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

Annotations already cover read-only, idempotent, non-destructive behavior. The description adds useful operational context absent from annotations: x402 pricing per successful call and an HTTPS endpoint, plus the validity condition that later terms are at least 1.

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 purpose is front-loaded, followed by constraint, example, canonical note, and cost/endpoint details. It is mostly efficient, though the sentence “The canonical field is the short Euclidean form” is ambiguous and slightly reduces clarity.

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?

For a simple one-parameter read-only tool, the description covers purpose, parameter meaning, validity, and cost. However, with no output schema, it does not clearly specify the return representation beyond an example, leaving a meaningful gap.

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?

Schema description coverage is 0%, so the description must explain the sole parameter. It does so by defining terms as a continued fraction [a0; a1, a2, ...] and noting that later terms are at least 1, with examples; the schema handles bounds and array size.

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?

Names a specific mathematical operation—computing the exact value of a continued fraction—and illustrates it with equivalent representations such as 355/113. It is clear what the tool does, though it does not explicitly distinguish itself from sibling tools like cf_expand or cf_convergent.

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 gives mathematical constraints and pricing but no explicit guidance on when to use this tool versus alternatives. With many cf_* siblings, it should state whether this is the inverse of cf_expand or when to prefer cf_convergent/cf_best.

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