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

Annotations already declare readOnly/idempotent/non-destructive, so the safety profile is covered. The description adds genuinely useful non-schema behavior: values beyond 15 digits are returned as a decimal string, and calls cost $0.001 USDC via x402 on Solana with an HTTPS alternative endpoint — payment/auth context an agent needs before invoking. No contradiction with the read-only annotation.

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 definition, then examples, domain bounds, output-format caveat, and pricing — each sentence carries information. Slightly dense with pricing/endpoint boilerplate at the tail, but no wasted text.

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 two-integer math tool with no output schema, the description covers definition, domain, example values, the decimal-string edge case, and cost. The only soft gap is that the boundary of the 15-digit rule and the return type below that threshold are 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 description coverage is 0%, so the description must carry parameter meaning. It restates the numeric domains (n 0–32, x −1000–1000), which the schema already encodes as minimum/maximum, but the worked examples do clarify what n and x mean in the formula. Interpretation of the output-type switch ('past 15 digits') is not tied explicitly to either parameter.

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 resource — the physicist Hermite polynomial H(n, x) — with a concrete mathematical definition and worked values, so an agent knows exactly what is computed. The 'physicist' qualifier implicitly separates it from the probabilists' variant (hermite_prob) and hermite_deriv, but those siblings are never named explicitly.

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 worked examples (H(0,x)=1, H(2,1)=2, H(3,1)=-4) make the semantics unambiguous, but there is no explicit statement of when to choose this over hermite_prob or hermite_deriv, and no exclusions. Usage is only implied by the definition.

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