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

Annotations already declare readOnly/idempotent/non-destructive, and the description still adds real behavioral facts: the 0 input is rejected, the supported range is capped at 10^12, and the call is billed $0.001 USDC per successful call via x402 with an equivalent HTTPS endpoint. Missing only error-shape or response-format detail.

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 mathematical definition and edge cases come first, followed by operational details (price, endpoint), so it is front-loaded. It is slightly dense in the tail with pricing and URL, but every sentence carries information.

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 one-parameter pure function with no output schema, the definition, edge cases, and range are sufficient to call it correctly, and the return value ('the number of divisors') is clear from the description. Only error behavior for out-of-range or paid-call failures is left implicit.

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 coverage is 0% and the single parameter is bare, but the description compensates by explaining that n must be positive (0 rejected) and that values above 10^12 are out of scope. That adds meaning beyond the schema's bare minimum/maximum bounds.

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 precisely what is computed — the count of positive divisors of n — with concrete examples ('a prime has 2, d(1) is 1') that pin down the semantics. An agent can immediately tell this apart from divisor_sum or divisor_record, which return sums or records rather than counts.

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 domain constraints (n runs up to 10^12, n = 0 is rejected) that implicitly bound when the tool applies, but it never names an alternative or says when to prefer this over divisor_sum or big_omega. Usage is inferable from the mathematical definition rather than stated.

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