optimized_wilson_test

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions 'better performance' but fails to describe critical behaviors: what the tool returns (e.g., boolean result, detailed output), error handling for invalid inputs, computational complexity, or any side effects. The performance claim is vague and unsupported by concrete details.

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 no wasted words. It front-loads the core purpose ('Optimized Wilson's theorem test') and adds a brief technical detail ('pairing technique for better performance'). However, the parenthetical domain/category note feels redundant given the tool name and could be omitted for better focus.

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 complexity of a primality testing tool with no annotations, no output schema, and 0% parameter documentation, the description is severely incomplete. It doesn't explain what the tool returns, how to interpret results, error conditions, or performance characteristics. The domain/category hint doesn't compensate for these fundamental gaps in a tool that likely has non-trivial behavior.

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 0% description coverage, with a single parameter 'n' undocumented in both schema and description. The description adds no semantic information about 'n' (e.g., that it should be a positive integer, its typical range, or its role in Wilson's theorem). This leaves the parameter meaning entirely ambiguous, failing to compensate for the schema gap.

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 performs 'Optimized Wilson's theorem test' with a 'pairing technique for better performance', specifying both the mathematical operation (Wilson's theorem test) and the optimization method. It distinguishes itself from siblings like 'wilson_theorem_check', 'wilson_theorem_test', and 'wilson_theorem_verify' by emphasizing performance optimization, though it doesn't explicitly contrast their functional differences.

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 its sibling tools (wilson_theorem_check, wilson_theorem_test, wilson_theorem_verify). It mentions 'better performance' but doesn't specify scenarios where this optimization is beneficial or when alternative tools might be more appropriate, leaving usage context entirely implicit.

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