Math MCP Server

by amichae2

Overview Schema Related Servers Score Discussions

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Server Quality Checklist

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Latest release: v0.1.0
Disambiguation3/5
Many tools have distinct purposes, but there is overlap between symbolic and numeric solvers (solve, solve_linear, find_root, dsolve, ode_solve) and between fitting tools (regression, curve_fit, lstsq). Descriptions often clarify, but an agent could still misselect.
Naming Consistency3/5
Tool names follow a mix of patterns: single verbs (factor, simplify), verb_noun (factor_int, find_root), and noun_verb (graph_create, matrix_decompose). Some use abbreviations (gpu_fft) or adjectives (max_flow). The inconsistency is notable across 51 tools.
Tool Count2/5
With 51 tools, the set is large and contains redundancies (e.g., multiple ODE solvers, multiple rendering tools). While the domain is broad, the granularity could be reduced for better usability.
Completeness4/5
The tool set covers a wide range of mathematical domains: symbolic, numeric, statistical, linear algebra, graph theory, number theory, transforms, and plotting. Minor gaps exist (e.g., optimization, special functions) but overall it's very comprehensive.
Average 2.6/5 across 51 of 51 tools scored. Lowest: 1.8/5.
See the Tool Scores section below for per-tool breakdowns.
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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?
With no annotations, the description must disclose behavioral traits. It only says 'perform operations,' omitting whether it modifies state, requires authentication, or has side effects. The minimal description fails to inform about behavior beyond a generic computation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is too brief, a single vague sentence. While concise, it sacrifices essential detail. Front-loading is irrelevant when the content is insufficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 5 parameters (2 required) and no parameter descriptions, the one-line description is grossly incomplete. Even with an output schema, critical details like operation types and input formats are missing, making the tool nearly impossible to invoke correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0%, and the description adds no meaning to parameters. The agent cannot determine valid values for 'operation,' format for 'a'/'b', or the role of optional parameters, making the tool nearly unusable without external knowledge.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states it performs modular arithmetic operations, which is a specific domain. However, it does not specify which operations (e.g., addition, multiplication, exponentiation) are supported, leaving ambiguity. It distinguishes from siblings like 'gcd_lcm' or 'factor' but lacks precision.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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. It does not explain context, prerequisites, or exclusions, leaving the agent to 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 present, so the description should disclose behavior. It only states 'evaluate', which implies computation but does not mention safety, side effects, or any constraints. The agent cannot infer whether this tool is read-only or has 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.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is too brief for a tool with 4 parameters and an output schema. It sacrifices informativeness for brevity, making it under-specified.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the number of parameters and the presence of an output schema, the description lacks details about return values and the meaning of input fields. The agent cannot confidently 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.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0% for the 4 parameters. The description does not explain what 'operation', 'n', 'k', or 'as_formula' mean, leaving the agent without guidance on how to fill these fields.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description 'Evaluate combinatorial number sequences and counting functions' gives a general sense but lacks specificity about which sequences or operations are supported. The input schema has an 'operation' parameter without enumerated values, making it unclear what operations are available.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 siblings like 'partitions' or other combinatorial functions. No when-not-to-use or alternative suggestions 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, and the description does not disclose any behavioral traits (e.g., assumptions, error handling, or side effects). For a tool with no annotations, the description carries full burden but fails to inform about what happens with invalid inputs or test results.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely short (5 words), but it is under-specified rather than concise. Every sentence should earn its place, but this single sentence omits critical details, making it insufficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of 6 parameters, no schema descriptions, no annotations, and a vague description, the tool definition is incomplete. While an output schema exists, the description does not reference it or indicate what the tool returns.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 6 parameters with 0% schema description coverage, and the tool description adds no meaning to any parameter. The phrase 'named statistical hypothesis test' does not clarify what 'test', 'data1', 'data2', 'params', 'alpha', or 'alternative' represent.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states it performs a 'named statistical hypothesis test,' which indicates the action and resource. However, it fails to specify what tests are available or how to specify them, leaving ambiguity. It is better than a tautology but not sufficiently clear to differentiate from siblings like 'bootstrap' or 'regression.'
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 'bootstrap' or 'distribution.' The description gives no context about appropriate scenarios, 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 exist, and the description fails to disclose any behavioral traits such as output format, error handling, or side effects. 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.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The single sentence is too terse to be informative, lacking structure. While short, it does not earn its place by providing adequate context.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's 6 parameters, 0% coverage, and no annotations, the description is severely incomplete. It fails to explain return values (output schema exists but unaddressed) or parameter roles.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description must compensate but adds no parameter information. Parameter names (e.g., x_data, method) are left entirely to the agent's inference.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description uses the specific verb 'interpolate' and resource 'scattered one-dimensional data', which clearly indicates the tool's function. While it distinguishes from sibling 'curve_fit' by nature, it does not 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 Guidelines2/5
Does the description explain when 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 curve_fit or find_root. No context on prerequisites or scenarios is given.
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?
With no annotations provided, the description must fully convey behavioral traits. It merely states the action without disclosing any details about accuracy, numeric methods, error handling, supported expressions, or output format.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
While the description is short, it is under-specified rather than concise. Every sentence should add value, but this one sentence lacks essential details, making it insufficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (9 parameters, 29 sibling tools, no annotations, and an output schema not described), the description is severely incomplete. It fails to equip the AI agent with enough information for correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no meaning to any of the 9 parameters. The agent has no clue what each parameter controls beyond defaults and types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool performs numerical integration of a scalar function, using a specific verb and resource. However, it does not differentiate from sibling tools like symbolic_integrate or other integration methods, missing context for distinction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool over siblings or alternatives. No mention of prerequisites, limitations, or appropriate use cases. The agent receives no decision support.
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 present, and the description fails to disclose any behavioral traits such as output format (e.g., rendered image), side effects, or error handling. The sole sentence says nothing 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.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but severely under-specified. It lacks necessary detail, making it insufficient for an agent to use the tool correctly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of 10 parameters, no annotations, and an output schema not described, the description is completely inadequate. It fails to provide essential context for parameter usage, output expectations, or typical use cases.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage and 10 parameters, the description adds no meaning to any parameter. It does not explain the required 'expression' parameter, its acceptable formats, or optional parameters like 'x_range' or 'num_points'.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool plots functions as 2D curves, which is clear. However, it does not explicitly differentiate from sibling tool 'plot_implicit' for implicit plots, missing an opportunity for specificity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool vs alternatives like 'plot_implicit'. No exclusions or context 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, and the description fails to disclose any behavioral traits such as return format, limitations (e.g., supported expression types), or computational method. The agent has no information 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.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but lacks structure. It does not front-load critical information, and every word is minimal, but for a complex mathematical function, more detail is needed.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of inverse Laplace transforms, the description is severely incomplete. It does not indicate what expressions are supported, whether an output schema exists, or any details about the result. The tool's sophistication demands more context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description does not elaborate on the parameters. While parameter names are somewhat self-explanatory, the absence of any explanation fails to guide the agent on correct usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes the inverse Laplace transform, which is specific and distinct from the sibling tool 'laplace_transform'. However, it does not explicitly differentiate itself or mention that it is the inverse operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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, such as 'laplace_transform'. No prerequisites or typical use cases 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, the description carries full burden but only says 'compute'. No mention of safety (read-only?), data format expectations, or performance. Very limited transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Extremely concise but at the expense of essential information. A single sentence that lacks detail; not a model of valuable conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (4 params, graph domain) and presence of an output schema, the description is woefully incomplete. No explanation of available metrics, edge format, or output structure.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no meaning for parameters like 'edges', 'weights', 'metrics', or 'edge_weights_attr'. Fails to clarify input formats or accepted values.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes 'graph-theoretic summary metrics', using a specific verb and resource. However, it does not list which metrics or distinguish from sibling tools like shortest_path or spanning_tree.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 (e.g., shortest_path, graph_create). No conditions or exclusions 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?
With no annotations, the description must disclose behavioral traits. It indicates a generation action but does not explain randomness, reproducibility, or side effects. The 'random_state' parameter implies seeding, but no details 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.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single short sentence, which is too minimal for a tool with 5 parameters and an output schema. While it is concise, it lacks necessary structure and detail, making it under-specified.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of parameter descriptions in the schema, the description should compensate but does not. It fails to explain input behavior, distribution options, or the role of parameters like 'size' and 'dimensions'. The output schema exists, but the description still feels incomplete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no explanation for any of the 5 parameters. It only mentions 'from NumPy distributions', which hints at the 'distribution' parameter but does not elaborate on valid values or the 'params' object.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool generates random samples from NumPy distributions, indicating a specific verb and resource. It doesn't differentiate from sibling tools like 'distribution' or 'bootstrap', but the purpose is still unambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 'distribution' for distribution functions or 'bootstrap' for resampling. The description lacks any context on appropriate usage 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 provided; description fails to disclose that it returns model coefficients and statistics (though output schema exists). No mention of edge cases, assumptions, or 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.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Under-specified single sentence; brevity sacrifices essential detail for a 7-parameter tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (7 parameters, output schema) and the presence of sibling tools, the description is critically incomplete—no parameter details, no return value explanation, no usage context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but description only hints at the model parameter. No explanation of x, y, degree, fit_intercept, standardize, or include_stats, leaving their meaning unclear.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states a clear action ('perform regression analysis') and lists three supported model types (linear, polynomial, logistic), which gives specific meaning beyond the tool name.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool vs. siblings like curve_fit or lstsq. No prerequisites or exclusions 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 fails to disclose default algorithm, behavior for disconnected graphs, or error conditions. The description adds little behavioral context beyond the tool name.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise but at the cost of informativeness. It is a single sentence that does not front-load key details or earn its place by covering necessary aspects.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 6 parameters and no schema descriptions, the description is far from complete. It does not mention output format, return values, or any execution nuance, making it insufficient for correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description must explain parameters, but it does not. The meaning of edges, source, target, weights, algorithm, and edge_weights_attr is entirely omitted.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'Compute' and the resource 'shortest paths on an edge-list graph', distinguishing it from sibling graph tools like spanning_tree or max_flow. However, it could be more specific about source-to-target computation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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. The description lacks context on prerequisites or when not to use it, leaving the AI agent without decision support.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, and the description does not disclose whether operations are read-only, modify state, or have side effects. The phrase 'evaluate, fit, and sample' suggests primarily read operations, but fitting may involve computation without persistence—uncertain.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but sacrifices critical details. It front-loads the main purpose but lacks structure and completeness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
With 7 parameters (2 required) and no parameter explanations, the description is inadequate. An output schema exists but is not described. The tool's complexity demands more detailed usage guidance.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does 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 any of the 7 parameters (name, operation, params, x, q, size, random_state). The agent must infer meaning from names alone, which is insufficient for correct invocation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'evaluate, fit, and sample probability distributions', which clearly identifies the tool's domain and actions. However, it lacks specificity to distinguish from the sibling 'random_sample' tool, which also involves sampling distributions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 'random_sample' or 'hypothesis_test'. The description 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.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description lacks behavioral details beyond 'solve'. It does not disclose potential errors, complexity, or side effects. Since no annotations are provided, the description carries full burden, and it fails to inform about behavior like handling of unsolvable equations or default methods.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence), which is positive, but it omits essential information about parameters and usage. It is not well-structured for an agent to understand how to use the tool effectively.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, low schema coverage, and no output schema details, the description is incomplete. It does not cover return format, examples, or edge cases. For a symbolic ODE solver, more detail is needed for correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not explain any of the four parameters (equation, function, ics, hint) beyond the main action. With 0% schema coverage, the agent has no guidance on how to use 'ics' or 'hint', leading to likely incorrect invocations. The defaults and titles in the schema are not sufficient.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states it solves ordinary differential equations symbolically. The verb and resource are specific, and the use of 'symbolically' distinguishes it from potential numerical solvers like the sibling 'ode_solve'. However, it does not explicitly contrast with 'ode_solve'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidelines are provided on when to use this tool versus alternatives like 'ode_solve' (likely numerical). There is 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 must carry the full burden of behavioral disclosure. It does not mention whether the tool is safe (read-only) or destructive, what errors may occur, the format of the output, or any edge cases. The brief statement only covers the high-level purpose, leaving significant behavioral details undisclosed.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence with seven words). While brevity is generally good, this level of conciseness omits necessary details (e.g., parameter meanings, output format). It is efficient but incomplete, balancing conciseness and utility only moderately.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The tool has an output schema (not shown), but the description does not indicate what the output represents (e.g., list of factors, sorted?). With no annotations and 0% parameter coverage, the description leaves significant gaps for an AI agent to understand how to correctly invoke and interpret results. It is not complete enough for reliable use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning neither schema nor description explain the parameters. The description does not clarify that 'n' expects a string representation of an integer, nor does it explain the 'method' parameter's options or default behavior ('auto'). The description adds zero semantic value beyond what the schema already sparsely provides.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description 'Factor an integer into prime factors' clearly states the action and resource. The verb 'factor' and resource 'integer' are specific, and the task (prime factorization) is distinct from general factorization or primality checking. However, it does not explicitly differentiate from the sibling 'factor' tool, which could perform similar or broader factorization, slightly reducing clarity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when 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 'factor' or 'is_prime'. There is no mention of prerequisites, limitations, or when not to use it. The context signals show many math-related siblings, but the description gives no comparative 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?
With no annotations, the description carries full burden for behavioral disclosure. It only states the core operation, omitting any conditions, assumptions, or side effects (e.g., convergence requirements, handling of discontinuities).
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but overly terse. It lacks sufficient detail to be effective, so it does not earn a high score for efficiency.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (Laplace transform with four parameters and many sibling tools), the description is incomplete. It neither explains return values nor provides enough context for correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, yet the description provides no additional meaning for the four parameters (expression, t_var, s_var, noconds). It does not explain defaults or semantics beyond what is in the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('Compute') and the resource ('Laplace transform of a time-domain expression'), providing a specific verb and resource. However, it does not differentiate from sibling tools like 'inverse_laplace' or other mathematical transforms, 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 Guidelines2/5
Does 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 when the expression is in the frequency domain or when inverse transform is needed. There is no mention of 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, the description bears full responsibility for behavioral disclosure, but it only mentions counting or listing partitions. There is no information about side effects, performance, valid operation values, or constraints, leaving the agent unaware of important behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely terse (only 5 words), which sacrifices necessary detail. While concise, it fails to be informative enough for an agent to select and invoke the tool correctly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has three parameters and an output schema, the description is starkly incomplete. It omits details on return values, operation types, and parameter semantics, making it inadequate for understanding the tool's full functionality.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage for its three parameters, and the description provides no additional explanation. The agent must guess that 'n' is the integer to partition, 'operation' controls count vs. list, and 'k' may limit part size, which is a significant gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool can count or list integer partitions, which clearly indicates its purpose. However, it does not distinguish itself from sibling tools like 'combinatorics' that may also handle partitions, slightly reducing clarity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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, nor on the different operations (count vs. list) or the role of the 'k' parameter. The description is too brief to inform 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, and the description does not disclose any behavioral traits (e.g., computational complexity, range limits, or side effects). The tool is likely read-only for computation, but that is not explicitly stated.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise with 8 words, fitting in a single sentence. However, it sacrifices clarity for brevity, as the dual-mode phrasing is ambiguous.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the presence of an output schema, the description does not explain return values or behavior. For 3 parameters and potential dual-mode usage, more context is needed, such as what happens when limit is specified alongside start/end.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0%, so the description must compensate. It associates start/end with 'range' and limit with 'first N primes', but it fails to explain how the limit parameter works when start and end are required, leading to confusion.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool lists primes, but it ambiguously mentions two modes ('in a range' and 'first N primes') while the schema requires both start and end, making the 'first N' mode unclear. It distinguishes from siblings like is_prime (which checks a single number) but doesn't fully resolve the dual-mode inconsistency.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool vs alternatives. Siblings include is_prime, factor_int, etc., but the description provides no context for selecting primes_range over checking primality or factoring 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 present, so the description carries full burden. It only says 'Estimate bootstrap confidence intervals and uncertainty,' missing details on randomness, computational cost, or assumptions. This is insufficient 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.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but overly brief. It lacks structure and does not prioritize key information; it could be more informative without being verbose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 6 parameters and no annotation coverage, the description fails to provide enough context for correct usage. Even with an output schema present, the description omits necessary behavioral and parameter details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description adds no information about what each parameter does. The input schema provides titles and defaults but no descriptions, and the tool description does not compensate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool estimates bootstrap confidence intervals and uncertainty, which specifies the purpose. However, it does not explicitly distinguish from siblings like hypothesis_test or curve_fit, though the unique 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 Guidelines2/5
Does 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 (e.g., other resampling or statistical methods). The description lacks contextual advice for the agent to decide.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided. The description mentions GPU acceleration but fails to explain what 'beneficial' means (e.g., matrix size, sparsity) or disclose fallback behavior, resource usage, 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.
Conciseness2/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence of 8 words, which is too terse for a tool with 3 parameters and complex GPU acceleration behavior. Essential details are omitted at the cost of brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema (not shown), the description fails to cover parameter semantics, usage guidelines, and behavioral nuances. The tool's complexity demands more context than provided.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage. The description does not explain any parameters: 'a' and 'b' lack shape requirements, and 'force_cpu' is undocumented despite its boolean default.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly specifies the verb 'multiply' and resource 'matrices', and adds nuance with 'GPU acceleration when beneficial', effectively distinguishing from the sibling 'matrix_multiply' tool.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 'matrix_multiply'. The phrase 'when beneficial' is vague and leaves the agent to infer optimal conditions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents 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 does not disclose side effects, permissions, rate limits, or what happens with existing graphs. Only a brief action statement.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, making it concise but too terse for a tool with 6 parameters. It lacks structured information, though it front-loads the purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The description omits important details like parameter constraints (e.g., mutually exclusive inputs), the meaning of 'specification', and does not reference the output schema to clarify return values.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does 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 three input methods but does not map them to specific parameters (edges, adjacency, specification) nor explain n and edge_weights. Incomplete parameter guidance.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states it creates a graph from three input methods, which clearly identifies the action and resource. However, 'named specification' is ambiguous and could be clarified.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool versus sibling graph tools like graph_metrics, shortest_path, etc. No exclusions or 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 full burden. It only states the basic function without disclosing behavior of the 'rigorous' parameter, performance characteristics, or edge cases like negative numbers or large inputs. The agent gets minimal insight into how the tool operates.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single short sentence, which is concise and front-loaded. However, it sacrifices necessary detail for brevity, making it under-specified rather than efficiently informative. Still, there is no wasted text.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given an output schema exists (though not detailed), the description doesn't need to explain return values. However, it fails to explain how to use parameters effectively, and the presence of sibling tools is not leveraged to provide usage context. The tool is simple but still incomplete without parameter semantics.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has two parameters with no descriptions (0% schema coverage). The description adds no meaning beyond parameter names. The 'rigorous' boolean parameter is not explained, leaving the agent unsure of its effect. This is a significant gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool's purpose: testing if an integer is prime. It uses a specific verb and resource, making the function immediately understandable. However, it does not differentiate from sibling tools like 'factor_int' or 'primes_range', which are also prime-related.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides no guidance on when to use this tool versus alternatives. For instance, it doesn't mention that this tool is for single number checks while 'primes_range' handles ranges. Without such context, an agent might choose the wrong 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, the description must disclose behaviors like handling of infinity, multiple variables, or side effects. The one-line description provides no such details, leaving the agent uninformed about return type or 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.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single concise sentence with no waste, but it is too brief to be informative. Still, conciseness alone earns a high score; the lack of detail affects other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given 4 parameters, zero schema descriptions, and no annotation context, the description is insufficient. An output schema exists but does not compensate for the lack of parameter guidance and usage context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no meaning to parameters like expression, variable, point, direction. Defaults are present but not explained; e.g., direction default '+-' is ambiguous.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Compute limits of expressions', which clearly indicates the verb and resource. However, it does not differentiate from sibling tools like symbolic_diff or series that also compute related limits. Slight lack of specificity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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, such as symbolic_diff for derivative limits or series for expansions. No prerequisites or exclusions 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?
With no annotations, the description should disclose behavioral traits. It only states the high-level goal, omitting details like default method, regularization effects, or handling of ill-conditioned systems.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single concise sentence, but it sacrifices essential detail. It is not verbose but could be restructured to include more context without being lengthy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description fails to provide sufficient context for the 4 parameters, especially method and regularization. It is incomplete for a tool of moderate complexity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema has 0% description coverage; the description adds nothing beyond parameter names. It implies a is matrix and b is vector but does not explain method or regularization meanings.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes a least-squares solution to Ax ≈ b, which is a specific verb and resource. It distinguishes from siblings like curve_fit or solve as a linear algebra operation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool over alternatives (e.g., curve_fit for non-linear, solve for exact). The description lacks context or examples.
Agents often have multiple tools that could apply. Explicit usage guidance like "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 bears full responsibility for behavioral disclosure. It fails to specify what decompositions are computed (e.g., LU, QR, SVD), input shape requirements, or impact on the input. The word 'compute' implies a read operation, but no safety details 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.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, efficient and to the point. However, it sacrifices necessary detail for brevity, making it slightly under-specified for its purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of matrix decompositions and the lack of schema descriptions, the description is insufficient. It does not address output format, error conditions, or limitations. The presence of an output schema does not excuse the lack of clarity in the description.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does 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 'matrix' parameter's shape constraints or the 'decomposition' parameter's allowed values (e.g., 'all', 'lu', 'qr'). The default 'all' is not defined. This is a critical gap.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description 'Compute standard matrix decompositions' clearly states the verb and resource, distinguishing from sibling tools like eigen_decomp which focus on a specific decomposition type. However, 'standard' is vague and could be more precise.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 eigen_decomp or matrix_info. There is no mention of prerequisites, input constraints, or recommended 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?
With no annotations, the description is too vague. It doesn't state whether the operation is read-only, has side effects, or requires any prerequisites. The minimal detail leaves behavioral expectations unclear.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single short sentence, which is concise but under-specified. It sacrifices informativeness for brevity, failing to add value beyond the tool name.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Although an output schema exists, its content is not visible. The description fails to define what 'structural and numerical information' entails, leaving significant ambiguity about the tool's output and capabilities.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does 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 adds no meaning about the 'matrix' parameter beyond its data type. The description does not explain format, constraints, or typical usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes structural and numerical information about a matrix, using a specific verb and resource. It distinguishes from siblings like matrix_decompose or matrix_multiply, though not explicitly.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 (e.g., matrix_decompose, eigen_decomp). No scenarios for appropriate use 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?
With no annotations, the description carries full burden for behavioral disclosure. It only gives a high-level purpose and omits details such as return format, error handling, side effects (e.g., state changes), or performance considerations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but under-specified. It is front-loaded with the primary action, but its brevity sacrifices completeness for the number of parameters involved.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (11 parameters, 3 required, output schema exits), the description is incomplete. It does not explain the return value structure or how the solver works, which the output schema alone may not fully convey.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description should clarify parameter meanings. The description adds no information about parameters like dydt (string expression format), y0, t_span, method options, or tolerance defaults, leaving the agent to guess from names alone.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Solve an initial value problem numerically,' which clearly indicates the tool is for numerical ODE solving. However, it does not distinguish from sibling tools like dsolve (symbolic ODE) or numerical_integrate, which could cause confusion for an agent.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No usage guidelines are provided. The description does not explain when to use this tool versus alternatives (e.g., dsolve for symbolic solutions), nor does it mention prerequisites or when not to use it.
Agents often have multiple tools that could apply. Explicit usage guidance like "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, the description must disclose behavioral traits but only states the computation type. It does not describe what the tool returns (e.g., list of edges, total weight), whether it mutates state, or any side effects. The maximize parameter hints at dual behavior but lacks detail.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise and front-loaded, but it omits critical details that make it under-specified. It earns its place but does not fully inform the agent.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 4 parameters, no annotations, an output schema (unseen), and numerous sibling tools, the description is incomplete. It lacks explanation of input format, output, and usage context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does 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 does not. The parameter names (edges, weights, maximize, edge_weights_attr) offer some hint, but 'edge_weights_attr' is ambiguous and no explanation is provided for how to structure input or the effect of each parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes a minimum or maximum spanning tree, which is a specific graph algorithm. It uses a specific verb ('compute') and resource ('spanning tree'), and distinguishes between two modes, but does not explicitly differentiate from sibling graph tools like graph_create or shortest_path.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is given on when to use this tool versus alternatives. There is no mention of prerequisites (e.g., graph connectivity) or situations where other tools like shortest_path would 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, the description bears full responsibility. It only mentions computing products, but fails to disclose return format, error handling, or expression constraints. The scope finite/infinite is mentioned, but not enough.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence with no fluff, but it sacrifices completeness. It earns its place but lacks essential details, balancing conciseness and informativeness poorly.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the existence of sibling tools and an output schema, the description should clarify the product range syntax and provide examples. It omits contextual details needed for correct invocation, such as the expected form of expression.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0%, yet description adds no parameter details. Parameter names and defaults are somewhat informative, but the description does not explain that expression is the term with index variable, or interpret start/end defaults.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes symbolic products, both finite and infinite. It distinguishes from siblings like symbolic_sum or symbolic_diff by specifying the operation (product vs sum/differentiation), though it does not explicitly name alternatives.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 such as symbolic_sum, or any prerequisites. The description provides no context for invocation 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 present, so the description carries full burden. It only states the fitting method ('least squares') but fails to disclose convergence criteria, error handling, or whether covariance is returned. The output schema exists but is not referenced.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence that clearly communicates the core action. However, it is overly terse and could be expanded to include parameter hints without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 7 parameters, an output schema, and multiple sibling tools, the description is severely incomplete. It provides no information on model syntax, optional parameters, or how results are returned, leaving the agent underinformed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does 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 any of the 7 parameters. The term 'nonlinear model' gives no clue about the 'model' string format (e.g., function expression), nor does it clarify parameters like p0, sigma, or absolute_sigma.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'fit', the resource 'nonlinear model', and the method 'least squares'. It distinguishes from sibling tools like 'regression' (likely linear) and 'lstsq' (generic least squares) by specifying nonlinear modeling.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 'regression' for linear fits or 'lstsq' for linear least squares. The agent cannot determine the appropriate context without explicit cues.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" 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 disclose behavior. It only mentions computation of eigenvalues and eigenvectors, but does not state what happens for non-square matrices, the order of eigenvalues, numerical precision, or whether the operation is destructive. The output schema exists but is not referenced.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that is front-loaded with the verb 'Compute'. It is concise with no redundant words. However, it may be too terse, lacking necessary details for a non-trivial tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the presence of an output schema, return values need not be explained, but the description omits input constraints (e.g., square matrix required) and does not mention potential errors or edge cases. With no annotations, the description is incomplete for a tool with two parameters.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does 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 minimal information beyond parameter names: 'compute_vectors' is hinted as controlling optional eigenvector computation. No details on matrix shape or constraints, and the boolean parameter's effect is only implied.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states it computes eigenvalues and optionally eigenvectors, which is a specific verb+resource. However, it does not differentiate from sibling tools like gpu_eigen_batch or matrix_decompose, which may perform similar decompositions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 gpu_eigen_batch or matrix_decompose. There is also no indication of prerequisites (e.g., matrix must be square) or when to set compute_vectors to true/false.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided. The description only says 'numerically' but fails to disclose key behaviors like required input shape, handling of multiple roots, convergence criteria, or error cases.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that front-loads the purpose. It earns its place but is perhaps too terse given the tool's 7 parameters and no other guidance.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description does not explain return values or behavior. With 7 parameters and no annotations or parameter docs, the description is far from complete for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does 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 parameters (expression, variable, method, etc.). It does not explain the role of any parameter beyond its name in the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states it finds a root of a scalar function numerically. It distinguishes from symbolic solving siblings like 'solve' but does not explicitly differentiate from other numeric root-finding tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool vs alternatives (e.g., 'solve', 'solve_linear'). No prerequisites or limitations 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 does not mention behavioral traits such as read-only nature, return format, or side effects. It only lists operations without explaining what 'extended' does or how steps are returned.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single concise sentence with no wasted words. However, it could benefit from more structure to cover parameters and usage, though it is appropriately sized for a simple tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has 3 parameters and no annotations, the description lacks completeness. It does not explain the operations or parameter semantics sufficiently. While an output schema exists, the description still fails to provide necessary context for parameter usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description should explain parameters. It mentions 'Compute GCD, LCM, or Euclidean algorithm steps' but does not clarify that 'operation' selects among these, nor what 'numbers' accepts (e.g., integers or strings), nor the effect of 'extended'. The description adds minimal value beyond the schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes GCD, LCM, or Euclidean algorithm steps, specifying the verb and resource. However, it does not differentiate from sibling tools like 'modular' or 'factor_int', which might have overlapping use cases.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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, nor any prerequisites or typical usage scenarios. For example, it doesn't explain when to choose GCD over LCM or how to configure the operation parameter.
Agents often have multiple tools that could apply. Explicit usage guidance like "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, the description must cover behavioral traits. It mentions 'GPU fallback' but fails to explain what triggers it, performance implications, or any side effects. The tool's read or write nature is not indicated.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
One concise sentence front-loading the verb and primary purpose. No extraneous words, ideal length for quick scanning.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description lacks details on input shape constraints, error handling, return format, and GPU requirements. Given the complexity of batched eigen decompositions, the description is insufficient for correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does 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 three parameters (matrices, symmetric, eigenvalues_only). The agent must rely solely on parameter names, which may be insufficient for correct usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('compute'), resource ('batched eigen decompositions'), and mentions GPU fallback, distinguishing it from the sibling eigen_decomp. However, 'GPU fallback' is somewhat ambiguous, lacking details on when fallback occurs.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 like eigen_decomp. The description does not mention prerequisites, performance considerations, or when not to use it.
Agents often have multiple tools that could apply. Explicit usage guidance like "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, the description must disclose behavioral traits. It only states the basic action without mentioning output format, error handling, plotting behavior, or constraints like supported equation syntax. Minimal transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very short and front-loaded, but it omits essential details. While concise, it sacrifices completeness for brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (implicit plotting) and lack of schema descriptions/annotations, the description is incomplete. It does not cover how to specify equations, default ranges, or output details. An output schema exists but is unmentioned.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no meaning to any of the 6 parameters. It does not explain equation format, range default behavior, or grid_size significance.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'Plot' and the resource 'implicit equations or inequalities in x and y', which distinguishes it from sibling tools like plot_function that plot explicit functions. The scope 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 Guidelines2/5
Does 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 plot_function. There is no mention of prerequisites, when not to use, or suggestions for 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?
No annotations provided; description only states the operation without disclosing behavior for singular systems, error handling, or method implications. Minimal behavioral insight.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence is concise but omits valuable context. Could include brief parameter hints without sacrificing brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
With 0% schema coverage, no annotations, and a minimal description, the tool definition lacks completeness for a mathematical operation that has common pitfalls (singularity, dimension mismatch).
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does 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 parameters a, b, or method. Parameters are entirely undocumented beyond schema types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
Description uses specific verb 'solve' and resource 'square linear system Ax = b', clearly indicating the tool's purpose. It differentiates from sibling tools like 'solve' or 'lstsq' by specifying the square system requirement.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 (e.g., lstsq for non-square systems). Missing context for prerequisites like matrix invertibility.
Agents often have multiple tools that could apply. Explicit usage guidance like "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, the description carries the burden of behavioral disclosure. It mentions indefinite/definite integrals but does not explain the output format, handling of special functions, or computational requirements.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single concise sentence. It is not verbose, but could benefit from additional context while remaining succinct.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (5 parameters, symbolic integration), the description is incomplete. It does not explain the role of parameters like 'method' or 'limits', nor the return value. The output schema exists but is not described.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description adds no meaning to parameters like 'method' or 'limits'. Parameter names and defaults provide some clarity, but the description fails to enhance understanding.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes symbolic indefinite or definite integrals, which distinguishes it from numerical integration or other transforms like Laplace transforms. However, it does not explicitly differentiate from sibling tools like 'numerical_integrate'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use symbolic integration versus numerical integration or other methods. The description lacks explicit usage context or 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 provided; description is minimal. It does not disclose behavior like handling of symbolic expressions, convergence checks, or output format. The term 'symbolic' is vague without further detail.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence is concise but overly brief. Lacks structure such as front-loading key behavioral traits or parameter roles beyond the core purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Output schema exists, which partially covers return values, but the description omits parameter semantics and usage context, leaving the agent underinformed for selecting or invoking the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema has 0% description coverage, and the description adds no parameter-level meaning. Parameters like expression, index, start, end are not explained beyond their names and defaults.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('Compute') and the resource ('symbolic finite or infinite summations'), distinguishing it from related tools like symbolic_integrate and symbolic_product.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 such as series or symbolic_integrate. Context of finite vs infinite or summand complexity is missing.
Agents often have multiple tools that could apply. Explicit usage guidance like "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, the description must disclose all behavioral traits. It reveals the adaptive GPU/CPU selection, but does not mention auth needs, rate limits, side effects, data size constraints, or response format. Significant gaps remain for a computation tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that efficiently conveys the core purpose and adaptive behavior. No wasted words, but some additional structure (e.g., separating parameter notes) could improve without harming conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description is too sparse for the tool's complexity (5 parameters, adaptive logic). It fails to explain parameter roles, usage context, or the selection criteria, 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.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0% and the description provides zero information about any of the 5 parameters (data, operation, etc.). The agent receives no guidance beyond the raw schema, making this dimension severely lacking.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'Compute' and the resource 'FFTs', and adds the nuance of GPU vs CPU selection. This distinguishes it from a generic FFT tool (e.g., if one existed). The adaptive behavior is a key differentiator and is explicitly mentioned.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description mentions 'when beneficial' but does not specify criteria for GPU vs CPU use, nor does it provide when-not-to-use or alternatives. Lacks explicit guidance on prerequisites or trade-offs, 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, and the description does not disclose behavioral traits such as error handling, performance, or shape requirements, which are essential for a matrix multiplication tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise (one sentence) and front-loaded with the action, but it lacks structure and completely omits necessary details.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has two parameters and no annotations, the description is too minimal. It does not cover shape requirements, return type, or error conditions, leaving the agent underinformed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, meaning the parameters have no descriptions. The tool description does not add any meaning beyond the schema, failing to explain that A and B should be 2D arrays with compatible shapes.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the operation ('Multiply two matrices A @ B.'), which is specific verb+resource and distinguishes from sibling tools like gpu_matrix_multiply.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool vs alternatives like gpu_matrix_multiply, or any context about inputs 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?
The description fails to disclose behavioral traits such as output format (string, image), error handling, or limitations. With no annotations, the description should cover these, but it only states the high-level action.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, efficient sentence with no fluff. It front-loads the key action, though 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.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the presence of an output schema and sibling tools, the description is moderately complete for a simple conversion tool but lacks differentiation from render_math and does not explain the rendering output.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description does not add meaning to the parameters. The schema has 0% description coverage for expression and style; the description only mentions 'mathematical expression' without detailing valid inputs or style options.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool converts mathematical expressions to LaTeX and renders them. It is specific and distinct from siblings, though it does not explicitly differentiate from render_math.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 like render_math or other expression tools. The description does not mention 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?
With no annotations, the description must fully disclose behavior. It only states 'comprehensive descriptive statistics' without details on what statistics are computed, return format, or handling of edge cases (e.g., empty data), despite the presence of an 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.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, concise sentence that quickly communicates the tool's purpose. It is front-loaded but perhaps too brief.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's statistical nature and the presence of an output schema, the description lacks sufficient detail about the statistics computed and does not help distinguish it from numerous similar sibling tools.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0% (only titles), and the description provides no additional meaning for the 'data' and 'percentiles' parameters beyond their types and defaults.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states 'Compute comprehensive descriptive statistics' which is a specific verb and resource. It clearly indicates the tool's purpose but does not differentiate from sibling tools like 'hypothesis_test' or 'distribution' that may also compute statistics.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies use for descriptive statistics but provides no explicit guidance on when to use this tool versus alternatives, nor 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?
With no annotations, the description must provide behavioral traits, but it only states the basic function without mentioning limitations, algorithm details, or error handling for no solutions.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The single-sentence description is brief but lacks necessary detail; it is not overly long but fails to convey important information that could fit concisely.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description is too sparse for a tool with three parameters; an agent would have incomplete context about input formats and output behavior.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema has 0% description coverage, and the description does not explain the three parameters (equation, method, bound), leaving the agent to infer meaning from names and defaults alone.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool solves Diophantine equations over integers, using a specific verb and resource, distinguishing it from sibling tools like 'solve' or 'factor'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 like 'solve' for real equations or 'factor_int' for integer factoring; no context on prerequisites or when not to 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?
With no annotations, the description carries full burden but only mentions 'GPU fallback' without explaining behavior on GPU failure, performance implications, side effects, or whether results are symbolic or numeric.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single concise sentence, but its brevity sacrifices necessary detail; it could include parameter semantics and usage context without becoming verbose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of batched linear systems and zero schema coverage, the description is incomplete—it does not explain output format, error conditions, or when GPU fallback applies.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, and the description provides no explanation of the parameters 'a_batch' and 'b_batch' beyond their names, leaving the agent to infer from schema structure alone.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool solves batched linear systems, with the specific verb 'Solve' and resource 'batched linear systems'. It distinguishes from siblings like 'solve' (likely symbolic) and 'lstsq' (least squares).
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for batched linear systems but provides no explicit guidance on when to use this tool versus alternatives like 'solve' or 'lstsq', 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 provided, and the description lacks behavioral details such as complexity, graph constraints (e.g., acyclicity), or handling of infeasible flows. It does not disclose what happens when no path exists.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, very concise, and front-loaded. However, it could be slightly expanded to cover key details without losing conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given 4 required parameters with no schema descriptions and no annotations, the description is insufficient. It does not provide enough context for correct invocation, relying on the user's domain knowledge.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description does not explain any of the 4 parameters. It only mentions 'capacitated directed graph' without detailing the format of edges, source, sink, or capacities.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes maximum flow in a capacitated directed graph, using specific verb and resource. It differentiates from sibling graph tools like shortest_path or spanning_tree.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool vs alternatives, no prerequisites or exclusions mentioned. The description only states the basic operation.
Agents often have multiple tools that could apply. Explicit usage guidance like "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 disclosing behavioral traits. It does not mention that the expansion point defaults to 0 (Maclaurin series), nor does it specify input constraints (e.g., expression must be symbolic) or output format. The description is insufficient for an agent to anticipate tool behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single short sentence, which achieves conciseness but at the cost of sacrificing necessary details. While it is front-loaded and efficient, it omits critical information that would fit in a slightly longer description without becoming verbose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of series expansion and the existence of an output schema (not shown here), the description should at least hint at the return format (e.g., a symbolic expression). It fails to mention what the tool returns, its error behavior, or the scope of supported expressions (e.g., rational functions, elementary functions). This lack of completeness limits the agent's ability to use the tool effectively.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does 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 clarify each parameter's meaning. Although the phrase 'Taylor or Laurent series expansions' implies the role of expression, variable, point, and order, it provides no explicit mapping or additional constraints. For example, it doesn't detail that 'point' is the expansion center or that 'order' indicates the truncation order.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes Taylor or Laurent series expansions, specifying the exact type of mathematical operation. It distinguishes from sibling tools like limit or symbolic_diff which handle different operations, leaving no ambiguity about the tool's core function.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when 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 limit or symbolic_integrate. There is no mention of prerequisites, typical use cases, or scenarios where a different tool would 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?
Without annotations, the description should disclose behavioral traits. It does not mention that the order parameter is integer, how the tool handles multiple variables, or what functions are supported. The phrase 'arbitrary order' is ambiguous given the schema restricts order to integer.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, highly concise. However, it omits critical details, making it too terse for a tool with multiple parameters.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool complexity and lack of schema descriptions, the description is incomplete. It does not cover input semantics or usage context. The presence of an output schema reduces the need to explain returns, but input-side guidance is insufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Since schema description coverage is 0%, the description must explain parameters. It does not describe any of the four parameters (expression, variable, order, show_steps), leaving the agent without additional context beyond schema titles.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool computes symbolic derivatives of arbitrary order. It uses a specific verb ('Compute') and resource ('symbolic derivatives'), distinguishing it from sibling tools like symbolic_integrate or series.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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. There is no mention of prerequisites, limitations, or comparison to similar tools like symbolic_integrate.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents 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 output format (PNG data URI) but fails to disclose limitations like supported LaTeX packages, rendering errors, or performance characteristics. For a rendering tool, more detail is needed.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, concise and front-loaded. It wastes no words, but improvements could include a slightly more structured listing of key points (e.g., output format, parameter hints).
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the output schema exists (not shown), the description can skip return value details. However, it fails to provide context for the three parameters (which have no schema descriptions) and does not differentiate this tool from similar rendering tools or explain proper LaTeX input format. The description is insufficient for correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage for parameters, and the description provides no additional meaning. It does not explain that 'latex' should be a valid LaTeX expression, nor the effect of 'fontsize' and 'dpi' beyond their names. This severely limits the agent's ability to use the tool correctly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('Render'), the resource ('arbitrary LaTeX math'), and the output ('to a PNG data URI'). It is specific and distinguishes itself from sibling tools which perform symbolic math, plotting, or other operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage when a rendered LaTeX image is needed, but it does not explicitly state when to use this tool over alternatives, nor does it mention any exclusions or prerequisites. Given the many math-related siblings, some guidance would be beneficial.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents 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 vaguely mentions a 'Standard result dictionary' without detailing its structure. It does not state limitations (e.g., only works for polynomial/rational expressions over rational numbers) or reveal failure modes. The output schema exists but is not referenced 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.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is highly concise with a docstring-like format including 'Args' and 'Returns' sections. It uses example values to illustrate usage without unnecessary words. Every sentence contributes to understanding.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the presence of an output schema and only one parameter, the description covers the essential inputs and purpose. However, it lacks details on expected behavior (e.g., error handling for invalid expressions) and does not reference the output schema or explain the return format beyond 'standard result dictionary'.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The sole parameter 'expression' is described as 'SymPy-compatible polynomial or rational expression' with examples, which adds significant meaning beyond the schema's type-only definition. This compensates for the 0% schema description coverage and helps the agent understand valid inputs.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states it factors mathematical expressions over rational numbers. The verb 'Factor' and the specification 'over the rational numbers' provide specific purpose. However, it does not explicitly distinguish from sibling tools like 'simplify' or 'factor_int', which could cause confusion for an AI agent.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 that integer factorization should use 'factor_int' or that simplification might be more appropriate for other manipulations. The agent is left to infer usage without 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, and the description does not disclose behavioral traits such as error handling, performance considerations, or limitations beyond stating it returns a standard result dictionary.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise (two short sections), well-structured with Args and Returns headers, and contains no superfluous information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
While the output schema reduces the need for return details, the description lacks usage context such as when to use expand over simplifying, and with no annotations, behavioral context is missing.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description adds value by providing SymPy-compatible expression examples, which compensate for the 0% schema description coverage on the single parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description uses a specific verb ('Expand') and resource ('mathematical expression'), clearly distinguishing it from siblings like 'simplify' or 'factor'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 like simplify or factor; the description only provides examples of input expressions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are present, so the description must disclose behavioral traits. It only states the purpose and parameter details but fails to mention limitations, algorithm type, or potential performance issues for complex systems.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise with a clear purpose sentence followed by parameter definitions. No redundant information; every part is necessary and front-loaded.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The output schema exists, so return value details are not needed. The parameter descriptions are complete, but the tool lacks context on when to use it versus siblings and behavioral details, making it slightly incomplete given the complexity of the tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters5/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description thoroughly explains each parameter including the domain's allowed values (real, complex, integer, positive) and the show_steps purpose. This fully compensates for the missing schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose4/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states it solves equations or systems symbolically, which is clear and specific. However, it does not explicitly differentiate from siblings like 'solve_linear' or 'dsolve', which would help an agent choose correctly.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does 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 'dsolve' for differential equations or 'solve_linear' for linear systems. 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.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries full burden. It indicates algebraic simplification (non-destructive) but lacks details on limitations, error cases, or specific behavior (e.g., handling of undefined expressions). It 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.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is short and front-loaded with the purpose. The 'Args' and 'Returns' sections are well-structured, and every sentence adds value without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (single parameter) and the presence of an output schema (not shown), the description covers the core function. It could mention potential edge cases or failure modes for completeness, but it is largely sufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must supplement. It provides examples ('(x**2 - 1)/(x - 1)', 'sin(x)**2 + cos(x)**2') that clarify the required format, adding value beyond the bare schema. However, it could specify SymPy compatibility more thoroughly.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states 'Simplify a mathematical expression algebraically.' It uses a specific verb ('simplify') and resource ('mathematical expression'), and the algebraic focus distinguishes it from siblings like 'factor', 'expand', or 'solve'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description does not provide any guidance on when to use this tool versus alternatives. It only states the action, leaving the agent to infer usage without explicit context or exclusions.
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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