Math-MCP

Server Quality Checklist

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Latest release: v0.3.0
Disambiguation5/5
Each tool has a distinct mathematical operation with clear descriptions. Overlaps are minimal (e.g., add vs. sum, round vs. round_to) but descriptions differentiate them. No two tools perform the same function.
Naming Consistency2/5
The naming convention is inconsistent: single-word names (min, add), snake_case (percentage_of, compose_transform_4x4), and camelCase (radiansToDegrees) are mixed. Verbs like 'division' instead of 'divide' break patterns. While many tools follow verb_noun or noun_verb, the overall pattern is chaotic.
Tool Count2/5
With 59 tools, the server is extremely heavy for an MCP server. While each tool is well-defined, the sheer number can overwhelm an agent's tool selection. A more focused scope (e.g., separating linear algebra from basic arithmetic) would improve usability.
Completeness4/5
The tool set covers a vast range of mathematical domains: arithmetic, trigonometry, statistics, number theory, finance, linear algebra, 3D graphics, and probability. Minor gaps exist (e.g., no general linear system solver beyond 2x2, no calculus operations), but overall it is very comprehensive for a general math server.
Average 3.6/5 across 59 of 59 tools scored. Lowest: 2.9/5.
See the Tool Scores section below for per-tool breakdowns.
- No community issues in the last 6 months
- 1 commit in the last 12 weeks
- No stable releases found
- No critical vulnerability alerts
- No high-severity vulnerability alerts
- No code scanning findings
- CI status not available
This repository is licensed under MIT License.
This repository includes a README.md file.
No tool usage detected in the last 30 days. Usage tracking helps demonstrate server value.
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{
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}
```
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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

Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Minimal disclosure: only states it returns real or complex roots. No mention of degenerate cases (a=0), number of roots returned, or output format. Annotations are absent, so description carries full burden but fails to provide sufficient behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
One sentence, 10 words, very concise. Front-loaded with purpose. However, missing important details reduces overall utility of 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?
For a simple quadratic solver with no output schema or annotations, description is inadequate. Does not specify output format (e.g., array of roots), handling of discriminant, or edge cases. AI agent may invoke incorrectly without additional context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Description implicitly defines parameters as coefficients of the quadratic equation, adding meaning beyond schema names. However, it does not explain constraints (e.g., a should not be 0) or potential types beyond numbers. With 0% schema coverage, description partially compensates but is not comprehensive.
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?
Clearly states the verb 'Solves' and the specific equation a*x^2 + b*x + c = 0, and mentions return type (real or complex roots). Distinguished from sibling tools as no other solves quadratic equations.
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. Does not mention edge cases or prerequisites like a != 0.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead 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 mentions using a 'numerically stable algorithm' but provides no information about output format, error handling, or side effects. Insufficient for an unannotated tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence with clear verb and immediate context. No extraneous words; efficient and front-loaded.
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 2 parameters and no output schema or annotations, the description fails to explain the numbers parameter, return value, or constraints beyond what is in the schema. Needed more detail for completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 50% (sample parameter described, numbers not). The description reiterates the sample parameter's role but adds no meaning for the 'numbers' parameter beyond the schema's type and minItems. Does not compensate for the missing schema description.
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 calculates variance (population or sample) using a numerically stable algorithm. It distinguishes variance from related sibling tools like standard deviation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
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 vs. alternatives (e.g., standard_deviation) or when to choose sample vs. population. The description merely states what it does.
Agents often have multiple tools that could apply. Explicit usage guidance like "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. It does not mention how the median is computed (e.g., sorting, averaging middle values for even-length lists), edge cases, or return format. This is insufficient for a math utility.
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 a single, efficient sentence with no wasted words. It is appropriately front-loaded and earns its place.
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 low complexity and lack of output schema, the description is minimally adequate. However, it omits behavioral details like sorting and handling of even-length arrays, which an agent would need to fully understand the tool's operation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so baseline is 3. The description does not add new meaning beyond what the schema provides; it merely echoes the function. No extra context like valid ranges or formatting is given.
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 that the tool calculates the median of a list of numbers, using a specific verb and resource. It implicitly distinguishes from siblings like mean and mode, but does not explicitly contrast them, preventing a perfect score.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
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 median over alternatives (e.g., mean, mode) or any context-specific advice. No when-not or alternative tool mentions are included, limiting 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?
With no annotations, the description carries full burden for behavioral transparency. It only states the core operation without disclosing error handling, return format, or edge cases (e.g., points exceeding maxItems, invalid matrix).
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 a single, concise sentence (18 words) that packs essential information. It is front-loaded and free of fluff.
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 (6 parameters, no output schema, batch operation), the description is incomplete. It does not describe the output format, constraints (e.g., maxItems), or behavior for invalid inputs. An output schema or richer description would improve completeness.
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 low (17%). The description only mentions the viewProjectionMatrix parameter ('combined projection*view matrix'), but does not explain other parameters like width, height, yDirection, clipDepthRange, or the structure of points. This leaves significant gaps.
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's purpose: it batch-projects named bone or joint world positions to 2D pixels using a combined projection*view matrix. This distinguishes it from sibling tools like world_to_screen (single point) and transform_point_3d (general transformation).
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 lacks guidance on when to use this tool versus alternatives. It does not mention prerequisites, limitations, or explicit conditions for use, such as handling of points behind the camera or out-of-view situations.
Agents often have multiple tools that could apply. Explicit usage guidance like "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. It only states basic addition, omitting return type, error handling (e.g., non-numeric inputs), or floating-point behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, front-loaded with the key action. While it could include more detail, 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 the tool's simplicity and lack of output schema, the description is incomplete. It does not state the return value (a number) or handle edge cases like single-element arrays. For a tool with many siblings, more context is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% for the single parameter 'numbers', which has a clear description. The tool description adds no further meaning beyond 'adds numbers together', so baseline 3 is appropriate.
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 clearly states the verb 'adds' and resource 'numbers', with scope 'any number'. It effectively distinguishes this tool from siblings like 'add' (which implies two operands) and 'mean' (average).
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 'add' for two numbers or 'sum' for arrays. Despite many sibling tools, the description provides no selection criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavior. It fails to mention critical prerequisites such as the requirement that the two arrays must be of equal length for a valid correlation, and it does not describe the return format or edge cases (e.g., constant arrays).
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 is front-loaded with the main action. It does not contain any waste, though it could include additional useful information 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?
For a simple tool with 2 parameters and no output schema, the description lacks necessary completeness. It does not mention the expected output (a single value between -1 and 1), the condition that arrays must be same length, or any assumptions like linearity. The information provided is adequate for a basic understanding but insufficient for correct invocation in all cases.
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 compensate by explaining the parameters. It describes 'paired numeric observations' but does not explicitly state that firstValues and secondValues are the two sequences or that they must be paired and of the same length. This adds minimal value beyond the schema structure.
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 'calculates' and the exact statistical measure 'Pearson correlation coefficient', distinguishing it from sibling tools like variance, standard_deviation, and linear_regression.
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 when to use (when needing correlation between paired observations) but provides no explicit guidance on when not to use or how it compares to alternative correlation measures or siblings like linear_regression.
Agents often have multiple tools that could apply. Explicit usage guidance like "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 mentions 'explicit handedness and NDC depth range' but does not describe side effects, error behavior (e.g., invalid near/far plane), or whether the function is pure. Lack of output specification also reduces transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, front-loaded sentence with no redundant information. Every word adds value, making it highly efficient for an AI agent to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no output schema, the description should clarify the return value (e.g., a 4x4 matrix format). It also lacks details on coordinate system assumptions or matrix ordering, which are critical for a projection matrix. This leaves important gaps for correct usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is only 33% (2 of 6 parameters described in schema). The description adds context for 'handedness' and 'clipDepthRange' by stating 'explicit handedness and NDC depth range', but does not explain common parameters like verticalFieldOfViewDegrees, aspectRatio, nearPlane, farPlane. It partially compensates but not sufficiently for a low-coverage schema.
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 creates a perspective view-to-clip matrix, specifying the key aspects of handedness and NDC depth range. This verb+resource construction effectively distinguishes it from sibling tools like 'look_at_view_matrix' or 'view_to_clip'.
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 vs alternatives. Among siblings are related tools like 'view_to_clip' and 'clip_to_ndc', but the description does not clarify the differences or use cases, leaving an 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?
Without annotations, the description carries the full burden, but it only states the operation. It does not disclose what the tool returns (e.g., the sum), nor does it mention edge cases like overflow or how non-numbers are handled.
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 a single, front-loaded sentence with no redundant information. Every word is necessary.
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?
For a simple two-number addition tool, the description is adequate but incomplete. It does not specify that the tool returns the sum, which would be expected given no output schema.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema already documents both parameters with descriptions ('The first addend' and 'The second addend'), so the description adds no additional meaning. Schema coverage is 100%.
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 (adds) and the resource (two numbers), distinguishing it from sibling tools that perform other arithmetic operations like subtraction or multiplication.
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 sum (which handles multiple numbers) or subtract. The description does not mention context or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description only says it normalizes data into posteriors but does not disclose validation behavior, output format, or handling of invalid inputs.
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?
Single sentence with zero wasted words, efficiently conveying the core function.
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?
Missing output schema and description does not explain return format, error handling, or edge cases, leaving the tool incomplete for an 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 minimal context beyond schema, not explaining constraints like priors summing to 1 or meaning of likelihood.
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 normalizes priors and likelihoods into posterior probabilities for mutually exclusive, exhaustive hypotheses, specifying the verb, resource, and conditions.
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 only for mutually exclusive, exhaustive hypotheses but does not explicitly compare with sibling like bayes_theorem or provide when-not-to-use guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description accurately outlines the core mathematical behavior. However, it does not disclose edge cases (e.g., division by zero if w=0, handling of w values near zero, or behavior with negative w). Since no annotations are provided, the description carries the full burden, and these gaps could lead to unexpected results or errors.
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?
A single, well-structured sentence that immediately conveys the tool's purpose and operation. No extraneous words, every part contributes to the description. The agent can quickly understand the transform being applied.
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 the tool's relative simplicity, there is no output schema, yet the description does not hint at the return format (e.g., a point object with x, y, z? an array?). Additionally, there is no mention of error handling for invalid input (like w=0). Given the graphics domain where precise coordinate transformations are critical, this lack of completeness could cause misuse.
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 zero description coverage (0%), so the description must compensate. It identifies the three derived values (x/w, y/w, z/w) but does not explain the role of each component (e.g., that x,y,z are homogeneous coordinates and w is the perspective divisor). It also omits constraints (e.g., w should not be zero) or the expected coordinate system.
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 specific operation: performing a 4D perspective divide (x/w, y/w, z/w) to convert clip-space coordinates to NDC. It uses a precise verb ('performs') and identifies the resource ('clip-space perspective divide') and the target ('normalized device coordinates'). This distinguishes it from sibling tools like 'view_to_clip' and 'ndc_to_screen' which handle adjacent pipeline stages.
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, such as the prerequisite that the input must already be in clip space (e.g., after 'view_to_clip'), or that the output is typically fed into 'ndc_to_screen'. There is no mention of alternatives or conditions where this tool is not appropriate, 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.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description carries full burden. It states the scaling operation and notes yDirection for origin, but does not describe how the z component of ndcPoint is handled, nor the return format (e.g., screen coordinates as floats or ints). Adequate but minimal.
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?
Single sentence, concise and front-loaded with purpose. However, it could be slightly more structured by separating the primary action from optional parameter behavior (yDirection).
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?
No output schema, no annotations, and a nested parameter object. The description covers the basic transformation but omits what the tool returns (e.g., an object with screen x,y) and how z is treated. For a simple math tool, it is marginally complete.
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 50% (ndcPoint and yDirection have descriptions, width and height have constraints). The tool description adds no additional explanation for parameters, missing an opportunity to clarify, e.g., the range of width/height or the mapping from NDC to screen pixels.
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 a specific verb ('Scales') and resource ('normalized device coordinates to a 2D screen resolution'), clearly distinguishing it from siblings like 'world_to_screen' which operate at a different coordinate stage.
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 such as 'world_to_screen' or 'clip_to_ndc'. The description does not mention prerequisites or preferred contexts.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It only states the basic operation but omits critical details like input domain (expected range -1 to 1) and output range (0 to π), nor error handling for out-of-domain inputs.
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 a single, concise sentence that front-loads the key action and resource. Every word is necessary and there is no 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 low complexity (single parameter, no nested objects, no output schema), the description is mostly adequate. However, it lacks specification of input domain constraints, which is a minor gap for a mathematical function.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, with the single parameter described as 'The number to find the arccosine of'. The description adds no extra meaning beyond the schema, so baseline score of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'calculates' and the specific resource 'arccosine' with units 'in radians'. It distinguishes from sibling tools like arcsin and arctan by naming the trigonometric 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?
No guidance is provided on when to use this tool versus alternatives. The description does not mention context, prerequisites, or exclusions, leaving the agent to infer usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It implies a straightforward arithmetic division but does not disclose behavior for zero denominator, precision, or error handling, which are important for a math 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 short sentence that immediately conveys the action. It is concise and focuses on the core functionality, though it could optionally discuss edge cases.
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?
For a simple two-parameter tool with no output schema, the description is partially complete but lacks discussion of division by zero and return value. Given the many sibling math tools, more context would improve differentiation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, with both parameters already described. The description adds no extra semantic meaning beyond the schema, so baseline score of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the operation 'divides the first number by the second number', specifying the verb and the two resources. This distinguishes it from sibling tools like add, multiply, or modulo.
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 division versus alternatives, no mention of edge cases like division by zero, and no comparison with related operations such as modulo.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations exist, so the description carries full burden. It does not disclose behavior for edge cases (empty array, non-numeric items), error handling, or return type (e.g., NaN).
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 a single sentence, concise and front-loaded with no extraneous 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?
For a simple mathematical function, the description provides adequate purpose but lacks behavioral details for edge cases. Given the lack of output schema and annotations, it is minimally complete.
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 100% with a clear description of the 'numbers' parameter. The tool description adds no new meaning beyond what the schema already provides.
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 it finds the maximum value from a list of numbers, using a specific verb and resource. It distinguishes from sibling 'min' and 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?
No explicit when-to-use or when-not-to-use guidance is provided. Usage is implied by the name and description, but edge cases like empty arrays are not addressed.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It only mentions the input range, but fails to disclose the output format (e.g., list of integers) or any edge-case behavior, which is critical for tool invocation.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, concise sentence with no extraneous words. It is front-loaded and efficient.
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?
For a simple tool, the description is adequate but misses key details like the return type (e.g., array of prime factors). Without output schema, the agent cannot infer the result structure, reducing completeness.
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%, yet the description adds no meaning beyond the schema. It repeats the range already defined in min/max constraints and does not explain the 'value' parameter's role (e.g., 'the integer to factorize').
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 'returns' and the resource 'prime factorization', with a specific input range. It distinguishes from sibling math tools as none perform factorization.
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 prime factorization but does not explicitly guide when to use vs alternatives like 'is_prime' or 'greatest_common_divisor'. No 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 must disclose behavioral traits. It states rounding to nearest integer but omits the tie-breaking rule (e.g., 0.5 rounds up), which is critical for accuracy.
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 a single, efficient sentence with no unnecessary words.
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?
For a simple tool with one parameter, the description is mostly sufficient but lacks the rounding rule. No output schema is needed given the simplicity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so baseline is 3. The description adds no new meaning beyond the schema's 'The number to round'.
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 'Rounds', the resource 'a number', and the result 'to the nearest integer'. This distinguishes it from siblings like floor (rounds down), ceiling (rounds up), and round_to (rounds to specified 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 given on when to use this tool versus alternatives like floor, ceiling, or round_to. It doesn't specify the rounding rule (e.g., half up) 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?
No annotations are provided, so the description must cover behavioral traits. It only states the basic function, omitting edge cases like tan(pi/2) returning infinity or errors, precision, or domain limitations. This is insufficient for safe usage.
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 a single concise sentence that directly states the tool's purpose with no wasted words. It is front-loaded and efficient.
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 simple one-parameter tool and no output schema, the description lacks completeness. It doesn't describe the return value (e.g., a number) or handle edge cases, which are important for a mathematical function.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, and the description adds no new meaning beyond what the parameter description already provides. The baseline is 3, with no extra value.
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 calculates the tangent of a number in radians, using a specific verb and resource. It distinguishes itself from sibling trigonometric tools like sin, cos, and arctan.
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 tangent calculations but provides no explicit guidance on when to use this tool versus alternatives. For instance, it could mention when to prefer tan over sin/cos or when to use arctan for inverse.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description carries full burden. It states exact arithmetic and result reduction, which are key behaviors. However, it does not disclose operand order (e.g., first minus second), error handling for zero denominators, or input constraints (e.g., strings representing integers). With zero annotations, more behavioral context would be expected.
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 very concise (12 words in one sentence). It is front-loaded with the verb 'adds, subtracts, multiplies, or divides'. While efficient, it lacks structure like bullet points or parameter explanations that could improve clarity without added length.
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?
With 5 required parameters and no output schema, the description is adequate but incomplete. It explains what the tool does but not how inputs map (order), what the output format is (implied fraction but not specified), or error cases. Gaps exist in parameter semantics and behavioral 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?
Schema description coverage is 0%, so description must compensate. It only mentions 'two fractions' without explaining specific parameters (firstNumerator, etc.) or the operation enum. The input format (string integers) is in schema but not reinforced. Minimal added value beyond schema.
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 performs arithmetic operations (add, subtract, multiply, divide) on two fractions exactly and returns the reduced result. It distinguishes from sibling tools like simplify_fraction (single fraction) and decimal arithmetic tools like add/subtract/multiply/division.
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 does not explicitly mention when to use this tool over alternatives. It implies use for fraction arithmetic but lacks guidance on selecting this over decimal tools or simplify_fraction. No exclusions or alternatives are named.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description must disclose behavioral traits. It states the output is a row-major matrix for a look-at view transformation and mentions handedness, but it does not address edge cases (e.g., up vector parallel to view direction) or failure modes. This is adequate but not comprehensive.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, concise sentence that front-loads the core purpose. It contains no extraneous words or redundant 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?
Given the absence of an output schema, the description should explain the return value more fully. It implies a 4x4 matrix but does not specify the format or structure. It also lacks explanation of error conditions or validation. While it covers the essential transformation, it is not fully complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%; all parameters have descriptive definitions. The tool description adds 'row-major' and coordinate system context, but this does not significantly enhance understanding beyond the schema. Baseline 3 is appropriate.
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 ('Creates') and clearly identifies the resource ('row-major look-at world-to-view matrix'). It distinguishes from siblings by mentioning support for right- or left-handed coordinate systems, which is a unique feature among related tools like 'world_to_view'.
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 guidance on when to use this tool versus alternatives such as 'world_to_view' or 'perspective_projection_matrix'. It lacks explicit context like prerequisites, suitable scenarios, 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?
No annotations are provided, so the description carries the full burden. It discloses the interpolation method but fails to mention edge-case behaviors (e.g., handling of empty arrays, behavior at percentile=0 or 100), which are important for safe usage.
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 a single, well-structured sentence that conveys core functionality without unnecessary words.
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?
For a simple mathematical tool with two parameters and no output schema, the description captures the essential behavior. However, it lacks details on edge cases and the fact that data is sorted internally.
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 50% (only 'percentile' has a description). The tool description adds no further detail about 'numbers' parameter meaning, format, or constraints. The method notation adds context but not parameter-level semantics.
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 'Calculates', the resource 'percentile', and specifies the exact method 'sorted linear interpolation (R-7 / Excel PERCENTILE.INC method)'. This distinguishes it from sibling tools like mean, median, etc.
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 provides no explicit guidance on when to use this tool versus alternatives. It only states what it does, leaving the agent to infer usage context from the tool name and siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden, but it does not disclose the return format, error handling for zero denominator, or how the result is presented. The agent cannot infer the output structure from a single sentence.
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?
Single sentence front-loaded with the main action, no fluff. Every word adds value.
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?
Despite the tool's simplicity, the description fails to mention the return value (expected to be simplified numerator and denominator as strings). With no output schema, this is a notable gap affecting completeness.
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 coverage is 100%, but the description adds the critical context that strings preserve large integers beyond JSON safe range, which adds meaning beyond the schema's basic pattern descriptions.
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 'Reduces' and the resource 'fraction', and emphasizes the preservation of large integer values, distinguishing it from sibling tools like fraction_arithmetic that perform 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 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 (e.g., greatest_common_divisor or fraction_arithmetic). The description only hints at use cases involving large integers but does not provide direct comparisons or when-not-to-use conditions.
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?
Discloses that output is in radians, but does not mention domain [-1,1] or handling of invalid inputs.
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?
Extremely concise; one sentence with no redundant information.
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?
Adequate for a simple math function, but lacks domain constraint; overall informative.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema already describes the number parameter well; description adds output unit but no additional parameter semantics.
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?
Clearly states it calculates arcsine in radians, distinguishing it from other trig functions like arccos and sin.
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 guidance; does not mention domain restrictions or compare to sibling tools like arccos.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must disclose behaviors. It states a pure computation (combining transforms) with no side effects, destruction, or auth needs. However, it does not clarify whether the operation mutates inputs or the nature of the output. The description is adequate but minimal for a math tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
A single sentence that precisely describes the operation without any redundant words. Every element is essential, and the structure is front-loaded with the core action.
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 lacks information about the return value (expected to be a world matrix or transform). No output schema exists, and the description does not clarify what the tool outputs. Given the complexity of 3D transforms and the presence of sibling tools with similar purpose, this is a notable gap.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 50% (only parentWorldMatrix and localRotation have descriptions). The description adds context by naming the three local components (position, rotation, scale) but does not explain the optionality of localScale, the exact output format, or the meaning of the matrix operation. It partially compensates for missing schema details.
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 explicitly states the operation: combining a parent bone world matrix with child local position, rotation, and scale. This clearly distinguishes it from siblings like 'bone_hierarchy_to_world' which processes a hierarchy of bones.
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 the tool is used for transforming a child bone's local transform to world space given a parent matrix, but it does not provide explicit guidance on when to use this vs. alternatives like 'bone_hierarchy_to_world' or other matrix tools. No exclusions or prerequisites are mentioned.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must carry full burden. It states 'rounds up', which implies towards positive infinity, but does not explicitly clarify behavior for negative numbers or special cases (NaN, infinity). It is adequate but lacks specificity.
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 a single short sentence with no filler. Every word is necessary. It is front-loaded and efficient.
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 (one parameter, no output schema, no annotations), the description is minimally complete. It explains the function and the parameter. It could mention edge cases, but for a basic mathematical operation this is sufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%: the only parameter 'number' has description 'The number to round up'. The tool description adds no new meaning beyond that. Baseline score of 3 is appropriate since the schema already documents the 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 clearly states the action: 'Rounds a number up to the nearest integer'. It uses a specific verb ('Rounds') and identifies the resource (number and integer). This distinguishes it from sibling tools like floor (rounds down) and round (rounds to nearest).
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 over alternatives (e.g., floor, round). There is no mention of context, prerequisites, or when not to use it. For a simple math function, no guidance is acceptable but keeps score low.
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 mentions 'exact' and 'safe integers', hinting at no overflow, and discloses the return type as decimal string. However, it does not address edge cases such as behavior with negative numbers or zero, nor does it state that LCM is always positive.
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 a single sentence that is direct and without any unnecessary words or repetition. Every part contributes to the understanding of the tool's function.
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 (two parameters, no output schema, no annotations), the description is fairly complete. It covers the input type, output format, and core functionality. However, it could be more complete by mentioning that the LCM is always positive or how zero is handled.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
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 mentions 'two safe integers', which aligns with the two parameters but offers no additional semantic detail about what each parameter represents (e.g., first number, second number). 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.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'Finds', the resource 'least common multiple', and specifies it operates on two safe integers, returning a decimal string. This distinguishes it from siblings like 'greatest_common_divisor' and clearly defines its purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
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 'greatest_common_divisor' or other mathematical operations. The description implies usage for LCM computation but lacks 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.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations exist. The description does not disclose behavior for edge cases like empty arrays or non-number inputs, which are not handled by the schema alone.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence, no redundancy, front-loaded with the core action.
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?
For a single-parameter, no-output-schema tool, the description covers the essential function. Missing edge case handling but acceptable given simplicity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with a clear description for the 'numbers' parameter; the tool description adds no extra meaning beyond what the schema already provides.
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 ('Finds') and resource ('minimum value from a list of numbers'), clearly distinguishing it from sibling tools like 'max' which does the opposite.
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?
No guidance on when to use vs alternatives (e.g., 'percentile' for other reductions), but the purpose is straightforward; adequate for a simple math tool.
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 must carry full burden. It states the core function but omits tie-breaking behavior, handling of empty arrays, or error conditions, leaving ambiguity.
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, efficiently conveying the purpose. However, it could include a brief note on edge cases without losing conciseness.
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?
Without an output schema, the description should specify return values for edge cases (e.g., ties, empty input). The current description leaves significant gaps for a statistical tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so the description adds minimal value beyond the schema. The parameter 'numbers' is already well-documented in the schema.
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 finds the mode (most common number) from an array, differentiating it from siblings like mean and median.
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 when to use (to find the mode) but lacks explicit guidance on alternatives or when not to use, such as for multimodal distributions.
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?
Describes the basic behavior (returns remainder) but does not disclose edge cases like division by zero or behavior with negative numbers. No annotations exist, so description carries full burden.
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?
Single sentence with no wasted words. Information is front-loaded and directly to the point.
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?
For a simple arithmetic operation with no output schema, the description is sufficient. It explains the core functionality. Could mention result constraints (e.g., remainder is always less than denominator) but not strictly necessary.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% and already describes both parameters clearly. Description adds minimal value beyond restating the parameter purposes. Baseline score 3 is appropriate given high schema coverage.
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 clearly states the operation: divides two numbers and returns remainder. It uses specific verb+resource and distinguishes from sibling 'division' which likely returns quotient.
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 modulo versus other math operations (e.g., division, remainder-related tools). Does not mention typical use cases 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.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description carries full burden. It states the calculation but doesn't mention return format, precision, or error handling (e.g., division by zero). Adequate for a simple pure function but could be more explicit.
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?
Single sentence with example, no wasted words. Front-loads the action and resource.
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?
For a simple mathematical tool with full schema coverage, the description is complete enough. It lacks only minimal context like return type or edge cases.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% and schema descriptions already define parameters clearly. Description adds an example but no new semantic information beyond schema.
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 'calculates' and resource 'percentage of a value', with an example that clarifies scope. It clearly distinguishes from sibling 'percentage_change' which computes change between two values.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
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 'percentage_change' or other math tools. The context is implied but not stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It correctly describes the core behavior but does not specify rounding mode (e.g., half up, half down) or edge cases. For a simple rounding tool, this is adequate but not exhaustive.
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?
Single sentence, 10 words, front-loaded with the action. Every word earns its place; no wasted text.
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?
For a simple tool with two documented parameters and no output schema, the description covers the essential behavior. It could mention rounding mode, but context is sufficient for basic usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so baseline is 3. The description adds 'specified count of decimal places', which reinforces the schema description of 'decimalPlaces'. No additional semantic value beyond 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 'Rounds a number to a specified count of decimal places', which specifies the verb and the resource. It differentiates from the sibling 'round' (which rounds to integer) by mentioning decimal places.
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?
No explicit guidance on when to use this tool versus siblings like 'round' or 'floor'. Usage is implied by the description but not directly stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description carries full burden. It discloses the transformation type and matrix convention but lacks details on return format, homogeneous coordinates, or error handling (e.g., non-invertible matrix). Adequate but not exhaustive.
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?
A single, clear sentence with no extraneous information. Every word is necessary and front-loaded.
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?
Lacks output schema and does not describe the return value (e.g., format, homogeneous coordinates). Given the technical nature of the transformation, the description should specify if the result is a 3D point or 4D homogeneous vector. Incomplete for effective use.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 50% (viewMatrix has a description, worldPoint has none). The description adds no new meaning beyond the schema; it merely restates the matrix convention. WorldPoint's structure is fully defined in the schema, so the description does not degrade value.
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 states exactly what the tool does: transforms a world-space 3D position to view space using a supplied view matrix. It specifies 'row-major' and distinguishes from sibling tools like 'world_to_screen' which go further, and 'view_to_clip' which starts from view space.
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 you have a world point and a view matrix) but provides no explicit when-to-use/not-use or alternatives. For instance, it doesn't mention that 'look_at_view_matrix' can generate the required matrix.
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 discloses detection of missing parents and cycles, but does not mention return format, side effects, or performance constraints.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, well-structured sentence that efficiently conveys the core functionality and two key behaviors (detection of missing parents and cycles) without extraneous content.
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 complexity of a bone hierarchy transformation and the absence of an output schema, the description lacks details on return values (world matrices/positions) and handling of detected issues, leaving some gaps for agent interpretation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The single parameter 'bones' has no description in the schema (0% coverage), and the tool description does not add semantic value beyond what the nested schema details provide, so baseline score of 3 applies.
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 'resolves', the resource 'complete bone hierarchy', and the transformation from local transforms to world matrices/positions, distinguishing it from single-bone tools like 'bone_local_to_world'.
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 hierarchy-wide transformation but does not explicitly specify when to use this tool over siblings or mention any prerequisites or limitations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided. Description only states what it does (calculates compound growth) without revealing return format, edge cases, or potential issues (e.g., overflow). Somewhat transparent but incomplete.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence that is front-loaded with the core purpose. No wasted words.
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 5 parameters, no output schema, and no annotations, the description is adequate but minimal. Does not explain return value or handle edge cases. Could be more complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with field descriptions. Description adds context about contribution timing ('end of every period') but does not significantly enhance understanding beyond the schema. Baseline 3.
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 clearly states the tool calculates compound growth with optional contributions. Verb 'calculates' and resource 'compound growth' are specific. Among sibling math tools, this is unique and distinguishable.
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?
No explicit guidance on when to use vs alternatives like loan_payment or other math functions. The description implies usage for compound growth but lacks when-not or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations exist, so description carries full burden. It discloses the fitting method and outputs but omits assumptions (e.g., linearity, equal variance), error handling, or input constraints beyond basics.
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?
Single sentence front-loads the equation and outcome. No wasted words.
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?
For a simple tool with two required arrays and no output schema, description covers core functionality. Missing return structure (e.g., object with keys) but adequate for basic use.
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% (no parameter descriptions). Description only names xValues and yValues without adding constraints (e.g., must be same length, min length 2) or format details.
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?
Clearly states the tool fits a least-squares line and returns slope, intercept, and R-squared. This specific verb-resource pair (fit line) distinguishes it from siblings like 'correlation' or 'mean'.
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?
No explicit guidance on when to use or avoid this tool. Among siblings, it's clear for simple linear regression, but no comparison to 'correlation' or 'solve_linear_system' is provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description bears full responsibility. It correctly describes a pure computation (no side effects), but lacks detail on edge cases like division by zero. However, the core behavior is transparent.
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?
Single, front-loaded sentence with no wasted words. The verb 'calculates' immediately conveys action, and the structure is efficient.
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?
Adequate for a simple tool, but missing details on return format, error handling (e.g., originalValue=0), and additional behavioral context. With no output schema, the description could be more complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The description maps parameters via 'from an original value to a new value', indicating which is which. However, schema description coverage is 0%, and the description adds no constraints, types, or examples beyond the basic mapping.
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 it calculates percentage change from original to new value. It distinguishes from sibling 'percentage_of', which calculates proportion, making the tool's specific purpose unambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
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 'percentage_of'. The description only states what it does, leaving the agent to infer usage context without help.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description carries full burden. It states exact calculation and decimal string output but does not disclose potential large number handling or constraints like r ≤ n.
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?
Single sentence, front-loaded with action verb, no wasted words. Highly concise and efficient.
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?
Sufficient for a simple math tool with two parameters and no output schema, but misses mention of constraints (e.g., r ≤ n) and edge cases.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema already describes both parameters (total, selected) with 100% coverage. Description adds no new parameter-level information, remaining at baseline.
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 'Calculates' and resource 'ordered selections nPr exactly; returns a decimal string'. Clearly differentiates from sibling 'combinations' by specifying 'ordered'.
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?
Implies usage through 'ordered selections' but no explicit when-to-use or when-not-to-use compared to sibling tools like 'combinations'. Lacks alternatives guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
There are no annotations provided. The description discloses that the tool handles no-solution and infinite-solution cases, which is useful behavioral context. However, it does not describe what the return value looks like (e.g., a struct, an array, error codes), leaving a gap in transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that conveys the core functionality and edge cases without unnecessary words. It is front-loaded with the primary purpose and efficiently communicates the tool's scope.
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?
For a simple mathematical tool, the description covers the essential functionality and special cases. However, since there is no output schema, the lack of information about the return format or structure is a notable gap. The description could be more complete by hinting at what the result looks like.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
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 individual parameter details. However, the parameter names (a1, b1, c1, etc.) combined with the explicit equation in the description make their roles clear. This compensates moderately, but explicit parameter documentation would strengthen understanding.
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 a 2x2 linear system of the form a1*x + b1*y = c1 and a2*x + b2*y = c2. It also mentions handling no-solution and infinite-solution cases, which distinguishes it from other math tools like solve_quadratic or linear_regression.
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 solving two linear equations but provides no explicit guidance on when to use this tool versus alternatives, nor does it mention when not to use it. Given the large set of sibling tools, more explicit usage context would be helpful.
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?
Description accurately captures the operation but provides no additional behavioral traits beyond the obvious; no annotations to contradict or enhance.
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?
Single sentence with no wasted words; efficiently communicates the essential information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple arithmetic tool with no output schema, the description is fully complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% and description adds no new meaning beyond what parameter descriptions already convey.
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?
Clearly states verb 'subtracts' and resources 'second number from the first number', distinguishing it from sibling arithmetic operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this vs alternatives like 'add' or 'multiply'; lacks context or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden. It discloses key behavioral traits: visibility and behind-camera flags. However, it does not mention error handling (e.g., division by zero) or performance implications, which would make it more transparent.
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 a single, front-loaded sentence of 19 words. Every word is necessary; it states the action, the inputs, and the outputs. No filler or redundancy.
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 the tool (3D projection, multiple parameters, enums) and lack of output schema, the description is insufficient. It does not explain the return value format, coordinate system conventions, or the effect of parameters like yDirection and clipDepthRange.
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 only 17%, but the description adds minimal parameter-specific meaning. It references the combined matrix but does not explain the other five parameters (e.g., yDirection, clipDepthRange), which are underdocumented in the schema as well.
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 projects a world-space 3D point to 2D pixels using a combined projection*view matrix, and mentions visibility and behind-camera flags. This is a specific verb+resource combination that distinguishes it from sibling tools like world_to_view or view_to_clip.
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 does not explicitly state when to use this tool versus alternatives. It implies usage for converting a world point to screen coordinates, but gives no guidance on prerequisites or when not to use it, especially given the presence of sibling tools for intermediate steps.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden. It explicitly gives the mathematical calculation, so an agent knows the exact transformation performed. No hidden behaviors are relevant for a deterministic mathematical tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description consists of a single, front-loaded sentence that states the exact formula. Every word is necessary and there is no wasted content.
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 simplicity of the tool (3 numeric parameters, no output schema), the description is largely sufficient. The formula implies the return value. However, it could explicitly state that the output is the posterior probability for completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100% (each parameter has a clear description like 'P(hypothesis)'). The description adds the formula but no extra semantic value beyond what the schema already provides, so baseline 3 is appropriate.
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 states the specific formula 'P(hypothesis|evidence) = P(evidence|hypothesis) * P(hypothesis) / P(evidence)', which clearly identifies the tool's purpose as calculating a conditional probability via Bayes' theorem. It differentiates from sibling tools like 'bayes_update_hypotheses' which likely handles multiple hypotheses.
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 'bayes_update_hypotheses'. The description only gives the formula without context for appropriate use cases or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description must cover behavioral traits. It mentions the output is a decimal string, but does not discuss edge cases (e.g., large results, validation of n >= r) or performance implications.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that efficiently conveys the tool's purpose, condition, and output format with no unnecessary words.
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, the description adequately explains what it does and its output. However, it could briefly mention constraints (e.g., integer inputs) or result size implications for completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with clear descriptions for both parameters. The description does not add new semantics beyond the mathematical context already implied, so baseline 3 is appropriate.
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 it calculates 'n choose r' exactly when order does not matter, and specifies the output is a decimal string. This distinguishes it from sibling tools like permutations and factorial.
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 phrase 'when order does not matter' implicitly guides usage against permutation tools, but it does not explicitly state when to use or avoid this tool, nor does it mention alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It correctly implies a pure mathematical conversion with no side effects. However, it does not explicitly mention edge cases or precision, but for a simple function, this is adequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, well-structured sentence with no unnecessary words. Every part is essential and efficiently conveys the tool's purpose.
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?
While the tool is simple and the description covers its core functionality, it omits mention of return value format or handling of edge cases. However, given the simplicity and lack of output schema, the description is nearly complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The single parameter 'number' is fully described in the schema with 100% coverage. The description adds no additional meaning beyond what the schema already provides, resulting in a baseline score.
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 clearly states the conversion from radians to degrees, using a specific verb and resource. It is distinct from its sibling tool degreesToRadians, which performs 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 is provided on when to use this tool versus alternatives, such as degreesToRadians for the inverse conversion. The agent receives no context for selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It only describes the basic transformation and does not address edge cases, constraints (e.g., matrix validity), or side effects, leaving potential behavioral gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that is direct and without superfluous information. Every word contributes to the purpose.
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 description adequately specifies the input and operation, but does not explicitly mention the output type or format (e.g., that output is also homogeneous 4D) or typical ranges. Given the lack of output schema, a bit more context could be helpful, but the description is nearly complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so the schema already documents both parameters well. The tool description adds no additional meaning beyond the schema, meeting the baseline expectation.
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 ('transforms') and the resources ('homogeneous view-space position' and 'projection matrix'), and specifies the output ('4D clip space'). This distinguishes it well from sibling tools like world_to_view or clip_to_ndc.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context for when to use the tool (converting view-space to clip-space), but does not explicitly state when not to use it or name alternatives. However, the context is sufficient for an agent to determine appropriate usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions 'safe integers' to clarify input constraints but does not disclose behavior for negative numbers, zero, or edge cases like GCD(0,0). The output format is also not described.
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 a single sentence with no wasted words, efficiently conveying the tool's purpose and input constraints.
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?
The description does not mention the return value or handle edge cases. Although the tool is simple, the lack of output schema and missing behavioral details (e.g., handling negative numbers) leave gaps for an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
With 0% schema description coverage, the description adds only the qualifier 'safe integers' beyond the schema's parameter names and ranges. Since the parameter names ('first', 'second') are self-explanatory, the added value is minimal but present.
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 finds the greatest common divisor (GCD) of two safe integers, using a specific verb and resource. It distinguishes from sibling tools like 'least_common_multiple' and other arithmetic functions.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for calculating GCD between two integers, and the term 'safe integers' provides context about valid input range. However, it does not explicitly mention when to use this tool over alternatives like LCM or prime factorization.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must disclose behavioral traits. It names the outputs (payment, total interest) but does not describe the return format, precision, or any potential side effects. For a simple calculator tool, this is minimally adequate 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.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that conveys the core purpose without unnecessary words. It is highly concise and front-loaded.
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?
With 4 required parameters and no output schema, the description should ideally clarify the output structure. It names the outputs but does not specify if they are returned as separate values, an object, or a tuple. The tool seems straightforward but could be more complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so the parameters are well-documented in the schema. The description adds no additional semantic meaning beyond what the schema provides. Baseline score of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states that the tool calculates payment and total interest for a standard fixed-rate amortizing loan. It uses a specific verb 'calculates' and identifies the resource. Among sibling tools which are generic math functions, this tool is distinct in purpose.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage context (standard fixed-rate amortizing loan), and the sibling tools are all general math operations, none of which handle loan calculations. The purpose alone is sufficient to guide an agent on when to use this tool, though no explicit when-not-to-use guidance is provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Without annotations, the description carries full burden. It discloses the conversion to a normalized quaternion and the order parameter's role. However, it doesn't specify input validation, edge cases, or the output's exact structure, which is acceptable for a pure math conversion.
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 sentence with 14 words, no wasted text, and front-loaded with the main action. Every word is necessary.
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?
The description lacks details about the output format (e.g., array or object structure) and does not provide examples or edge cases. Given the tool's moderate complexity and no output schema, this is a gap.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so baseline is 3. The description adds clarification that the order parameter specifies rotation order (first-to-last), which slightly enhances the schema's enum values but is not a major addition.
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 it converts Euler rotations in radians to a normalized quaternion, using a specific verb ('Converts') and resource. This distinguishes it from sibling tools like 'compose_transform_4x4' or 'radiansToDegrees'.
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?
No explicit when-to-use or alternatives are given beyond the generic purpose. The description implies usage for converting Euler angles to quaternions, but does not mention exclusions or scenarios where other tools might be preferred.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the burden. It mentions a numerically stable algorithm, which is a positive behavioral trait. However, it does not disclose any side effects, authorization needs, or edge-case behavior. The description is adequate for a simple calculation tool 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.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that is front-loaded with the verb 'Calculates', immediately conveying the action. Every part is purposeful with no wasted words.
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 it is a simple mathematical function with no output schema, the description is nearly complete. It specifies the two modes (population/sample) and mentions algorithmic stability. It could mention the return type (a number) but this is implicitly clear. Sibling tools are covered by distinct names.
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 50% (only 'sample' has a description). The tool description does not add any additional meaning about the 'numbers' parameter beyond what the schema implicitly states. It falls short of compensating for the missing schema description for half the parameters.
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 it calculates population or sample standard deviation with a numerically stable algorithm. The name 'standard_deviation' matches exactly, and it distinguishes from sibling tools like variance, mean, etc. No ambiguity.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description does not explicitly mention when to use this tool versus siblings, but the specific name and explanation of population/sample make the intended use very clear. A brief mention of alternatives would improve it, but it is not misleading.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It states the function is deterministic and safe, but does not mention edge cases (e.g., 0 and 1 not prime) or return type. Adequate but not detailed.
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 short, front-loaded sentence with no wasted words. Every part is essential.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the single parameter, no output schema, and simple pure function nature, the description is fully sufficient for an agent to understand and invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters2/5
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 'non-negative safe integer' and 'prime' context, but the schema already defines the parameter type and constraints. Minimal additional value.
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 'determines' and the resource 'whether a non-negative safe integer is prime'. It specifies the input type and the action, distinguishing it from sibling tools like 'prime_factors'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description provides clear context for when to use the tool (checking primality). It implicitly excludes negative numbers and non-integers via schema, but lacks explicit guidance on when not to use or alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description bears full responsibility. It accurately describes the operation without ambiguity. It does not cover edge cases, but the schema enforces a minimum of one number, mitigating risk.
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 a single concise sentence with no extraneous words. Every word adds value.
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?
For a simple mathematical tool with one parameter and no output schema, the description sufficiently covers the purpose. It could optionally mention return type, but not necessary given the context.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100% (the 'numbers' parameter is described in the schema). The description adds no additional meaning beyond restating the schema, so baseline score of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description explicitly states 'Calculates the arithmetic mean' with the specific verb 'calculates' and resource 'arithmetic mean of a list of numbers'. It clearly distinguishes from sibling tools like median or mode.
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 does not provide explicit guidance on when to use this tool versus alternatives. Usage is implied through the tool's name and description, but 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.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It discloses the homogeneous coordinate convention (w=1) and the return format (x,y,z,w), but omits edge cases (e.g., w=0 point) or potential issues like matrix singularity.
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?
Single sentence, no wasted words, and front-loaded with the core action. Every part of the description adds value.
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?
For a mathematical tool with two parameters and no output schema, the description sufficiently explains the transformation process and output format. It could mention that w may change after transformation, but overall it is complete enough for an agent to understand usage.
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 50% (only matrix has a description). The description adds significant value by explaining the homogeneous coordinate usage and the return values, going beyond the schema types. This compensates for the limited schema documentation.
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 clearly states the action (transforms), the resource (3D position), and specific details (row-major 4x4 matrix, homogeneous w=1, returns x,y,z,w). It distinguishes from sibling tools like multiply_matrices_4x4 or compose_transform_4x4 which operate on matrices or multiple points.
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?
No explicit guidance on when to use this tool versus alternatives. The description implies its use for transforming a single 3D point, but does not mention when not to use it or suggest alternatives like compose_transform_4x4 for building transformations.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations present; description only states the operation and unit (radians). No disclosure of edge cases or domain restrictions, which is acceptable for a simple math function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
A single, clear sentence with no wasted words, effectively communicating the tool's purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple one-parameter math function without output schema, the description and schema provide sufficient information for an agent to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so the description does not add additional meaning beyond the schema. Baseline score of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly specifies that the tool calculates the arctangent in radians, distinguishing it from sibling tools like arcsin and arccos.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The name and description clearly indicate this is for arctangent calculation, but no explicit guidance is given on when to use versus alternatives like atan2.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It states the conversion but does not mention edge cases, precision, or range of valid inputs. For a simple mathematical conversion, this is minimally adequate.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is one concise sentence with no unnecessary words. It is front-loaded and efficiently communicates the tool's purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, no nested objects), the description provides sufficient context. The conversion is straightforward and the return value (radians) is implied.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with a clear description for the 'number' parameter: 'The number in degrees to convert to radians'. The tool description does not add additional meaning beyond the schema, so baseline 3 applies.
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 'Converts a degree value to its equivalent in radians' clearly states the action (converts) and the resource (degree value to radians). It distinguishes from the sibling 'radiansToDegrees' which does the inverse.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit when/when-not guidelines are provided, but the context is clear: use this tool when you need to convert degrees to radians. The sibling 'radiansToDegrees' implies the alternative for the reverse operation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries full burden. It accurately describes the behavior (rounds down to nearest integer), though negative number handling is implied.
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 a single concise sentence that directly states the tool's purpose with no unnecessary words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple one-parameter math function, the description is complete. It explains the operation and no output schema is needed since the result is obvious.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with the single parameter 'number' already described as 'The number to round down'. The description adds no additional semantic value beyond the schema.
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 'Rounds a number down to the nearest integer', specifying the verb (rounds down) and resource (number). This distinguishes it from siblings like 'ceiling' and 'round'.
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?
No explicit guidance on when to use this tool vs alternatives, but the context of siblings like 'ceiling' and 'round' makes the usage clear by implication.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries full burden. It accurately describes the operation as multiplication of two numbers, which is straightforward. No hidden traits or side effects are omitted.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence, no excess verbiage. Every word is functional and necessary.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a trivial arithmetic operation with no output schema and simple numeric parameters, the description fully conveys the tool's effect. No additional detail is needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so the baseline is 3. The description adds no further meaning beyond what the schema already provides for firstNumber and secondNumber.
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 (multiplies) and resource (two numbers), making the tool's purpose unmistakable. It effectively distinguishes from sibling arithmetic operations like add or subtract.
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?
No explicit guidance on when to use this tool versus alternatives like multiply_matrices_4x4 or compound_interest. The context implies use for simple scalar multiplication, but exclusions are not stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description accurately reflects the tool's behavior for a standard mathematical function. Without annotations, it carries the full burden but is sufficient given the simplicity.
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 a single sentence with no unnecessary words, making it highly concise and front-loaded.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple math function with full schema coverage and no output schema needed, the description is complete enough. No additional information is required.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, and the description adds no additional meaning beyond what the schema already provides (parameter 'number' in radians). Baseline 3.
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 it calculates the sine of a number in radians, which is a specific verb+resource. It is easily distinguished from sibling tools like arcsin (inverse), cos, and tan.
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 specifies that the input must be in radians, implying usage context. However, it does not explicitly mention when to use this tool versus alternatives or provide any exclusion criteria.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries full burden. It discloses row-major storage, column vector convention, and T*R*S order. However, it omits coordinate system handedness and potential issues with unnormalized quaternions, leaving minor gaps.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
A single 17-word sentence that is front-loaded with key information. Every word is necessary and there is no 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 3 parameters, nested objects, no output schema, and complexity of 3D transforms, the description adequately covers inputs and combination logic. Missing details like output format (a 4x4 matrix) and coordinate system, but overall sufficient for selection.
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 covers 67% with descriptions for scale and rotation. The description adds meaning by explaining how parameters combine into a T*R*S transform, compensating for the missing position description in schema. It clarifies that rotation is a quaternion and scale defaults to 1,1,1.
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 builds a row-major 4x4 T*R*S transform from position, quaternion rotation, and scale. This specific verb and resource combination distinguishes it from sibling tools like multiply_matrices_4x4 and transform_point_3d.
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 composing a transform from components but does not explicitly state when to use this over alternatives or when not to use it. Sibling tools include matrix multiplication and other transforms, but no direct comparison 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.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It describes a pure computation with no side effects, but does not mention error behavior or safety (e.g., input validation). The omission is acceptable given the mathematical nature, but a higher score would require explicit statements like 'no 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.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence that contains all necessary information without any redundant words. It is front-loaded with the action and key details, earning its place.
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 (two parameters, no output schema), the description is nearly complete. It explains the operation and matrix convention. A minor gap: it does not explicitly state the return type (another row-major 4x4 matrix), but this can be inferred.
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 schema has 50% coverage (first parameter described, second via $ref). The description of 'first' adds meaning beyond the name: 'Row-major 4x4 matrix used with column vectors: output = matrix * vector'. This clarifies the convention, which is crucial for correct usage.
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 (multiplies), the resources (two row-major 4x4 matrices), and the order (first * second) with specific use case (column-vector transforms). It distinguishes from sibling tools like compose_transform_4x4 by noting the matrix convention.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description includes the context 'for column-vector transforms,' which helps the agent decide when to use this tool. However, it does not explicitly state when not to use it or mention alternatives, though siblings like 'compose_transform_4x4' suggest other options.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided; description accurately describes a pure mathematical computation with no side effects. Could mention return range but not necessary for standard function.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence with no unnecessary words, directly conveys the tool's purpose.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple one-parameter math function without output schema, the description fully explains what the tool does and what input is expected.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
100% schema description coverage; parameter 'number' is already explained in schema. Description adds no new meaning beyond stating radians, which is already in schema.
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 'Calculates the cosine of a number in radians' uses a specific verb and resource, clearly distinguishing it from sibling tools like sin, tan, etc.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage for computing cosine, but does not explicitly state when not to use or mention alternatives. However, given simplicity, it is clear enough.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden of behavioral disclosure. It reveals that the computation is exact (not an approximation), the valid input range (0-1000), and the return type (decimal string, implying support for large numbers). This adds valuable context beyond the input schema, which only specifies the parameter constraints. For a pure mathematical function, this level of detail is sufficient.
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 a single sentence that front-loads the core action and includes all essential details: operation, exactness, input range, and output format. Every word contributes meaning, with no redundancy or filler. It exemplifies conciseness while being fully informative.
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 low complexity and the absence of an output schema, the description covers the critical aspects: what the tool does, its input constraints, and its output format. It does not mention error handling or performance, but for a straightforward mathematical function, these omissions are acceptable. The description is complete enough for an AI agent to use the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The single parameter 'value' is described in the input schema as an integer with min 0 and max 1000. The description complements this by clarifying that 'value' is the integer for which factorial is computed, and it explicitly repeats the valid range ('integer from 0 through 1000'). Since schema description coverage is 0%, the description effectively compensates by providing the necessary meaning.
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 explicitly states the action ('Calculates n! exactly'), the resource ('factorial of an integer'), the valid input range ('0 through 1000'), and the output format ('returns a decimal string'). This uniquely identifies the tool's functionality and clearly distinguishes it from sibling tools, which cover other mathematical operations.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description clearly implies when to use the tool (for exact factorial calculations within the specified range). Although it does not explicitly state when not to use it or name alternatives, the context of sibling tools (e.g., combinations, permutations) makes the appropriate usage obvious. The lack of explicit exclusions is minor given the tool's straightforward purpose.
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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