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

Annotations already establish read-only, idempotent, non-destructive, and open-world behavior. The description adds useful behavioral context beyond annotations by disclosing the $0.001 USDC per-successful-call x402/Solana pricing model and the equivalent HTTPS endpoint.

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 purpose is front-loaded and the examples are useful rather than decorative. The pricing and HTTPS endpoint add relevant operational detail, though the description is slightly longer than strictly necessary for a one-parameter math tool.

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 simple one-parameter computation with no output schema, the description gives enough context to invoke the tool correctly: it explains the input domain, return concept, examples, cost, and alternate transport. It does not specify exact response field names, but the numerator/denominator framing and examples are sufficient for this tool.

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 for the single parameter is 0%, so the description carries the full burden. It fully compensates by defining the n range 0 to 20 and giving concrete mappings such as n=0 -> 2/1, n=1 -> 3/1, n=2 -> 8/3, and n=5 -> 87/32.

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 states a specific computation and resource: the nth convergent of e, returned as numerator and denominator, with concrete examples. It is clear what the tool does, but it does not distinguish itself from adjacent siblings such as e_cf_term, e_cf_sum, e_cf_prefix, or cf_convergent.

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 provides the valid n range and pricing, but gives no explicit guidance on when to use this tool versus alternatives like e_cf_term or cf_convergent. There are no when-to-use or when-not-to-use instructions.

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