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

Annotations already declare readOnly/idempotent/openWorld, so the description correctly focuses on what they cannot say: the price ($0.001 USDC per successful call via x402 on Solana) and an alternate HTTPS endpoint. The 'per successful call' billing detail and the payment scheme are exactly the kind of operational context an agent needs before invoking. It stops short of describing the response payload, which would have made it complete.

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 essential definition and the three examples come first, and the cost/endpoint metadata trails at the end where it belongs. Each sentence carries information, though the HTTPS URL is somewhat bulky for a tool description.

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-integer predicate with no output schema, the description covers the math question, the domain, and the paid-access mechanics. The one real gap is the return shape — it says 'whether', but an agent cannot be certain if the result is a bare boolean, a string, or a JSON object with fields.

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 three integer parameters carry no descriptions at all — so the description must supply meaning, and it does: a and b are coin denominations, n is the target amount, plus the worked example fixes the argument ordering. The stated ranges duplicate the schema's min/max, so that portion adds nothing, keeping it below a 5.

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 decision problem — whether n is representable as a non-negative combination of denominations a and b — with concrete worked examples ('10 can be made with 2 and 5. 3 cannot. 0 can.'). This clearly separates it from coin_count/coin_min/coin_ways by the boolean framing, but it never names those siblings explicitly to make the distinction airtight.

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 examples imply when the tool applies (single-target feasibility, zero is trivially representable), which is useful. However there is no explicit 'use this instead of coin_ways/coin_min' guidance and no stated preconditions; the agent must infer the boundary from the sibling names alone.

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