, compensating for the lack of schema details. However, it does not specify constraints (e.g., integer range), keeping it from a perfect score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a number is narcissistic (equals sum of its digits raised to the power of digit count).' It specifies the verb ('Check'), resource ('a number'), and provides a precise mathematical definition, distinguishing it from siblings like 'is_perfect_number' or 'is_palindromic_number'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes a domain and category ('Domain: arithmetic, Category: iterative_sequences'), which implies usage in mathematical contexts, but it does not explicitly state when to use this tool versus alternatives (e.g., 'is_armstrong_number' or 'narcissistic_numbers'), nor does it provide any exclusions or prerequisites. This lack of explicit guidance limits its utility for an AI agent.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the calculation but doesn't disclose behavioral traits like input constraints (e.g., n must be positive integer, handling of edge cases like n=0 or 1), performance characteristics, or error handling. The description is minimal beyond the core purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise—a single sentence that directly states the tool's purpose and includes domain/category tags. Every word earns its place with zero redundancy, and the information is front-loaded.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, arithmetic function) and no annotations or output schema, the description is minimally complete. It defines the function but lacks details on input constraints, output format, or error cases. For a simple calculator tool, this is adequate but leaves gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage (parameter 'n' is undocumented in schema), but the description implicitly defines 'n' as the input integer for ω(n). It adds essential semantic meaning by linking 'n' to the arithmetic function, though it doesn't specify constraints like n>0. With one parameter and no schema documentation, this provides adequate compensation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb 'calculate' and the specific arithmetic function ω(n) with its mathematical definition 'number of distinct prime factors', clearly distinguishing it from sibling tools like 'big_omega' (total prime factors) or 'prime_factors' (list of factors). It also includes domain/category context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like 'big_omega' (which counts total prime factors with multiplicity) or 'prime_factors' (which lists prime factors). The description only states what it calculates without comparative context.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the mathematical domain and category, but does not specify error handling, input constraints (e.g., x > 0), or output format, leaving significant gaps for a mutation-free tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded with the core functionality, uses a single efficient sentence, and includes a parenthetical note for context without unnecessary elaboration, making it highly concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity and lack of annotations or output schema, the description is minimally adequate but incomplete. It covers the basic purpose and parameter semantics but omits important behavioral details like input domain restrictions or error conditions.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaning by clarifying that 'x' is the number for which the base-10 logarithm is calculated. However, with 0% schema description coverage and no additional details on parameter constraints or examples, it only partially compensates for the schema's lack of documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific verb ('calculate'), resource ('base-10 logarithm of a number'), and output ('Returns log₁₀(x)'), clearly distinguishing it from sibling tools like 'ln' or 'log2' that compute different logarithms.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for base-10 logarithm calculations but does not explicitly state when to use this tool versus alternatives like 'ln' or 'log2', nor does it provide any exclusions or prerequisites for its use.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool's function but lacks behavioral details such as performance characteristics (e.g., computational limits for large inputs), error handling for invalid inputs (e.g., negative numbers), or output format. This is a significant gap for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose, followed by domain/category tags. There is no wasted verbiage, making it highly concise and well-structured for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one integer parameter) and no output schema, the description is minimally adequate but incomplete. It lacks details on output (e.g., returns an integer prime), error cases, or performance limits, which are important for an agent to use it correctly without annotations.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaning by specifying that the input 'n' is the number to start from ('greater than the given number'), which clarifies the parameter's role beyond the schema's basic integer type. With 0% schema description coverage and only one parameter, this adequately compensates, though it doesn't detail constraints like non-negative integers.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Find the next prime number') and the resource ('greater than the given number'), with domain/category context. It distinguishes from siblings like 'is_prime', 'nth_prime', or 'first_n_primes' by focusing on the next prime after a given input.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives (e.g., 'is_prime' for primality testing, 'nth_prime' for a specific prime index, or 'prime_count' for counting primes). The description implies usage for finding the next prime but lacks comparative context with sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool counts primes up to n, but does not disclose behavioral traits such as performance characteristics (e.g., handling large n), error handling, or output format. This is inadequate for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and mathematical function, followed by domain/category tags. Every word earns its place with no redundancy or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is minimally complete. It explains what the tool does and the parameter's role, but lacks details on output format, limitations, or error cases, which are needed for full contextual understanding.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds significant meaning beyond the input schema, which has 0% coverage. It explains that parameter 'n' is the upper bound for counting primes (less than or equal to n), clarifying its role in the prime counting function. With only one parameter, this provides sufficient semantic context.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Count') and resource ('prime numbers'), explicitly defines the mathematical function (prime counting function π(n)), and distinguishes it from sibling tools like 'is_prime' or 'first_n_primes' by focusing on counting rather than testing or listing primes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify use cases, prerequisites, or compare it to sibling tools like 'prime_counting_sieve' or 'prime_density_analysis', leaving the agent without contextual usage direction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions 'high precision and overflow protection', which are valuable behavioral traits beyond basic calculation. However, it doesn't describe error handling, input constraints beyond being a number, or what happens with invalid inputs like NaN or infinity.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded with essential information in a single sentence. Every word earns its place: 'Calculate hyperbolic sine' states the core function, 'with high precision and overflow protection' adds important behavioral context, and the domain/category in parentheses provides additional classification.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical function with 1 parameter, no annotations, and no output schema, the description is minimally adequate. It covers the basic purpose and some behavioral traits but lacks details about parameter semantics, return values, error conditions, and usage context relative to sibling tools. The absence of output schema means the description should ideally mention what the tool returns.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema description coverage is 0%, but the description doesn't add any parameter-specific information beyond what's implied by the function name. It doesn't explain what 'x' represents (angle in radians vs degrees, real vs complex number) or any constraints on its value. With 0% schema coverage and 1 parameter, the baseline would be 4 if the description fully compensated, but it doesn't.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('hyperbolic sine'), and distinguishes it from siblings by specifying 'high precision and overflow protection'. It also provides domain/category context ('trigonometry, hyperbolic'), which helps differentiate from other mathematical functions in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain/category, it doesn't specify when to choose hyperbolic sine over other trigonometric or hyperbolic functions, nor does it mention any prerequisites or constraints for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool returns a constant value (√3 ≈ 1.73205), which implies it's a read-only, deterministic operation with no side effects. However, it doesn't specify the return format (e.g., numeric vs. string), precision, or any error conditions. For a zero-parameter tool, this is minimal but acceptable, though more detail would improve transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured: it front-loads the core purpose ('Get √3 ≈ 1.73205'), adds relevant context ('Square root of 3, appears in equilateral triangles'), and includes domain/category tags efficiently. Every sentence earns its place, with no wasted words, making it easy for an AI agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is reasonably complete. It explains what the tool does, provides the constant value, and offers contextual usage hints. However, it could be more thorough by explicitly stating the return type or any limitations, but for a basic constant-fetching tool, this is sufficient to guide an agent effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the input schema has 100% description coverage (though empty). The description doesn't need to explain parameters, so it appropriately focuses on the output. It adds value by providing the approximate value (1.73205) and context about equilateral triangles, which goes beyond what the schema alone would indicate. A baseline of 4 is justified since no parameters exist to document.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get √3 ≈ 1.73205. Square root of 3, appears in equilateral triangles.' It specifies the verb ('Get') and resource (√3), and distinguishes itself from sibling tools like 'sqrt2' and 'sqrt5' by focusing on the square root of 3. However, it doesn't explicitly differentiate from other mathematical constant tools like 'pi' or 'e' beyond its domain/category mention.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through context: 'appears in equilateral triangles' suggests applications in geometry, and the domain/category tags ('arithmetic, general') provide broad context. However, it lacks explicit guidance on when to use this tool versus alternatives like 'sqrt' (for general square roots) or other constant tools, and doesn't mention any prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It describes the tool as returning a constant value (√5 ≈ 2.23607), which implies it is a read-only, deterministic operation with no side effects. However, it does not explicitly state that it requires no inputs, has no rate limits, or other behavioral traits, leaving some gaps in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it starts with the core purpose ('Get √5 ≈ 2.23607'), adds mathematical context, and ends with domain/category tags. Every sentence earns its place by providing essential information without redundancy, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is reasonably complete. It explains what the tool does, provides the approximate value, and gives mathematical context. However, it could be more complete by explicitly stating that it requires no inputs or has no side effects, but for a constant-returning tool, the description is largely adequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, meaning no parameters are documented in the schema. The description does not mention any parameters, which is appropriate since the tool likely takes no inputs. This aligns with the schema, and the description adds value by implying the tool's parameterless nature through its focus on returning a constant.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get √5 ≈ 2.23607. Square root of 5, appears in golden ratio formula.' It specifies the verb ('Get') and resource (√5), and provides the approximate value and mathematical context. However, it does not explicitly distinguish this tool from sibling tools like 'sqrt', 'sqrt2', or 'sqrt3', which likely compute other square roots, so it misses full sibling differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. It mentions the golden ratio formula as context, but does not specify scenarios where this constant is needed over other mathematical constants or tools. There are no explicit instructions on when to use it or when not to, nor does it reference sibling tools for comparison.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states what the tool does (generates square numbers) but lacks behavioral details such as: what happens if n is negative or zero, whether there are limits on n, the format of the output (list, array, string), or error handling. The description provides basic functionality but misses important operational context needed for reliable use.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core purpose, the second provides the mathematical rule, and the third adds domain context. Every sentence earns its place with no wasted words, making it easy to parse quickly while remaining informative.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, simple arithmetic function) but lack of annotations and output schema, the description is minimally complete. It explains what the tool does and the parameter's role, but fails to describe output format, edge cases, or error behavior. For a tool with no structured output documentation, this leaves significant gaps in usability despite adequate basic coverage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It adds meaning by explaining that parameter 'n' determines 'the first n square numbers' and provides the formula 'n²', clarifying the mathematical relationship. However, it does not specify constraints (e.g., n must be positive integer) or examples beyond the sequence snippet, leaving some semantic gaps despite adding value over the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific verb ('Generate') and resource ('first n square numbers'), with a precise mathematical definition ('nth square number = n²') and example sequence. It explicitly distinguishes this tool from sibling tools like 'cube_numbers', 'nth_perfect_square', and 'perfect_squares' by focusing on generating a sequence of squares rather than testing or retrieving individual squares.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the mathematical context ('Domain: arithmetic, Category: general'), but does not explicitly state when to use this tool versus alternatives like 'nth_perfect_square' (which returns a single square) or 'perfect_squares' (which might list squares up to a limit). No explicit when-not or alternative guidance is provided, leaving usage contextually implied rather than clearly defined.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the calculation purpose but lacks behavioral details: no information on input constraints (e.g., n must be non-negative integer, typical range limits), computational characteristics (e.g., recursion, large-n handling), or output format (e.g., integer result, potential overflow). For a computational tool with zero annotation coverage, this is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
Extremely concise and front-loaded: the core purpose is stated in the first phrase, with domain/category tags efficiently appended. Every word earns its place—no redundancy, no unnecessary elaboration. The structure is optimal for quick comprehension.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer parameter, no output schema, no annotations), the description is minimally adequate. It defines the mathematical operation but lacks behavioral context (constraints, performance) and output details. For a basic computational tool, it meets the bare minimum but leaves gaps an agent would need to infer or test.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates by defining the parameter's meaning: 'n items' in the context of derangements. This clarifies that 'n' represents the number of items for the subfactorial calculation, adding essential semantics beyond the schema's bare integer type. However, it doesn't specify constraints like non-negative values or typical bounds.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific mathematical operation: 'Calculate subfactorial !n (derangements of n items).' It includes both the mathematical notation (!n) and the combinatorial interpretation (derangements), which precisely distinguishes it from sibling tools like factorial, double_factorial, or other sequence tools. The domain/category tags further clarify its mathematical context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance is provided on when to use this tool versus alternatives. The description mentions the domain (arithmetic) and category (basic_sequences), but does not specify scenarios where subfactorial is appropriate compared to similar tools (e.g., factorial for permutations, derangement calculations in combinatorial problems). Usage must be inferred from the mathematical definition alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden for behavioral disclosure. It states what the tool does but doesn't describe behavioral traits like error handling (e.g., what happens with non-numeric inputs), performance characteristics, or side effects. The description is minimal and doesn't compensate for the lack of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with zero wasted words. The core operation is stated in the first clause, and the domain/category tags are efficiently appended. Every element serves a purpose without redundancy, making it easy to parse and understand quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple arithmetic tool with 2 parameters, no annotations, and no output schema, the description is minimally adequate. It explains the basic operation but lacks details about return values, error conditions, or numerical limitations. Given the tool's simplicity, it meets minimum requirements but leaves gaps in behavioral context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description must compensate. It explicitly defines the semantic relationship between parameters ('Subtract the second number from the first number'), clarifying that parameter 'b' is subtracted from parameter 'a'. This adds meaningful context beyond the schema's type definitions, though it doesn't specify numeric constraints or examples.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Subtract') with the exact resource relationship ('the second number from the first number'), making the purpose unambiguous. It distinguishes itself from sibling tools like 'add' by specifying subtraction rather than addition, and the domain/category tags provide additional context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags imply it's for arithmetic operations, there's no explicit mention of when subtraction is appropriate versus other arithmetic tools like 'add' or 'divide', nor any prerequisites or constraints for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses key behavioral traits: 'Calculate tangent' implies a read-only computation, and 'with singularity handling' suggests it manages undefined cases (e.g., returns an error or special value). However, it doesn't specify error handling details, performance characteristics, or output format. The description adds some context but lacks depth on behavioral aspects.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: the first sentence states the core purpose and key feature ('singularity handling'), and the second provides domain/category context. Every word earns its place with no redundancy or fluff, making it efficient for an AI agent to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is minimally complete. It covers the basic operation and unit, but lacks details on return values (e.g., numeric result or error), edge cases beyond singularity, or examples. For a mathematical function, more context on output behavior would be beneficial, though the simplicity keeps it adequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter ('angle') with 0% description coverage, so the schema provides no semantic information. The description adds meaning by specifying the angle must be 'in radians', which clarifies the unit beyond the schema's 'number' type. However, it doesn't explain valid ranges, constraints (e.g., handling of large angles), or the effect of singularity handling on parameter values. Baseline is 3 due to low schema coverage, with the description partially compensating.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Calculate tangent of an angle in radians with singularity handling.' It specifies the verb ('calculate'), resource ('tangent'), and domain ('trigonometry'), distinguishing it from other trigonometric tools like 'tan_degrees' or 'tanh'. However, it doesn't explicitly differentiate from 'atan' (inverse tangent) or other trigonometric functions beyond the category label.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through context: 'Domain: trigonometry, Category: basic_functions' suggests it's for trigonometric calculations. It mentions 'singularity handling', which hints at when the tool is applicable (angles where tangent is undefined, like π/2). However, it doesn't provide explicit guidance on when to use this tool versus alternatives like 'tan_degrees' (for degrees) or other trigonometric functions, nor does it specify prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It implies a read-only, deterministic operation (returning a constant value) and mentions the domain/category, but doesn't disclose behavioral traits like error handling, precision, or performance characteristics. For a zero-parameter tool, this is minimally adequate but lacks depth.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is efficiently structured in two sentences: one stating the core functionality and value, another providing domain/category context. Every phrase adds value (mathematical definition, approximate result, geometric interpretation, classification). It could be slightly more front-loaded by leading with 'Cube root of 3' instead of 'Get ∛3,' but overall it's concise and well-organized.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is reasonably complete. It explains what the tool does and provides context (domain/category). However, for full completeness, it could mention that this is a constant-returning function with no inputs, and perhaps note its relationship to sibling tools like cbrt2. The absence of output schema isn't critical here since the return value is explicitly stated.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters (schema coverage 100%), so there are no parameters to document. The description appropriately doesn't waste space on parameter explanations. A baseline of 4 is justified since the schema fully covers the absence of parameters, and the description doesn't need to compensate for any gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get ∛3 ≈ 1.44225. Cube root of 3, edge length of cube with volume 3.' It specifies the exact mathematical operation (cube root of 3), provides the approximate value, and gives a geometric interpretation. This distinguishes it from siblings like cbrt2 (cube root of 2) and sqrt3 (square root of 3).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions 'Domain: arithmetic, Category: general,' this is too vague to help an agent choose between this and other mathematical tools like cbrt2, sqrt3, or general-purpose calculators. No explicit when/when-not instructions or alternative recommendations are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions the algorithm but does not disclose behavioral traits such as performance characteristics (e.g., time/memory complexity for large n), error handling for invalid inputs (e.g., negative n), or output format (e.g., list of integers). This is a significant gap for a computational tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core functionality ('Generate the first n prime numbers') and adds algorithm context. The parenthetical domain/category is concise and informative. Zero wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on output format, error handling, performance, and input constraints. For a tool with one parameter but no structured documentation, this is inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description compensates by explaining that 'n' represents the count of prime numbers to generate (first n primes). This adds essential meaning beyond the schema's bare type declaration. However, it does not specify constraints (e.g., n must be positive).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Generate the first n prime numbers') and the algorithm used ('Sieve of Eratosthenes'), distinguishing it from other prime-related tools like 'next_prime', 'nth_prime', or primality tests. It explicitly identifies the resource (prime numbers) and scope (first n).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage when needing a sequence of primes starting from 2, but does not explicitly state when to use this tool versus alternatives like 'sieve_of_eratosthenes' (which might return primes up to a limit) or 'prime_count' (which counts primes). No exclusions or prerequisites are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It indicates this is a read-only operation (implied by 'Get'), but does not disclose other behavioral traits such as performance characteristics, error handling, or output format. The description adds some context about the constant's mathematical relationships, but lacks details on how the tool behaves beyond returning a value.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it immediately states the tool's purpose in the first clause, followed by supplementary mathematical context and domain tags. Every sentence earns its place by providing relevant information without redundancy or fluff.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is adequate but minimal. It explains what constant is returned and its mathematical context, which is sufficient for basic use. However, it does not specify the output format (e.g., numeric precision, data type) or any limitations, leaving some contextual gaps for an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the input schema has 100% description coverage (though empty). The description does not need to explain parameters, and it correctly omits any parameter discussion. This meets the baseline for zero parameters, as there is no schema information to compensate for.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the Glaisher-Kinkelin constant A ≈ 1.28243.' It specifies the exact mathematical constant being retrieved, including its approximate value. However, it does not explicitly differentiate from siblings like 'e', 'pi', or 'golden_ratio', which also return constants, though the constant name itself provides inherent differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage by stating the constant's mathematical context ('Related to Barnes G-function and hyperfactorials') and domain/category tags, which suggest when this tool might be relevant. However, it does not provide explicit guidance on when to use this tool versus alternatives (e.g., other constant-retrieval tools like 'e' or 'pi'), nor does it mention any prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the tool 'checks' a condition, implying a read-only operation, but doesn't disclose behavioral traits like error handling (e.g., for zero denominators), performance, or output format. The description is minimal and lacks necessary context for safe invocation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose ('Check if a fraction is proper') and includes essential context in parentheses. Every word earns its place with no redundancy or fluff.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't explain the return value (e.g., boolean), error conditions, or edge cases (like negative numbers or zero denominators). For a tool with two parameters and mathematical logic, more context is needed for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description compensates by explaining that parameters represent 'numerator' and 'denominator' for fraction checking. It adds meaning beyond the bare schema types (integers) by clarifying their roles in the fraction propriety condition, though it doesn't detail constraints like non-zero denominators.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('fraction'), and distinguishes it from siblings by specifying the mathematical condition 'numerator < denominator'. The domain/category context further clarifies its niche in arithmetic/egyptian fractions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for checking fraction propriety but provides no explicit guidance on when to use this tool versus alternatives like 'is_unit_fraction' or 'improper_to_egyptian'. The domain/category hints at context but lacks explicit when/when-not statements or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the basic operation but lacks details on edge cases (e.g., division by zero, negative numbers), error handling, or performance characteristics. This is insufficient for a mutation-like operation (division remainder) without safety disclosures.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with every word contributing value: it defines the operation, provides the return format, and adds domain/category context in a single efficient sentence, with no wasted information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage, the description is incomplete. It explains the basic operation but omits critical details like return value format, error conditions, and behavioral nuances, which are essential for safe and correct tool invocation in an arithmetic context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaning by naming parameters 'a' and 'b' and explaining they are used in 'a % b.' However, it does not specify expected types (e.g., integers vs. floats) or constraints beyond what the schema implies, leaving gaps in semantic understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific operation: 'Calculate the modulo (remainder) of division. Returns a % b.' It explicitly distinguishes this from sibling tools like 'remainder' by specifying the mathematical notation (a % b) and providing domain/category context, making its purpose unambiguous and distinct.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for arithmetic modulo operations by stating 'Domain: arithmetic, Category: core,' which provides clear context. However, it does not explicitly mention when to use this versus alternatives like 'remainder' or 'fmod' among siblings, leaving some ambiguity in tool selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details such as error handling (e.g., for non-numeric inputs), performance characteristics, or output format. The description is minimal and doesn't disclose operational traits beyond the basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, stating the core function in the first sentence. The additional domain/category information is brief and relevant, with no wasted words, making it efficient for quick understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is adequate but minimal. It covers the basic purpose but lacks details on output (e.g., returns a number) and error cases, which could be helpful for an agent despite the simplicity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description mentions 'a number' which aligns with the single parameter 'x' of type number in the schema. With 0% schema description coverage, the description compensates by clarifying the parameter's purpose, though it doesn't specify constraints like integer vs. float or handling of special values (e.g., NaN).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('absolute value of a number'), making it immediately understandable. It distinguishes itself from sibling tools by focusing on absolute value calculation rather than other arithmetic or mathematical functions listed.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain and category tags ('arithmetic, core'), suggesting it's for basic mathematical operations. However, it doesn't explicitly state when to use this tool versus alternatives (e.g., when to calculate absolute value instead of using other arithmetic tools like 'negate' or 'sign').
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses 'singularity handling' which is a key behavioral trait beyond basic calculation, indicating robustness for edge cases. However, it lacks details on error handling, precision, or output format, leaving gaps in behavioral understanding.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core purpose ('Calculate hyperbolic cotangent') and adds value with the formula and singularity handling. The domain/category tags are concise and informative, with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single input, no nested objects) and lack of annotations/output schema, the description is minimally adequate. It covers the core operation and a key behavioral trait (singularity handling), but does not address return values, error conditions, or mathematical constraints (e.g., domain restrictions beyond singularities), leaving room for improvement.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description does not explicitly mention parameters. However, for a single-parameter mathematical function where the parameter's role is implicit (input value 'x'), the description's focus on the operation and singularity handling provides adequate context. The baseline for 0 parameters would be 4, but here the single parameter's semantics are reasonably inferred.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb ('Calculate'), the resource ('hyperbolic cotangent'), and provides the mathematical formula ('1/tanh'), which clearly distinguishes it from sibling tools like 'cot' (regular cotangent) or 'tanh' (hyperbolic tangent). The domain/category tags further contextualize it within trigonometry/hyperbolic functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description mentions 'singularity handling' which implies usage when input values might cause division by zero, but it does not specify when to use this tool versus alternatives like 'acoth' (inverse hyperbolic cotangent) or other hyperbolic functions. No explicit guidance on when-not-to-use or prerequisites is provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions what the tool does but does not disclose behavioral traits such as performance characteristics (e.g., computational complexity for large limits), output format (e.g., list of pairs, sorted order), or error handling (e.g., for invalid limits). This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded with the core purpose in the first sentence, followed by domain/category context. It uses minimal words efficiently, with no redundant or unnecessary information, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and a simple input schema with 0% coverage, the description is adequate for basic understanding but incomplete. It lacks details on output format, performance, or error handling, which are important for a computational tool. The domain/category hint adds some context but doesn't fully compensate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage for the single parameter 'limit', but the description adds meaning by explaining that 'limit' defines the upper bound for searching cousin prime pairs. This compensates well for the lack of schema documentation, though it could specify constraints like 'limit must be a positive integer'.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb ('Find') and resource ('cousin prime pairs'), specifies the mathematical definition ('primes differing by 4'), and includes the scope ('up to limit'). It distinguishes itself from sibling tools like 'twin_prime_pairs' by focusing on a different prime gap (4 vs 2).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for finding cousin primes within a limit, but does not explicitly state when to use this tool versus alternatives (e.g., 'twin_prime_pairs' for primes differing by 2, or 'prime_constellations' for other patterns). It provides basic context but lacks explicit comparisons or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It describes what the tool does (generates cube numbers) but doesn't disclose behavioral traits like error handling, performance characteristics, input validation, or output format. For a mathematical tool with no annotations, this represents a significant gap in behavioral transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is perfectly concise and well-structured: one sentence stating the purpose with examples, one sentence providing the mathematical formula, and a brief domain/category tag. Every element adds value with zero wasted words, and the most important information (what the tool does) comes first.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a single-parameter mathematical tool with no annotations and no output schema, the description is adequate but has clear gaps. It explains what the tool does and the parameter meaning, but doesn't describe the output format (list? array? string?), error conditions, or performance considerations. Given the simplicity of the tool, it's minimally viable but could be more complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaningful context about the parameter 'n' by explaining 'nth cube number = n³' and providing examples, which goes beyond the schema's simple integer type declaration. With 0% schema description coverage, the description effectively compensates by clarifying what 'n' represents mathematically, though it doesn't specify constraints like minimum/maximum values.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Generate') and resource ('first n cube numbers'), provides the mathematical formula (n³), and gives concrete examples (1, 8, 27, 64, 125, ...). It distinguishes itself from sibling tools by focusing specifically on cube numbers rather than other mathematical sequences or operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the mathematical context ('Domain: arithmetic, Category: general'), but doesn't explicitly state when to use this tool versus alternatives. While it's clear this is for generating cube numbers, there's no guidance about when this would be preferred over other sequence-generation tools or mathematical operations in the sibling list.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states the conversion action without addressing behavioral aspects like input constraints (e.g., negative numbers, large integers), output format (e.g., string representation, bit length), error handling, or performance considerations. This leaves significant gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that directly states the tool's purpose without any redundant information. It is front-loaded with the core functionality and includes helpful domain/category tags, making it highly concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, no output schema, no annotations), the description is adequate for basic understanding. However, it lacks details on behavioral traits (e.g., input validation, output format) and does not fully address the absence of annotations, making it minimally complete but with clear room for improvement.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one required parameter 'decimal' of type integer. The description adds minimal semantics by clarifying it's a 'decimal number (base-10)', but does not elaborate on allowed ranges, formatting, or examples. This provides some value over the bare schema, but not enough to fully compensate for the low coverage, aligning with the baseline expectation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Convert'), the input resource ('a decimal number (base-10)'), and the output ('to binary (base-2)'). It also distinguishes itself from siblings by specifying the exact conversion direction (decimal to binary), unlike the more general 'base_conversion' or the reverse 'binary_to_decimal' tools in the sibling list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context for when to use this tool—when converting from decimal to binary—and the domain/category tags ('arithmetic', 'number_systems') help situate it. However, it does not explicitly mention when not to use it or name specific alternatives (e.g., 'binary_to_decimal' or 'base_conversion'), which prevents a perfect score.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool 'checks' a condition, which implies a read-only, non-destructive operation, but does not specify the return format (e.g., boolean, string), error handling for non-numeric inputs, or performance characteristics. The description is minimal and lacks details on what the agent should expect beyond the basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: a single sentence directly states the tool's function, followed by domain/category tags. There is zero waste or redundancy, and every element (the check operation and context tags) earns its place without unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (simple arithmetic comparison), no annotations, no output schema, and minimal parameters, the description is adequate but incomplete. It covers the basic operation but lacks details on return values, error cases, or usage nuances. For such a simple tool, it meets minimum viability but could be more informative about behavioral expectations.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates by naming the parameters ('first number', 'second number') and clarifying their roles in the comparison. It adds meaning beyond the schema's generic 'a' and 'b' by specifying the semantic relationship (greater than or equal). However, it does not detail data types beyond 'number' or constraints like integer vs. float, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if the first number is greater than or equal to the second number.' It specifies the verb ('Check'), the resource (two numbers), and distinguishes it from siblings like 'greater_than' and 'less_than_or_equal' by its exact comparison operation. The domain and category tags further clarify its arithmetic/comparison nature.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for comparing two numbers in arithmetic contexts, but does not explicitly state when to use this tool versus alternatives like 'greater_than' or 'less_than_or_equal'. No guidance is provided on prerequisites, edge cases, or performance considerations. The domain/category tags offer some contextual hint but lack explicit alternatives or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks for perfect numbers but does not describe any behavioral traits such as input validation (e.g., handling negative numbers or non-integers), performance characteristics, error handling, or output format. For a tool with no annotations, this is a significant gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with no wasted words. It directly states the tool's function and includes domain/category information efficiently. Every sentence earns its place, making it easy to grasp the purpose quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is minimally adequate. It covers the basic purpose but lacks details on behavior, output, or edge cases. For a simple arithmetic check, this might suffice, but it does not provide a complete picture for reliable agent invocation without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, but the description compensates by implicitly defining the parameter 'n' as the number to check. It adds semantic meaning by explaining what a perfect number is, which helps understand the parameter's role. However, it does not specify constraints (e.g., integer range) or examples, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('a number'), and defines what constitutes a perfect number ('equals sum of its proper divisors'). It also distinguishes itself from siblings by specifying its domain and category ('Domain: arithmetic, Category: arithmetic_functions'), which helps differentiate it from other mathematical tools in the list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage in arithmetic contexts but does not explicitly state when to use this tool versus alternatives. While it mentions the domain and category, it lacks guidance on specific scenarios, prerequisites, or comparisons to similar tools (e.g., 'is_abundant_number' or 'is_deficient_number' from the sibling list). This leaves usage somewhat open to interpretation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does (checks primality) but doesn't describe behavioral traits such as performance characteristics (e.g., handling large numbers), error handling (e.g., for non-integer inputs), or output format (e.g., boolean or detailed result). The description is minimal and lacks context beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, with two sentences that directly state the tool's purpose and definition. Every sentence earns its place: the first defines the action, and the second provides essential context with domain/category tags. There is no wasted text or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, simple boolean-like output), no annotations, and no output schema, the description is minimally complete. It covers the basic purpose but lacks details on behavior, output format, or error handling. For a primality check tool, more context (e.g., algorithmic approach or limitations) would enhance completeness, but it's adequate for the simple use case.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds meaning by specifying that 'n' is a 'number' to check for primality, clarifying the parameter's role. However, it doesn't detail constraints (e.g., positive integers only) or examples. With zero parameters documented in the schema, the description compensates adequately but could be more informative.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('if a number is prime'), and provides a precise mathematical definition ('A prime number is only divisible by 1 and itself'). It distinguishes itself from siblings by focusing on primality testing, unlike other tools that perform different mathematical operations (e.g., 'abs_value', 'add', 'fibonacci').
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain/category tags ('Domain: arithmetic, Category: number_theory'), suggesting it's for mathematical contexts. However, it lacks explicit guidance on when to use this tool versus alternatives (e.g., 'fermat_primality_test' or 'miller_rabin_test' among siblings) or any prerequisites like input constraints. No exclusions or clear alternatives are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the mathematical check but lacks behavioral details such as input validation (e.g., handling non-prime q, negative numbers, or large integers), performance characteristics, error handling, or return format. The description is minimal and does not compensate for the absence of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted text, and every element (definition and context) earns its place efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is minimally adequate. It defines the safe prime check but lacks details on output (e.g., boolean result or additional info), error cases, or usage examples. For a simple mathematical tool, it meets basic needs but could be more informative to fully guide an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The description adds meaning by specifying that 'q' is a prime number to check for safe prime status, which clarifies the parameter's role beyond the schema's type definition. However, it does not provide additional details like constraints (e.g., q must be positive) or examples, so it partially compensates for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a prime q is a safe prime (q = 2p + 1 where p is prime).' It includes a specific verb ('Check'), resource ('prime q'), and mathematical definition, clearly distinguishing it from sibling tools like 'is_prime' or 'is_sophie_germain_prime' by focusing on the safe prime property.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context with the domain and category tags ('Domain: arithmetic, Category: special_primes'), indicating it's for arithmetic operations on special primes. However, it does not explicitly state when to use this tool versus alternatives like 'is_sophie_germain_prime' or other primality tests, nor does it mention prerequisites (e.g., that q must be prime).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks a condition but does not describe error handling (e.g., what happens if p is not prime or negative), performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding its behavior beyond the basic function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's function and includes domain/category tags. There is no wasted verbiage; every word contributes to understanding the tool's purpose and context efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is adequate for basic use but incomplete. It lacks details on output (e.g., boolean result or error messages) and edge cases, which are important for a mathematical tool. The domain/category tags help, but more behavioral context would improve completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, but the description adds crucial semantics: it explains that 'p' must be a prime number and defines the Sophie Germain prime condition (2p + 1 is also prime). This compensates well for the lack of schema descriptions, providing clear meaning beyond the schema's type information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a prime p is a Sophie Germain prime (2p + 1 is also prime).' It includes a specific verb ('Check'), resource ('prime p'), and mathematical definition, clearly distinguishing it from sibling tools like 'is_prime' or 'is_safe_prime' by focusing on this specific prime property.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage by specifying the domain ('arithmetic') and category ('special_primes'), which suggests it should be used for prime number analysis in mathematical contexts. However, it does not explicitly state when to use this tool versus alternatives like 'is_safe_prime' or other primality tests, nor does it provide exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks for twin prime pairs but does not describe the return value (e.g., boolean or detailed result), error handling for non-integer inputs, or performance considerations. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and includes domain/category tags. There is no wasted text, and every part of the sentence contributes essential information, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is adequate but incomplete. It covers the purpose and parameter semantics but lacks details on behavioral aspects like return values or error handling. For a simple tool, this is minimally viable but leaves room for improvement in providing a fuller context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has one parameter 'p' with 0% description coverage, but the description adds meaningful context by explaining that 'p' is the number to check as part of a twin prime pair (p, p+2). This clarifies the parameter's role beyond the schema's type information, compensating well for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a number is part of a twin prime pair (p, p+2).' It uses a specific verb ('Check'), identifies the resource ('a number'), and defines the mathematical concept ('twin prime pair'), clearly distinguishing it from sibling tools like 'is_prime' or 'twin_prime_pairs'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage by specifying the domain ('arithmetic') and category ('special_primes'), which suggests it's for mathematical contexts involving prime numbers. However, it does not explicitly state when to use this tool versus alternatives like 'is_prime' or 'twin_prime_pairs', nor does it provide exclusions or prerequisites, leaving the guidance somewhat implicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool checks a condition (numerator = 1), which implies a read-only operation, but does not disclose other behavioral traits such as error handling (e.g., for invalid inputs like zero denominator), performance characteristics, or output format. The description is minimal and lacks context beyond the basic check.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence: 'Check if a fraction is a unit fraction (numerator = 1). (Domain: arithmetic, Category: egyptian_fractions)'. It is front-loaded with the main purpose, and the domain/category tags add context without redundancy. Every part earns its place, making it highly concise and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (a simple boolean check), 2 parameters with no output schema, and no annotations, the description is minimally complete. It states what the tool does but lacks details on behavior, error cases, or return values. For such a simple tool, this is adequate but leaves gaps that could be addressed with more context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 2 parameters with 0% description coverage, but the description adds meaning by specifying that the tool checks if 'numerator = 1', clarifying the purpose of the numerator parameter. It does not explain the denominator's role beyond being part of the fraction, but since there are only 2 parameters and the description compensates for the coverage gap by defining the core logic, it merits a score above baseline.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a fraction is a unit fraction (numerator = 1).' It uses a specific verb ('Check') and resource ('fraction'), and distinguishes itself from siblings by focusing on unit fraction verification, which is unique among the many arithmetic and number theory tools listed.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain and category tags ('Domain: arithmetic, Category: egyptian_fractions'), suggesting it's for arithmetic operations related to Egyptian fractions. However, it does not explicitly state when to use this tool versus alternatives (e.g., other fraction-checking tools like 'is_proper_fraction'), nor does it provide exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It implies this is a read-only operation that returns a constant value, which is straightforward. However, it doesn't mention potential limitations like precision, computational behavior, or error handling. The description adds basic context about the constant's mathematical definition but lacks operational details an agent might need.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first phrase states the core purpose, followed by mathematical context and categorization. Every sentence earns its place - the constant value, its mathematical definition, and domain/category context are all relevant. No wasted words or redundant information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter tool with no annotations and no output schema, the description provides adequate but minimal information. It tells what constant is returned and its approximate value, which is the essential information. However, it doesn't specify the return format (e.g., numeric precision, data type) or any behavioral constraints. Given the tool's simplicity, the description is complete enough to be functional but lacks some operational details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters (schema description coverage 100%), so there are no parameters to document. The description appropriately doesn't waste space discussing nonexistent parameters. The baseline for zero parameters is 4, as the description correctly focuses on what the tool does rather than parameter documentation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get Khinchin's constant K ≈ 2.68545.' It specifies the exact mathematical constant being retrieved and provides its approximate value. The additional context 'Geometric mean of continued fraction coefficients' helps distinguish it from other constant-retrieval tools like 'e', 'pi', or 'golden_ratio' among the siblings.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain ('arithmetic') and category ('general'), it doesn't specify scenarios where Khinchin's constant is needed over other constants or mathematical tools. There's no mention of prerequisites, typical use cases, or comparisons with sibling tools that might provide similar functionality.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool calculates the natural logarithm and returns a value, but does not disclose behavioral traits such as error handling (e.g., for non-positive inputs), precision, or performance characteristics. The description adds minimal context beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it directly states the tool's purpose in the first sentence, adds a clarifying mathematical identity, and includes domain/category tags. Every sentence earns its place without redundancy or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is adequate but incomplete. It covers the basic operation and input semantics but lacks details on output format, error conditions, or mathematical constraints. For a simple arithmetic tool, it meets minimum viability but could be more informative.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter (x) with 0% description coverage. The description adds meaning by specifying that x is 'a number' and relates it to the natural logarithm operation, but does not provide details like valid ranges (e.g., x > 0) or examples. With low schema coverage, the description partially compensates but leaves gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Calculate the natural logarithm (base e) of a number.' It specifies the mathematical operation (natural logarithm), the base (e), and the input (a number). It also distinguishes from siblings by focusing on natural logarithm rather than other logarithmic functions (e.g., log, log10, log2) or other mathematical operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context for usage by stating 'Calculate the natural logarithm (base e) of a number' and adding a mathematical identity 'Returns ln(x) where e^ln(x) = x.' It implies when to use this tool (for natural logarithm calculations) but does not explicitly mention when not to use it or name alternatives among siblings (e.g., log for base-10, log2 for base-2).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the tool returns a constant value (ln(10) ≈ 2.30259), which implies it's a read-only, deterministic operation with no side effects. However, it doesn't explicitly state behavioral traits like whether it requires inputs, error conditions, or performance characteristics. The description adds basic context but lacks depth for a tool with zero parameters.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it states the core purpose in the first phrase ('Get ln(10) ≈ 2.30259'), adds explanatory context ('Natural logarithm of 10, conversion factor for logarithms'), and includes domain/category tags efficiently. Every sentence earns its place with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is reasonably complete. It explains what the tool returns and its mathematical significance. However, it could be more explicit about the tool's behavior (e.g., that it always returns the same constant) and usage compared to siblings. For a basic constant-fetching tool, this is adequate but not exhaustive.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters with 100% schema description coverage (empty schema). The description doesn't need to explain parameters, and it appropriately doesn't mention any. It focuses on the constant output, which is sufficient given the parameterless nature. Baseline is 4 for zero parameters as per guidelines.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get ln(10) ≈ 2.30259. Natural logarithm of 10, conversion factor for logarithms.' It specifies the exact mathematical constant returned and its application context. However, it doesn't explicitly differentiate from sibling tools like 'ln' (which computes natural logarithms generally) or 'log10' (which computes base-10 logarithms), though the constant nature is implied.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context with 'conversion factor for logarithms' and domain/category tags, suggesting it's for arithmetic/general calculations. However, it lacks explicit guidance on when to use this specific constant tool versus computing ln(10) dynamically with the 'ln' tool or using other logarithm-related tools. No alternatives or exclusions are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It mentions efficiency for large numbers, which is a useful behavioral trait, but fails to disclose other critical aspects: whether it handles negative inputs, overflow/underflow behavior, error conditions (e.g., modulus zero), computational limits, or performance characteristics. For a computational tool with no annotations, this leaves significant gaps in understanding its behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence states the core functionality, the second adds efficiency context, and the third provides domain/category tags. Every sentence adds value without redundancy, and there is no wasted verbiage. It effectively communicates the tool's essence in minimal space.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (3 parameters, no output schema, no annotations), the description is partially complete. It covers the purpose and parameters well but lacks details on behavior, error handling, and output format. For a computational tool, users need to know what to expect in terms of results and limitations, which are not addressed. It meets a basic threshold but has clear gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It clearly defines all three parameters (base, exponent, modulus) by name and their role in the formula '(base^exponent) mod modulus', adding essential semantic meaning beyond the schema's type definitions. However, it does not specify constraints (e.g., modulus > 0) or input domains, leaving some ambiguity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Calculate modular exponentiation: (base^exponent) mod modulus.' It specifies the exact mathematical operation with all three parameters, clearly distinguishing it from siblings like 'power' (which lacks modulus) or 'modulo' (which lacks exponentiation). The domain/category tags further clarify its arithmetic nature.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for modular exponentiation with large numbers ('Efficient for large numbers'), but does not explicitly state when to use this tool versus alternatives. Among siblings, tools like 'power' (general exponentiation) and 'modulo' (remainder operation) exist, but no guidance is given on choosing between them. The context is clear but lacks explicit alternatives or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the calculation formula but does not disclose behavioral traits such as input validation (e.g., handling negative integers), error handling, performance characteristics, or output format. This leaves gaps in understanding how the tool behaves beyond the basic computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's function and formula, followed by domain/category tags. Every element earns its place without redundancy or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer parameter, no output schema, no annotations), the description is adequate for basic use but incomplete. It lacks details on output format, error handling, and behavioral context, which are important for a tool with no structured annotations to guide the agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, but the description compensates by defining 'n' in the formula context: 'nth pentagonal number P_n = n(3n-1)/2.' This clarifies that 'n' is an integer index for the pentagonal number, adding meaningful semantics beyond the schema's type declaration.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Calculate the nth pentagonal number P_n = n(3n-1)/2.' It includes the specific verb 'calculate,' the resource 'pentagonal number,' and the exact mathematical formula, which clearly distinguishes it from siblings like 'is_pentagonal_number' or 'pentagonal_sequence' that serve different purposes.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the formula and domain/category tags ('arithmetic, basic_sequences'), suggesting it's for computing pentagonal numbers in mathematical contexts. However, it lacks explicit guidance on when to use this tool versus alternatives like 'pentagonal_sequence' or 'is_pentagonal_number,' and does not mention any prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It implies a read-only operation ('Get') and specifies the exact value returned, which is helpful. However, it does not disclose potential behavioral traits like computational complexity, precision limits, or error handling. The description adds basic context but lacks depth for a tool with no annotation support.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured in a single sentence. It front-loads the core purpose ('Get the plastic number'), provides the value and mathematical definition, and adds relevant context (domain/category) without unnecessary elaboration. Every part earns its place, making it efficient and clear.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is adequate but has gaps. It explains what the tool returns but does not cover output format (e.g., numeric precision, data type) or potential usage constraints. For a constant-fetching tool, it's minimally viable but could be more complete by addressing these aspects.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so no parameter documentation is needed. The description appropriately does not discuss parameters, focusing instead on the tool's output. This meets the baseline for zero-parameter tools, as it adds value by explaining what is returned without redundant parameter details.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the plastic number ρ ≈ 1.32472.' It specifies the exact mathematical constant returned, distinguishes it from siblings by mentioning its unique properties (real root of x³ = x + 1, relation to Padovan sequence), and includes domain/category context. This goes beyond a tautology and provides specific, differentiating information.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. While it mentions the plastic number's mathematical properties, it does not indicate scenarios where this constant is needed over other constants (like golden_ratio or pi) available in sibling tools. There is no explicit when/when-not usage advice or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not mention potential issues like overflow for large n, handling of non-integer x, or error conditions. For a mathematical tool with no annotation coverage, this lack of behavioral details is a significant gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, with the core purpose stated in the first sentence and additional context efficiently added in parentheses. Every word contributes to understanding, with no redundant or verbose elements.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's mathematical nature, 2 parameters, no annotations, and no output schema, the description is minimally adequate. It covers the basic purpose and parameter roles but lacks details on behavior, constraints, or return format, which are important for a calculation tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaningful context beyond the input schema, which has 0% description coverage. It explains that x is the base and n is the exponent limit in the series, clarifying the mathematical roles. However, it does not specify constraints (e.g., n must be non-negative) or examples, leaving some semantic gaps.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific mathematical formula: 'Calculate the sum of a power series: x⁰ + x¹ + x² + ... + xⁿ for given x and n.' It clearly distinguishes this from sibling tools like 'series_sum' or 'geometric_sum' by specifying the exact power series structure, avoiding ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes a domain and category ('Domain: arithmetic, Category: general'), which provides some implied context for when to use this tool. However, it does not explicitly state when to choose this over alternatives like 'geometric_sum' or 'series_sum', nor does it mention any prerequisites or exclusions, leaving usage guidance incomplete.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the operation is equivalent to 'a // b', which clarifies the integer division behavior, but it does not disclose other behavioral traits such as error handling (e.g., division by zero), performance, or output format, leaving gaps for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with every sentence earning its place: it defines the tool's purpose, provides a programming equivalent, and adds domain/category tags without any wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (two integer parameters) and no output schema, the description is somewhat complete but lacks details on error cases and exact return values. It covers the basic operation but doesn't fully compensate for the absence of annotations or output schema, making it adequate but with clear gaps.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates by explaining the parameters implicitly through the example 'a // b', where 'a' and 'b' correspond to 'dividend' and 'divisor'. This adds meaningful context beyond the bare schema, though it doesn't detail constraints like non-zero divisors.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific verb ('Return') and resource ('integer quotient of division without remainder'), and distinguishes it from siblings by noting its arithmetic domain and general category, which helps differentiate it from other mathematical tools like 'divide' or 'remainder'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through the domain and category tags ('Domain: arithmetic, Category: general'), suggesting it's for arithmetic operations, but it does not explicitly state when to use this tool versus alternatives like 'divide' or 'remainder', nor does it provide any exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full behavioral disclosure burden. It states the conversion action but does not describe error handling (e.g., invalid Roman numerals), output format, or any constraints like input validation rules. This leaves significant behavioral gaps for a tool with no structured safety hints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence with zero redundant information. It front-loads the core purpose and includes helpful domain/category tags without unnecessary elaboration, making it optimally concise.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and a single parameter with 0% schema coverage, the description provides basic purpose and domain context but lacks details on behavior, error handling, and output format. It is minimally adequate for a simple conversion tool but misses completeness for reliable agent invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description adds meaningful context by specifying that the input is a 'Roman numeral' (string type). However, it does not detail format expectations, valid characters, or case sensitivity, leaving the single parameter partially documented but incomplete.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Convert'), resource ('Roman numeral'), and target representation ('Arabic number'), with explicit domain/category context. It precisely distinguishes from its sibling 'arabic_to_roman' by specifying the opposite conversion direction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through the domain/category tags ('arithmetic, general'), but does not explicitly state when to use this tool versus alternatives like 'arabic_to_roman' or other conversion tools. It provides clear functional intent but lacks explicit comparative guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses key behavioral traits: it computes continued fraction expansions, specifically for square roots, and notes that results are periodic for non-perfect squares. This adds valuable context beyond the input schema, though it could include more details like output format or error handling.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, with a single sentence that directly states the tool's function and a key property, followed by domain/category tags. Every word earns its place, with no redundancy or unnecessary elaboration.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (mathematical computation), no annotations, no output schema, and low schema coverage, the description is minimally adequate. It covers the core purpose and a behavioral trait, but lacks details on output format, error cases, or performance considerations, which could hinder effective use by an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, and the description does not explicitly mention the parameter 'n'. However, it implies that 'n' is the number whose square root is processed, as it refers to '√n'. This adds some semantic meaning, but does not fully compensate for the lack of schema documentation, such as constraints on 'n' (e.g., non-negative integers).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Find continued fraction expansion of √n (periodic for non-perfect squares).' It specifies the verb ('Find'), resource ('continued fraction expansion of √n'), and a key behavioral characteristic (periodicity for non-perfect squares). However, it does not explicitly differentiate from sibling tools like 'continued_fraction_expansion' or 'sqrt', which could cause ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through the domain and category tags ('Domain: arithmetic, Category: continued_fractions'), suggesting it's for mathematical computations involving square roots and continued fractions. However, it lacks explicit guidance on when to use this tool versus alternatives like 'sqrt' or 'continued_fraction_expansion', and does not mention prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden and discloses key behavioral traits: it specifies rounding direction ('toward zero'), which is crucial for negative numbers, and mentions the arithmetic domain. However, it doesn't address error handling or edge cases like zero significance.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded with the core functionality in the first sentence. The parenthetical domain/category adds minimal but useful context without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple arithmetic tool with 2 parameters, no output schema, and no annotations, the description is minimally adequate but lacks details on parameter semantics and edge cases. It covers the basic operation but leaves gaps in full usability.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate, but it only vaguely references 'number' and 'significance' without explaining their roles, constraints, or examples. No additional meaning beyond the bare parameter names is provided.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Round down') and resource ('a number'), and distinguishes it from siblings by specifying 'toward zero' behavior, unlike generic rounding tools. It also includes domain/category context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for arithmetic rounding operations but doesn't explicitly state when to use this tool versus alternatives like 'floor', 'ceil', or 'ceiling_multiple'. No specific exclusions or prerequisites are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses key behavioral traits: the exclusive default behavior and the mathematical interval notation analogy. However, it lacks details on edge cases (e.g., what happens if lower > upper), return format (e.g., boolean or detailed result), or error handling, leaving some gaps in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured in a single sentence, front-loading the core purpose and efficiently adding domain/category context. Every word contributes value without redundancy, making it easy to parse and understand quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (3 parameters, no output schema, no annotations), the description is adequate but incomplete. It covers the basic purpose and behavior but lacks details on return values, error conditions, or examples. For a comparison tool with numeric inputs, more context on output format or usage scenarios would enhance completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description adds meaningful context by explaining that parameters represent 'value', 'lower', and 'upper' bounds for an interval check. It clarifies the exclusive default behavior, which is not evident from the schema alone. However, it does not detail parameter constraints or interactions, so it partially compensates for the low schema coverage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Check if a value is between two bounds (exclusive by default, like mathematical interval notation).' It specifies the verb ('Check'), resource ('value'), and distinguishes it from siblings by noting its exclusive default behavior and domain/category context, which is unique among the listed sibling tools focused on arithmetic and comparison.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context for when to use this tool by stating its domain ('arithmetic') and category ('comparison'), and implies usage for checking numeric intervals. However, it does not explicitly mention when not to use it or name alternatives (e.g., 'in_range' or 'clamp' from the sibling list), which prevents a perfect score.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the tool's behavior (checking for normality) but does not disclose additional traits such as error handling, performance characteristics, or return format. While the core functionality is clear, more behavioral context would be beneficial given the lack of annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and context. There is no wasted verbiage, and every word contributes to understanding the tool's function and domain.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is adequate but minimal. It covers the basic purpose and context but lacks details on return values, error conditions, or examples. For a simple comparison tool, this is acceptable but not comprehensive.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, and the tool has one parameter ('x'). The description does not add any parameter-specific semantics beyond implying 'x' is a number. Since schema coverage is low, the description does not compensate by explaining the parameter's role or constraints, resulting in a baseline score.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific verb ('Check') and resource ('a number'), and defines the mathematical condition ('normal' meaning finite, non-zero, and not subnormal). It distinguishes itself from sibling tools like 'is_finite', 'is_infinite', or 'is_nan' by specifying this particular combination of properties.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context by specifying the domain ('arithmetic') and category ('comparison'), which helps situate the tool. However, it does not explicitly state when to use this tool versus alternatives (e.g., 'is_finite' or 'is_nan'), nor does it mention any prerequisites or exclusions, leaving some guidance implicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the method ('optimized sieve') and output format ('returns count, not list'), which are useful behavioral traits. However, it does not mention performance characteristics, memory usage, error handling, or limitations (e.g., maximum limit), leaving gaps in behavioral understanding.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, with a single sentence that efficiently conveys the tool's purpose, method, and output. The parenthetical domain and category annotations add useful context without redundancy, making every word earn its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (algorithmic prime counting), no annotations, no output schema, and low schema coverage, the description is minimally adequate. It covers the basic purpose and output but lacks details on performance, error conditions, or example usage, which would be helpful for an AI agent to invoke it correctly in varied contexts.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds meaning by specifying that the 'limit' parameter is used to count primes up to that value, which clarifies the parameter's purpose beyond the schema's basic type definition. With 0% schema description coverage and only one parameter, this compensates adequately, though it could provide more detail (e.g., valid range or constraints).
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Count primes up to limit'), the method ('using optimized sieve'), and the output ('returns count, not list'), distinguishing it from sibling tools like 'prime_count' or 'sieve_of_eratosthenes' that might return lists or use different methods. The domain and category annotations further clarify its algorithmic nature.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for counting primes with an optimized sieve method, but does not explicitly state when to use this tool versus alternatives like 'prime_count' or 'sieve_of_eratosthenes' (which are siblings). It provides some context via the domain/category but lacks explicit guidance on trade-offs or specific scenarios.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'high precision,' which adds useful behavioral context beyond the basic function. However, it does not disclose other traits like error handling, performance, or output format (e.g., numeric range or special cases). The description is adequate but lacks depth for a tool with no annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that front-loads the core functionality: 'Calculate sine of an angle in radians with high precision.' The domain/category tags are appended concisely. There is no wasted verbiage, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no annotations, no output schema, and low schema coverage (0%), the description is minimal but functional. It covers the basic purpose and unit, but for a mathematical tool, it could benefit from more context like precision details or usage examples. It's complete enough for a simple function but lacks richness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, with one parameter 'angle' of type 'number.' The description adds meaning by specifying 'in radians,' clarifying the unit, but does not provide further details like valid ranges (e.g., any real number) or examples. With low schema coverage, it partially compensates but not fully.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Calculate sine of an angle in radians with high precision.' It specifies the verb ('Calculate'), resource ('sine'), and input unit ('radians'), distinguishing it from sibling tools like 'sin_degrees' which uses degrees. The domain/category tags further clarify its mathematical context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage by specifying 'in radians,' which differentiates it from 'sin_degrees.' However, it does not explicitly state when to use this tool versus alternatives like 'sin_series' or other trigonometric functions, nor does it mention any prerequisites or exclusions. The guidance is clear but not comprehensive.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the return values (1, -1, 0) and domain/category, which is useful, but lacks details on edge cases (e.g., handling of zero, negative zero, or non-numeric inputs), error behavior, or performance considerations. It adds some value but is not comprehensive.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded, consisting of two short sentences that directly state the tool's function and return values, with no wasted words. Every sentence earns its place efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (one parameter, no output schema, no annotations), the description is complete enough for basic use. It covers purpose and return values, though it could benefit from mentioning edge cases or examples. The simplicity of the tool makes the description largely adequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates by implying the parameter 'x' is a number for sign determination. Since there is only one parameter, the description adequately conveys its purpose without needing detailed syntax, earning a high score for simplicity.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Determine') and resource ('sign of a number'), and distinguishes it from siblings by specifying the return values (1, -1, or 0). It also includes domain/category context, making it highly specific.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for arithmetic sign determination but does not explicitly state when to use this tool versus alternatives (e.g., for numeric classification vs. other mathematical operations). No exclusions or specific contexts are provided, leaving usage somewhat open-ended.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool returns a specific approximation ('≈ 1.41421'), which is useful behavioral context about precision. However, it doesn't mention whether this is a read-only operation, if it has side effects, or any error conditions. For a zero-parameter tool, this is minimally adequate but lacks depth.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise and front-loaded: the first sentence ('Get √2 ≈ 1.41421.') directly states the tool's core function. The second sentence adds historical/mathematical context, and the parenthetical provides domain categorization. Every sentence earns its place with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter tool with no output schema and no annotations, the description is reasonably complete. It specifies what the tool returns (√2 approximation) and provides mathematical context. However, it doesn't detail the exact return format (e.g., numeric type, precision) or potential errors, which could be helpful for an agent. Given the simplicity, it's mostly adequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the input schema has 100% description coverage (empty object). The description doesn't need to explain parameters, and it doesn't. It correctly focuses on the tool's output. With no parameters, the baseline is 4, as there's nothing to compensate for.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get √2 ≈ 1.41421. Square root of 2, first known irrational number.' It specifies the exact verb ('Get') and resource (the mathematical constant √2), and distinguishes it from siblings like sqrt, sqrt3, sqrt5 by focusing specifically on √2. The domain/category context further clarifies its mathematical nature.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through its mathematical context ('Domain: arithmetic, Category: general'), suggesting it's for arithmetic calculations involving √2. However, it doesn't explicitly state when to use this tool versus alternatives like sqrt (which calculates square roots generally) or other constant tools (like pi, e). The guidance is implied rather than explicit.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the core behavior (returning the ceiling) but does not disclose additional traits such as error handling for non-numeric inputs, performance characteristics, or output format details. The description is accurate but lacks depth beyond the basic operation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is front-loaded with the core purpose in the first sentence, followed by contextual tags. It is highly concise with zero wasted words, making it easy to parse quickly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single parameter, no output schema, no annotations), the description is adequate but minimal. It covers the basic operation and context but lacks details on return values, error cases, or examples, which could enhance completeness for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage, but the description adds meaning by defining 'x' as 'a number' and explaining the ceiling operation. This compensates for the schema gap, though it does not specify constraints like integer vs. float or range limits.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the verb ('Return') and resource ('ceiling of a number'), with a precise mathematical definition ('smallest integer greater than or equal to x'). It clearly distinguishes from siblings like 'floor' or 'round_number' by specifying the ceiling operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes domain and category tags ('Domain: arithmetic, Category: core'), which imply usage in arithmetic contexts and as a fundamental operation. However, it does not explicitly state when to use this tool versus alternatives like 'floor' or 'round_number', nor does it provide exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It effectively describes key behavioral traits: the rounding direction ('up'), the rule ('away from zero'), and the domain/category context. However, it does not cover edge cases like negative numbers or zero significance, which could be relevant.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, with two sentences that directly state the tool's function and behavior. Every sentence earns its place by providing essential information without redundancy or fluff.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (2 parameters, no output schema, no annotations), the description is reasonably complete but could be improved. It covers purpose and behavior but lacks details on parameter handling, edge cases, or example outputs, which would enhance usability for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, so the description must compensate. It explains the parameters' roles ('number' to round, 'significance' as the multiple) but does not provide details on constraints, formats, or examples. This adds basic meaning but leaves gaps in parameter understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Round up') and resource ('a number'), and distinguishes it from siblings by specifying 'to the nearest multiple of significance' and 'Always rounds away from zero.' It differentiates from generic rounding tools like 'ceil' or 'round_number' by focusing on multiples.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context for when to use this tool (rounding up to a multiple), but does not explicitly state when not to use it or name alternatives. It implies usage for arithmetic rounding scenarios but lacks explicit exclusions or sibling comparisons.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the tool's behavior (checking divisibility by 2) but does not disclose additional traits like error handling, input constraints beyond integer type, or output format. It adds basic context but lacks depth for a tool with no annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence with zero waste. It front-loads the core purpose and includes helpful domain/category tags without unnecessary elaboration. Every word earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (single integer input, simple boolean output), no annotations, and no output schema, the description is adequate but minimal. It covers the basic purpose and parameter semantics but lacks details on behavior, error cases, or return values, leaving some gaps for an agent to infer.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 1 parameter with 0% description coverage. The description adds meaning by specifying the parameter's purpose ('a number') and the divisibility condition ('divisible by 2'), which compensates well for the schema's lack of documentation. However, it does not detail constraints like negative numbers or zero.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Check if a number is even (divisible by 2).' It uses a specific verb ('Check') and resource ('a number'), and distinguishes from sibling tools like 'is_odd' by focusing on evenness. The domain/category tags add further context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for arithmetic/number theory contexts, but does not explicitly state when to use this tool versus alternatives like 'is_odd' or 'is_divisible'. However, the purpose is clear enough to infer appropriate contexts, so it provides clear context without exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the tool 'Get[s]' π, implying a read-only operation that returns a constant value. However, it does not disclose behavioral traits such as whether this is a static retrieval, if there are any rate limits, or what the return format is (e.g., a float, string, or object). The description adds basic context but lacks details on behavior beyond the core purpose.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it immediately states the purpose, provides the value and definition, and adds domain/category context in parentheses. Every sentence earns its place with no waste, making it easy for an agent to quickly understand the tool's function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is adequate but could be more complete. It explains what the tool does but does not specify the return type or format (e.g., float precision, string representation). For a constant-retrieval tool, this is a minor gap, but the description is mostly sufficient for basic use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage (empty object), so no parameter documentation is needed. The description does not discuss parameters, which is appropriate. Baseline is 4 for 0 parameters, as the schema fully covers the absence of inputs, and the description correctly focuses on the tool's purpose without redundant parameter info.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get the mathematical constant π (pi) ≈ 3.14159. The ratio of a circle's circumference to its diameter.' It specifies the exact resource (the mathematical constant π) and provides its approximate value and mathematical definition. This distinguishes it from sibling tools like compute_pi_chudnovsky or compute_pi_leibniz, which are algorithms for computing π, whereas this tool simply retrieves the constant value.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context with 'Domain: arithmetic, Category: general,' indicating this is a general-purpose arithmetic constant. However, it does not explicitly state when to use this tool versus alternatives like compute_pi_chudnovsky (which computes π via an algorithm) or pi_digits (which might return more digits). The guidance is implied but not explicit about alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the operation ('truncate') and direction ('towards zero'), which implies a deterministic, non-destructive mathematical function. However, it lacks details on edge cases (e.g., negative numbers, non-numeric inputs) or performance characteristics.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence with no wasted words. It front-loads the core action ('Truncate a number towards zero') and appends only essential domain/category tags. Every part earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple mathematical tool with one parameter and no output schema, the description is adequate but minimal. It covers the basic operation but lacks details on return values or error handling. Given the low complexity, it meets the minimum viable threshold.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not mention the parameter 'x', but with 0% schema description coverage and only one parameter, it compensates by clearly explaining what the tool does to the input ('truncate a number towards zero'). This adds meaningful context beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific verb ('truncate') and resource ('a number'), and distinguishes it from siblings by specifying 'towards zero (remove decimal part)'—unlike tools like 'floor' or 'ceil' that round differently. The domain/category tags further clarify its mathematical context.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for truncating numbers toward zero, but does not explicitly state when to use it versus alternatives like 'floor', 'ceil', or 'round_number' among siblings. However, the phrase 'towards zero' provides clear context for its rounding behavior.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden. It clearly indicates this is a read-only operation that returns a specific mathematical constant value (ζ(3) ≈ 1.20206). It doesn't mention computational complexity, precision, or error handling, but for a zero-parameter constant lookup tool, the behavioral disclosure is reasonably complete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is perfectly concise: one sentence stating the constant value and its mathematical definition, followed by domain/category tags. Every element earns its place - the value, definition, and context tags all provide essential information with zero waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter tool with no annotations and no output schema, the description provides complete context: what constant is returned, its approximate value, its mathematical definition, and domain/category classification. The only minor gap is lack of precision/format information about the returned value, but for a constant lookup tool, this is reasonably complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters with 100% schema description coverage (empty schema). The description appropriately doesn't discuss parameters since none exist. It focuses instead on what constant is returned, which is the correct semantic information for this tool type.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get Apéry's constant ζ(3) ≈ 1.20206' with the specific mathematical definition 'Sum of cubes reciprocals: 1 + 1/8 + 1/27 + ...'. It distinguishes itself from all 300+ sibling tools by focusing on this specific mathematical constant, which is unique in the list.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides implied usage through the domain/category tags 'Domain: arithmetic, Category: general', suggesting this is a general arithmetic constant lookup. However, it doesn't explicitly state when to use this tool versus alternatives (like computing ζ(3) through other methods or accessing other mathematical constants from sibling tools).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses that the tool returns a constant value (G ≈ 0.91597) and its mathematical definition, which is useful behavioral context. However, it does not mention any side effects, performance characteristics, or error conditions, which are typical gaps for a tool with zero annotation coverage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it immediately states the tool's purpose in the first phrase, followed by the constant's value and series representation, and ends with domain/category tags. Every sentence adds value without redundancy, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no output schema, no annotations), the description is nearly complete: it explains what the tool does, provides the constant's value and mathematical definition, and includes domain/category context. The only minor gap is the lack of explicit output format details, but for a constant-retrieval tool, this is acceptable.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so no parameter documentation is needed. The description appropriately does not discuss parameters, focusing instead on the tool's output and mathematical background, which aligns with the schema's completeness.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Get Catalan's constant G ≈ 0.91597.' It specifies the exact mathematical constant being retrieved, distinguishes it from sibling tools like 'catalan_number' and 'catalan_sequence' by focusing on the constant value rather than sequences or numbers, and provides the specific alternating series representation for clarity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes context with 'Domain: arithmetic, Category: general,' which implicitly guides usage toward mathematical constant retrieval in arithmetic contexts. However, it does not explicitly state when to use this tool versus alternatives (e.g., other constant tools like 'e' or 'pi'), nor does it provide exclusions or prerequisites, leaving some ambiguity in sibling differentiation beyond the purpose statement.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full behavioral disclosure burden. It states this is a 'Get' operation (implying read-only) and specifies the exact value returned (e ≈ 2.71828). However, it doesn't mention precision, format, or any computational characteristics. For a zero-parameter tool with no annotations, this is adequate but minimal behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise yet complete: one sentence stating the tool's purpose and return value, followed by parenthetical domain/category tags. Every element earns its place—no wasted words, perfectly front-loaded with the core functionality. This is model efficiency for a simple tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter tool with no output schema and no annotations, the description provides sufficient context: it states what constant is returned and its approximate value. However, it doesn't specify the return format (e.g., numeric precision, data type) or any error conditions. Given the tool's simplicity, this is reasonably complete but could slightly enhance clarity about output characteristics.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage (empty object). The description appropriately doesn't discuss parameters since none exist. It focuses instead on what the tool returns. With zero parameters, the baseline is 4, and the description correctly avoids unnecessary parameter discussion.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Get Euler's number e ≈ 2.71828.' It specifies the exact mathematical constant returned, distinguishes it from siblings by focusing on this specific fundamental constant, and provides domain/category context. This is a clear, specific verb+resource statement with no ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through the domain/category tags ('Domain: arithmetic, Category: general'), suggesting this is a general-purpose mathematical constant tool. However, it doesn't explicitly state when to use this versus alternatives (like compute_e_limit or compute_e_series from the sibling list), nor does it provide exclusion criteria. The guidance is clear but lacks sibling differentiation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It clearly states the tool's behavior (checking if a number is finite), but doesn't disclose additional traits like error handling, performance characteristics, or what happens with non-numeric inputs. The description is accurate but lacks depth for a tool with no annotation support.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence plus domain/category) with zero wasted words. It's front-loaded with the core functionality and uses parentheses efficiently for additional context. Every element earns its place in this minimal but complete description.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple comparison tool with one parameter and no output schema, the description provides sufficient context about what the tool does and what it expects. The domain/category annotation adds helpful context. However, without annotations or output schema, it could benefit from mentioning the return type (likely boolean) or edge case behavior.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage and only one parameter ('x'), the description adds meaningful context by specifying that the input should be 'a number'. This compensates well for the lack of schema documentation, though it doesn't provide format details or examples. The baseline would be lower with more parameters, but for a single parameter tool this is adequate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose with a specific verb ('Check') and resource ('a number'), clearly distinguishing it from siblings like 'is_infinite' and 'is_nan' by specifying 'finite (not infinite and not NaN)'. It also includes domain/category context that helps differentiate it from other comparison tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through the domain/category annotation ('arithmetic, comparison'), which helps situate it among mathematical tools. However, it doesn't explicitly state when to use this tool versus alternatives like 'is_infinite' or 'is_nan', nor does it provide exclusion criteria or prerequisites for usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the tool as a simple retrieval ('Get') of a constant value, which implies it is a read-only, non-destructive operation with no side effects. However, it does not disclose potential behavioral traits like error handling, performance, or output format details. The description adds basic context but lacks depth for a tool with zero parameters and no output schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and well-structured: a single sentence front-loaded with the core purpose ('Get ln(2) ≈ 0.69315'), followed by clarifying context. Every word earns its place, with no wasted information, making it easy for an AI agent to quickly understand the tool's function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is reasonably complete. It explains what the tool returns (ln(2) ≈ 0.69315) and provides domain context. However, it could be more complete by explicitly stating the output type or format, especially since there is no output schema. The description covers the essential aspects but has a minor gap in output specification.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so no parameter documentation is needed. The description appropriately does not discuss parameters, focusing instead on the tool's purpose and context. This meets the baseline for tools with no parameters, as it avoids unnecessary repetition and adds value through domain information.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Get ln(2) ≈ 0.69315. Natural logarithm of 2, appears in information theory.' It provides a specific verb ('Get'), the exact resource (ln(2)), and distinguishes it from siblings by focusing on this specific constant rather than general logarithmic calculations. The additional context about its appearance in information theory further clarifies its domain relevance.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context through the phrase 'appears in information theory' and categorizes it under 'arithmetic, general,' which helps identify when this constant might be needed. However, it does not explicitly state when to use this tool versus alternatives like the general 'ln' tool or other constant tools (e.g., 'e', 'pi'), nor does it provide exclusions or prerequisites. The guidance is clear but lacks explicit sibling differentiation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the tool as a constant retrieval ('Get log₂(e)'), implying it's a read-only, deterministic operation without side effects. However, it doesn't detail behavioral aspects like error handling, precision, or performance, which are relevant for a mathematical constant tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it immediately states the tool's output and purpose in the first sentence, followed by brief context. Every sentence earns its place without redundancy, making it efficient and easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is mostly complete: it explains what the tool returns and its mathematical context. However, it could be more complete by specifying the return type or precision, though this is minor for a constant tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so no parameter documentation is needed. The description appropriately adds no parameter information, focusing instead on the tool's output and purpose. A baseline of 4 is applied since it compensates adequately for the lack of parameters by explaining the constant value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states the tool's purpose: 'Get log₂(e) ≈ 1.44270. Logarithm base 2 of e, conversion factor for binary logarithms.' It specifies the exact mathematical operation (log base 2 of e), provides the approximate numerical value, and explains its use as a conversion factor, clearly distinguishing it from sibling tools like log2 or log10e.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes context with 'Domain: arithmetic, Category: general,' which implies when to use it—for arithmetic calculations involving binary logarithms. However, it does not explicitly state when not to use it or name alternatives (e.g., using log2 for other bases), so it lacks full comparative guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes the output behavior (generates a random float) and range constraint, but doesn't mention distribution (likely uniform), determinism, or seed behavior. For a zero-parameter tool with no annotations, this is adequate but not comprehensive.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
Extremely concise single sentence with no wasted words, front-loading the core functionality. The parenthetical domain/category adds useful metadata without bloating the description.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple zero-parameter random number generator with no output schema, the description provides sufficient context: what it does, output range, and domain. It could mention the distribution (uniform) or lack of seed control, but overall it's reasonably complete for this complexity level.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters with 100% schema description coverage (empty schema). The description doesn't need to explain parameters, but it does clarify the output range constraint which is semantically relevant. Baseline for zero parameters is 4.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the specific action ('Generate a random float') and the exact range ('between 0 and 1 (exclusive of 1)'), distinguishing it from sibling tools like random_int or random_array. It also includes domain/category context that helps with tool selection.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implicitly indicates when to use this tool (when needing a random float in [0,1)) but doesn't explicitly mention when not to use it or name alternatives like random_int. However, the domain/category hint provides some contextual guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It effectively discloses that this is a constant-returning tool with no inputs, as indicated by 'Get log₁₀(e) ≈ 0.43429.' and the empty input schema. It adds context about its domain (arithmetic) and category (general), which helps the agent understand its scope. However, it doesn't mention error handling or performance, though these are less critical for a simple constant tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded: it immediately states the tool's output and purpose in the first sentence, followed by additional context in parentheses. Every sentence earns its place by providing essential information without redundancy. It's appropriately sized for a simple, parameterless tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 parameters, no output schema, no annotations), the description is complete. It explains what the tool does, provides the approximate return value, and adds domain/category context. For a constant-returning mathematical tool, this is sufficient and well-rounded, with no missing elements that would hinder an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0 parameters with 100% coverage, so the baseline is 4. The description adds no parameter information, which is appropriate since there are no parameters. It compensates by explaining the output value and its significance, which is valuable for the agent's understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: 'Get log₁₀(e) ≈ 0.43429. Common logarithm of e, conversion factor for base 10 logarithms.' It specifies the exact mathematical operation (log base 10 of e), provides the approximate value, and explains its utility as a conversion factor. This distinguishes it from sibling tools like 'log10' (general log base 10) or 'ln' (natural log).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage through its explanation of the conversion factor role, suggesting it's for mathematical calculations involving base 10 logarithms. However, it does not explicitly state when to use this tool versus alternatives like 'log10' or 'ln', nor does it provide any exclusions or prerequisites. The context is clear but lacks explicit guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the tool's behavior of checking exact equality and hints at precision issues with floating-point numbers, but does not cover other behavioral aspects like error handling, performance, or return format. It adds some context but lacks comprehensive behavioral details.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise and front-loaded, with two sentences that directly state the tool's purpose and provide usage guidance. Every sentence adds value, and there is no redundant or unnecessary information, making it efficient and well-structured.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's low complexity (2 parameters, no output schema, no annotations), the description is reasonably complete. It covers purpose, usage guidelines, and parameter semantics adequately. However, it could be more complete by specifying the return value or handling edge cases, though the simplicity of the tool mitigates this gap.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the description compensates by explaining that parameters 'a' and 'b' are 'two numbers' to be compared for exact equality. This adds meaningful semantics beyond the schema's type definitions, though it doesn't specify number types (e.g., integer vs. float) or constraints.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose with a specific verb ('Check') and resource ('two numbers'), and explicitly distinguishes it from its sibling tool 'approximately_equal' by noting the exact equality requirement and recommending the alternative for floating-point numbers. This provides immediate clarity and differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines5/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description explicitly provides usage guidance by stating when to use this tool ('Check if two numbers are exactly equal') and when to use an alternative ('For floating-point numbers, consider using approximately_equal instead'). This directly addresses the tool's context relative to its sibling, offering clear decision criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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