phi

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

No annotations are present, so the description must disclose behavioral traits. It only states the function's purpose without any details about side effects, input restrictions beyond 'positive integer', or return value format. The output schema exists but is not described.

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 a single sentence with no extraneous words. It is as concise as possible while still communicating the purpose.

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 mathematical function, the description covers the core purpose, but it lacks any behavioral or output context. Given the existence of an output schema, some hint about the return value would improve completeness.

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 100% coverage with a description for the single parameter 'n'. The description adds no additional meaning beyond 'positive integer', which is already in the schema. Baseline score of 3 is appropriate.

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 it computes Euler's totient function phi(n). The verb 'compute' and the specific mathematical function are unambiguous, and the tool is easily distinguished from siblings like moebius or gcd.

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?

No guidance is provided on when to use phi versus alternative functions like moebius or znorder. There is no mention of prerequisites, typical use cases, or exclusions.

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