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

The annotations already declare readOnly, idempotent, non-destructive, and openWorld behavior. The description adds meaningful context beyond that: the paid-call price, x402/Solana payment method, alternate HTTPS endpoint, and explicit denominator rejection rule.

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 definition is front-loaded, followed by input constraints, then pricing and transport details. Every sentence adds useful information and there is no boilerplate or repetition.

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 integer calculator with no output schema, the description provides the formula, reduction rule, input restrictions, pricing, and alternate endpoint. It could explicitly state the return type, but the formula makes the expected integer result sufficiently clear.

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 explain the four parameters. It does so indirectly through the fraction notation a/b and c/d, the formula (a+c)/(b+d), and the note that numerators may be zero while denominators may not. It does not clarify the +/-1,000,000 bounds or separately define each parameter.

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 names a specific mathematical operation and gives the exact formula: the mediant of a/b and c/d is (a+c)/(b+d) reduced by their gcd. This is unambiguous and distinguishes it from the many neighboring number-theory tools in the sibling list.

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 explains input constraints such as zero numerators being allowed and non-positive denominators being rejected, but it gives no guidance on when to choose this tool over alternative computations. There is no comparison to siblings such as farey_adjacent or farey_child.

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