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

Annotations already cover safety (readOnly/idempotent/non-destructive), and the description adds genuinely useful context beyond them: a worked example, the valid domain, a per-call price of $0.001 USDC via x402 on Solana, and a mirror HTTPS endpoint. It still doesn't say what happens on out-of-range input or payment failure.

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 formula, then example, then domain, then commercial details — a sensible order with no filler. The bounds sentence largely restates the schema's minimum/maximum, a small redundancy, but it also states the domain in prose for a 0%-coverage schema.

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 say what is returned; the example implies a numeric value but never states the return type or precision. Payment and endpoint info is thorough, but error/out-of-range behavior is unaddressed for a tool with hard bounds.

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% — the properties carry bounds but no meaning. The description compensates by defining n as the polynomial degree and x as the evaluation point through the formula and the n=3, x=1 → 12 example, which lets an agent sanity-check inputs. It omits stating the parameter types explicitly, but the math semantics are clear.

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 verb+resource ('derivative of the physicist Hermite polynomial') and backs it with the closed-form identity H'(n,x)=2*n*H(n-1,x). The word 'physicist' implicitly separates it from the sibling hermite_prob (probabilist), but no sibling is named outright.

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 statement of when to call this versus the closely related siblings hermite, hermite_prob, poly_deriv, or derivative_fixed. The identity hints that the value could be derived from hermite, but the agent is left to infer whether this tool is preferable to composing those calls.

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