pythagorean_identity

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

No annotations are provided, so the description carries the full burden. While it mentions 'verify and compute', it doesn't disclose what verification entails, what gets computed, whether there are precision limitations, or what the output format looks like. For a mathematical tool with no annotation coverage, this leaves significant behavioral questions unanswered.

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 appropriately concise with a single sentence that gets straight to the point. The domain/category information is efficiently appended in parentheses. There's no wasted verbiage, though the structure could be slightly improved by separating the core functionality from the metadata.

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 mathematical nature of the tool, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain what Pythagorean identities are being verified/computed, what the expected output looks like, or how the parameters influence the operation. For a tool with two parameters and mathematical complexity, 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?

With 0% schema description coverage and two parameters (angle, tolerance), the description provides no information about parameter meanings. It doesn't explain what 'angle' represents (radians/degrees), what 'tolerance' controls, or how these parameters affect the verification/computation. The description fails to compensate for the complete lack of schema documentation.

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 with a specific verb ('verify and compute') and resource ('Pythagorean trigonometric identities'), and provides domain/category context. However, it doesn't differentiate from sibling tools like 'verify_identity' or 'verify_hyperbolic_identity', which could cause confusion about when to choose this specific identity verification tool.

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. With many sibling tools for identity verification and trigonometric calculations, there's no indication of when this specific Pythagorean identity tool is appropriate versus general identity verification tools or other trigonometric functions.

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