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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, yet the description still adds real value: the constant-input case yields an empty list, the modulus reduces each coefficient, and a zero modulus is rejected. The pricing line ($0.001 USDC per successful call, x402/Solana) and the HTTPS fallback endpoint are exactly the kind of operational context an agent cannot get from the schema.

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 operation, then edge case, then modulus, then cost/transport. Four compact sentences with no filler, though the pricing and endpoint details sit in the same breath as the semantics and could be separated for scanning.

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 must explain the return value; it does so only by example (constant → empty list) and never states that the result is a coefficient list in a particular order. For a two-parameter numeric tool this is adequate but leaves a real gap in how to interpret the response.

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 identifies `a` as an integer polynomial and `mod` as an optional coefficient modulus that rejects zero, but it never states coefficient ordering (ascending vs descending) or the 12-item cap and per-coefficient bounds — the ordering omission is material for a polynomial tool.

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 opens with a specific verb+resource pair — "Differentiate an integer polynomial" — which is far clearer than the opaque name `poly_deriv`. It cleanly separates the tool from poly_add/poly_mul/poly_div, though it never mentions near-neighbours like derivative_fixed, arithmetic_derivative, or bezier_derivative, so a small ambiguity remains.

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?

Usage is implied by the operation itself, but there is no explicit statement of when to choose this over `derivative_fixed` or `arithmetic_derivative`, and no prerequisites. The edge-case note (constant input) is helpful but is about behavior, not tool selection.

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