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

Annotations already establish that this is a safe, read-only, idempotent, non-destructive operation. The description adds useful behavioral context by disclosing the algorithm, cost per successful call, and an alternate HTTPS endpoint, though it does not discuss rate limits or error behavior.

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 front-loaded and efficient: the purpose and examples come first, followed by pricing and alternate endpoint details. The pricing and URL are extra but operationally relevant, so they do not materially harm conciseness.

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 two-parameter math tool with no output schema, the examples successfully demonstrate the expected return format, such as 22/7 and 311/99. It could be more complete by stating the accepted value format and exact response shape, but it is generally sufficient to invoke the tool correctly.

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 coverage is 0%, so the description must carry parameter meaning. It explains maxDen well with concrete examples, but value is only implicitly described as the number being approximated, leaving its accepted format ambiguous for an 80-character string input.

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 clearly identifies the operation as finding a best rational approximation with a bounded denominator, and it mentions convergents and intermediate fractions, which distinguishes the algorithm from generic convergent tools. It does not explicitly differentiate itself from siblings such as cf_convergent or cf_expand, so it stops short of a 5.

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 clarify how maxDen affects the result, giving implied guidance for common use. However, the description never states when to use this tool instead of alternatives like cf_convergent, cf_expand, or cf_value, nor does it give exclusions or prerequisites.

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