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

Adds real behavior beyond the readOnly/idempotent annotations: match returns the reduced sum, mismatched sums and non-positive denominators are rejected, and calls cost $0.001 USDC per successful invocation via x402 on Solana, with an HTTPS endpoint alternate. The only gap is not stating the failure output shape (error vs. false).

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?

Four short sentences, front-loaded with the core check, followed by return/rejection semantics and then billing/endpoint metadata. Payment and URL details are last, which is the right ordering; nothing is redundant.

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?

No output schema, so the description does the work for the success path (reduced sum) and rejection path, plus the non-obvious paid-call requirement an agent must know before invoking. It falls short only on the exact error/response shape and the parameter-level constraints.

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 burden. It establishes that a/b is the target fraction and that 'dens' supplies unit-fraction denominators (1/d), but it never names the parameters or mentions the 30-item cap, the ±1,000,000 range, or what a zero denominator does beyond rejection.

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 verb ('check that... equals') and a specific resource (sum of unit fractions vs. fraction a/b), which is concrete and clearly distinct from calculation siblings. It does not name an alternative (e.g. egyptian_sum computes summed denominators, egypt_greedy expands), so sibling routing is left to inference.

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?

Usage is implied by the wording: use it to verify a candidate decomposition rather than to compute one. There is no explicit 'use this instead of X' guidance despite many adjacent egyptian_* siblings, and no stated preconditions beyond the rejection cases.

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