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

Annotations already declare read-only, idempotent, non-destructive behavior, so the description does not need to restate those traits. It adds useful behavioral context beyond annotations by disclosing the $0.001 USDC price per successful call, the x402/Solana payment mechanism, the equivalent HTTPS endpoint, and the a+b <= 64 constraint. It could still say more about the return value, but the added payment and endpoint details are meaningful.

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 short and mostly front-loads the mathematical identity and the key a+b constraint. The sentence 'twice is the left side and sum is the right side' is awkward and less clear than the formula itself, but the overall length is appropriate for a paid math endpoint.

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 three-parameter paid mathematical tool with no output schema, the description gives the identity, the sum constraint, pricing, and an alternate HTTPS endpoint. The major missing piece is a clear statement of what the tool actually returns; the identity is suggestive but ambiguous about whether the output is the product, the sum, or both sides.

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 compensate. It does add meaning for a and b by placing them in the Chebyshev identity and by adding the a+b <= 64 constraint, which is not in the schema. However, it does not clearly define what a, b, and x represent (degrees versus evaluation point) or what value is returned, leaving much of the parameter semantics to inference.

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 gives the Chebyshev product identity and the constraint that a+b must be at most 64, which implies the tool computes something related to 2*T(a,x)*T(b,x). However, it never states the operation explicitly (e.g. 'computes the Chebyshev product') or what is returned, and it does not differentiate this tool from sibling Chebyshev tools such as chebyshev_t, chebyshev_u, chebyshev_rec, or chebyshev_disc.

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 guidance on when to use this tool versus the many sibling Chebyshev or general math tools. The a+b <= 64 statement is a parameter constraint rather than usage guidance, and there are no exclusions or recommended alternatives.

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