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

Annotations already declare readOnlyHint, idempotentHint, destructiveHint=false, and openWorldHint, so the safety profile is covered. The description adds useful behavioral context: pricing at $0.001 USDC per successful x402 call on Solana and an alternate HTTPS endpoint. It does not describe error behavior for invalid fractions, but there is no annotation contradiction.

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, then clarified with brief examples before constraints, pricing, and the alternate endpoint. Every sentence adds useful information and there is no filler.

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 read-only numeric tool with no output schema, the description is complete enough: it explains the computation, gives examples, states input validity, and discloses payment/access details. The return value is implied clearly as the first denominator.

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 defines the a/b fraction, repeats the 1..30 bounds with b >= 2, and adds the non-schema constraint that the fraction must be proper. It relies on the a/b notation for numerator/denominator roles, so it compensates well but not exhaustively.

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 the specific computation clearly: the first denominator in the greedy Egyptian expansion of a/b, with examples that make the output concrete. The word 'first' implicitly distinguishes it from siblings such as egyptian_last, egyptian_length, and egyptian_sum.

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?

It gives validity preconditions such as 'The fraction must be proper' and the a/b ranges, which helps avoid invalid calls. However, it never explicitly says when to use this tool versus sibling Egyptian-expansion alternatives.

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