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

Annotations already cover the safety profile (read-only, idempotent, non-destructive, open-world), so the description does not need to repeat those. It adds useful operational context: the cost is $0.001 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint is provided. It does not describe error behavior or output details beyond the implied integer result.

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 description is compact and front-loads the core definition before examples, constraints, pricing, and endpoint. Every sentence adds useful information, though the HTTPS endpoint and pricing details could arguably be separated from the mathematical definition.

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 read-only math tool with no output schema, the description supplies the computation, examples, input ranges, cost, and endpoint. Combined with annotations covering safety, this is sufficient for an agent to call it correctly, though it could explicitly say the return value is a single integer.

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?

With 0% schema description coverage, the description must carry parameter meaning. It defines the equation a*x + b*y = n, clarifies that x and y are non-negative integers, provides an example mapping (a=2, b=5, n=10 yields 2), and gives the allowed ranges for a, b, and n.

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 gives a precise mathematical definition: counting non-negative integer solutions to a*x + b*y = n, with examples. It is clearly not a generic coin tool, but it does not explicitly distinguish itself from nearby siblings such as coin_count, coin_check, coin_min, or mcnugget_ways.

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 and equation imply when this tool is appropriate: computing the number of unordered two-denomination representations of n. However, the description gives no explicit when-to-use guidance, no exclusions, and no comparison to alternative sibling tools.

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