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

Annotations already declare this is a read-only, idempotent, non-destructive open-world call, so the safety profile is covered. The description adds genuinely new operational facts beyond the annotations: a per-call price ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint — both important for an agent deciding whether and how to invoke it.

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, then domain, then cost/endpoint — a sensible order with no filler sentences. The pricing and URL add length but each carries real information an agent needs.

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 single-parameter, read-only, no-output-schema tool, the description is complete: the operation is defined, the input domain is bounded, several input-to-output examples effectively convey the return value, and cost/transport are disclosed. Nothing needed to call it correctly is missing.

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 the weight. It defines what n means, states the meaningful range (0 to 1,000,000, matching the schema bounds), and maps several concrete n values to their results, which clarifies semantics well beyond a bare integer property.

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 'The arithmetic derivative of n' — a specific named operation on a specific input — and backs it up with worked examples (4→4, 6→5, 8→12, 12→16) that pin down which variant of the arithmetic derivative is meant. It does not explicitly distinguish itself from near siblings such as derivative_fixed or arithmetic_sum, but the operation itself is unambiguous.

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 description supplies the valid input domain (n from 0 to 1,000,000) which is usage-relevant, but gives no guidance on when to pick this over derivative_fixed or the other arithmetic_* siblings, and no statement of when not to use it. An agent must infer the usage context.

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