farey_sequence_length

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

No annotations are provided, so the description carries the full burden. It states the tool calculates a length, implying a read-only operation, but does not disclose behavioral traits such as computational complexity, input constraints (e.g., n must be non-negative), error handling, or output format. This is inadequate for a tool with no annotation coverage.

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

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 purpose, followed by domain/category in parentheses. There is no wasted verbiage, and the structure is efficient, though it could benefit from more detail given the lack of other documentation.

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

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

Given the complexity of mathematical tools, no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what a Farey sequence is, how the length is computed, or what the output looks like (e.g., integer result). This leaves significant gaps for an AI agent to understand and use the tool effectively.

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

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

The input schema has 0% description coverage, with one parameter 'n' of type integer. The description does not add any semantic meaning beyond the schema—it does not explain what 'n' represents (e.g., order of the Farey sequence), valid ranges, or units. This fails to compensate for the low schema coverage.

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

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

The description clearly states the tool's purpose: 'Calculate the length of Farey sequence F_n.' It specifies the verb ('calculate') and resource ('length of Farey sequence'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'farey_sequence' or 'farey_sequence_properties', which could provide overlapping functionality.

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

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 and category but gives no explicit when/when-not instructions, prerequisites, or references to sibling tools like 'farey_sequence' (which might generate the sequence itself) or 'farey_sequence_properties' (which might offer other calculations).

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