best_rational_approximation

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

No annotations are provided, so the description carries the full burden. It states what the tool does but lacks behavioral details: it doesn't explain the algorithm (e.g., based on continued fractions), performance characteristics, error handling, or output format. For a computational tool with no annotations, this leaves significant gaps in understanding its 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 extremely concise: one sentence stating the purpose, followed by domain/category in parentheses. Every word contributes directly to the tool's function, with no redundant information. It's front-loaded and efficiently structured.

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?

Given the tool's computational nature, 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain the approximation algorithm, output format (e.g., numerator/denominator pair), error bounds, or usage examples. For a tool that likely returns a rational number, more context is needed.

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 schema provides no parameter documentation. The description mentions 'x' and 'max_denom' but doesn't elaborate on their semantics: 'x' is described as the number to approximate, but 'max_denom' lacks clarification (e.g., must be positive integer). It adds minimal value beyond naming the parameters.

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 states the tool's purpose: 'Find best rational approximation to x with denominator ≤ max_denom.' It specifies the verb ('Find'), resource ('best rational approximation'), and constraints (denominator bound). However, it doesn't explicitly differentiate from sibling tools like 'best_approximation_farey' or 'cf_to_rational', which appear related.

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 minimal guidance: it mentions the domain ('arithmetic') and category ('continued_fractions'), which hints at context. However, it offers no explicit advice on when to use this tool versus alternatives (e.g., 'best_approximation_farey' or 'cf_to_rational' among siblings), nor does it specify prerequisites or exclusions.

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