best_approximation_farey

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe how it behaves—e.g., what 'best' means (e.g., closest approximation within denominator limit), whether it returns a single fraction or sequence, error handling, or computational characteristics. This leaves significant gaps for a tool with no annotation coverage.

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 very concise—a single sentence with domain/category tags—and front-loaded with the core purpose. There's no wasted text, but it might be overly terse given the complexity of the tool. It earns points for efficiency but loses some for potential under-specification.

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 complexity (mathematical approximation with Farey sequences), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the tool returns, how approximations are selected, or any behavioral nuances, making it inadequate for effective use by an AI agent.

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?

The input schema has 2 parameters with 0% description coverage, and the tool description adds no information about what 'target' and 'max_denom' mean. Without any parameter semantics in the description, it fails to compensate for the lack of schema descriptions, leaving parameters undocumented and unclear in purpose.

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 states the tool 'Find best rational approximation using Farey sequences' which provides a clear verb ('Find best rational approximation') and method ('using Farey sequences'), distinguishing it from general approximation tools. However, it doesn't specifically differentiate from sibling tools like 'best_rational_approximation' (which appears to be a similar tool) or other approximation methods in the list, making the purpose somewhat vague in context.

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 no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('farey_sequences'), but this doesn't help an AI agent decide between this tool and other approximation or Farey-related tools in the sibling list. There are no explicit when/when-not instructions or named alternatives.

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