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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), but the description adds meaningful context they cannot: a $0.001 USDC x402 payment per successful call and an equivalent HTTPS endpoint. It also clarifies that the reported period is the true repeating length even when fewer terms are requested, which is a real behavioral nuance. Missing only error/limit behavior.

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?

Front-loaded with the core definition, followed by illustrative examples and then the operational details (price, alternate endpoint). Each sentence carries information; only the perfect-square sentence is arguably redundant with the period discussion.

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?

With no output schema, the description should pin down the return shape, and it only gestures at it via notation like [1; 2, 2, 2, ...] and 'the period'. It never says whether the response is a single continued-fraction string, a term array, or an object containing both terms and period, which matters for consumption.

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 carry the parameter burden. It partially does: the sqrt(2)/sqrt(3) examples implicitly map the required integer s, the perfect-square case explains an edge condition of s, and 'even when fewer terms are requested' hints at count. It never names or bounds either parameter, leaving the 1-64 range and default of 8 undocumented.

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?

States a specific computation ('continued fraction of a square root') and reinforces it with concrete examples (sqrt(2) = [1; 2, 2, 2, ...]) plus the notion of period. It is genuinely clear what the tool returns, though it never distinguishes itself from the near-identical siblings sqrt_cf, sqrt_period, and sqrt_tail.

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?

There is no explicit when-to-use or when-not-to-use guidance, and the crowded sibling set (sqrt_cf, sqrt_period, sqrt_tail, cf_expand, cf_best, cf_convergent) makes routing ambiguous. The description leaves all selection logic to inference.

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