farey_mediant_path

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'Find path' and 'using mediant operations', but does not explain what the tool returns (e.g., a sequence of fractions, steps), any constraints (e.g., input validity, performance limits), or error conditions. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is brief and to the point, consisting of a single sentence followed by domain/category tags. It avoids unnecessary verbosity and is front-loaded with the core purpose. However, the lack of detail makes it somewhat under-specified rather than optimally concise.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of a tool with 5 parameters, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not compensate for the missing structured information by explaining parameters, return values, or behavioral details, making it inadequate for effective tool invocation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 5 parameters with 0% description coverage, and the tool description does not mention any parameters or their meanings. It fails to explain what 'start_p', 'start_q', 'end_p', 'end_q', and 'max_denom' represent (e.g., numerators and denominators of fractions, maximum denominator limit), leaving all parameters undocumented and unclear to the agent.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description states the tool 'Find path through Farey sequence using mediant operations' which provides a general purpose (verb+resource). However, it lacks specificity about what 'path' means or how the mediant operations are applied, making it somewhat vague. It distinguishes from siblings by mentioning Farey sequences, but does not clearly differentiate from other Farey-related tools like 'farey_sequence' or 'farey_neighbors' beyond the 'path' concept.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description includes domain and category tags ('Domain: arithmetic, Category: farey_sequences'), which imply a mathematical context, but it does not provide explicit guidance on when to use this tool versus alternatives. There is no mention of prerequisites, specific use cases, or comparisons to sibling tools like 'farey_sequence' or 'mediant', leaving the agent with no clear usage instructions.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.