farey_fraction_between

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the method ('using Farey sequence properties') but does not describe key behavioral traits such as error handling (e.g., what happens if inputs are invalid or if no fraction exists), performance characteristics, or output format. This leaves significant gaps in understanding how the tool behaves in practice.

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

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

The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no unnecessary information, and it efficiently communicates the core function without waste.

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

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

Given the complexity of a mathematical tool with 4 parameters, no annotations, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral details, or output expectations. While it states the purpose, it lacks the necessary context for an agent to use the tool effectively, especially in a server with many sibling tools where differentiation is needed.

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

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

The input schema has 4 parameters (p1, q1, p2, q2) with 0% description coverage, meaning the schema provides no semantic information. The description does not explain what these parameters represent (e.g., numerators and denominators of two fractions), their constraints (e.g., q1 and q2 must be non-zero), or their relationships. This lack of parameter semantics makes it difficult for an agent to invoke the tool correctly.

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

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

The description clearly states the tool's purpose: 'Find a fraction between two given fractions using Farey sequence properties.' It specifies the verb ('Find'), resource ('a fraction'), and method ('using Farey sequence properties'), making it understandable. However, it does not explicitly distinguish this tool from sibling tools like 'farey_mediant_path' or 'farey_neighbors', which are also related to Farey sequences, so it misses full sibling differentiation.

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

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

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), but does not specify scenarios, prerequisites, or exclusions. For example, it does not indicate if the input fractions must be in reduced form or if there are constraints on the range, leaving the agent with no usage context.

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