atan

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 the tool calculates arctangent and returns radians, which covers the basic operation. However, it doesn't disclose important behavioral traits like input domain restrictions (e.g., valid ranges for 'value'), error handling for invalid inputs, precision, or output format. For a mathematical function with no annotation coverage, this leaves significant gaps.

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 and front-loaded: a single sentence in Chinese that directly states the tool's function and output unit. There's zero wasted text, and every word earns its place by conveying essential information efficiently.

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 mathematical nature, no annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't cover parameter details, output format beyond 'radians', error conditions, or mathematical context. While simple tools might need less, this leaves too many gaps for reliable agent use without additional context.

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 one parameter 'value' of type number. The description doesn't add any parameter semantics beyond implying it's the input for arctangent calculation. It doesn't explain what 'value' represents (e.g., tangent ratio, numeric input), valid ranges, or units. With low schema coverage, the description fails to compensate adequately.

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: '计算反正切值' (calculate arctangent value) with the specific detail that it returns radians. This distinguishes it from tools like 'atan2' (two-argument arctangent) and 'atanh' (inverse hyperbolic tangent) in the sibling list. However, it doesn't explicitly differentiate from 'atan2' beyond the parameter count, which is why it's not a perfect 5.

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 like 'atan2' or 'atanh'. It doesn't mention the single-argument limitation compared to 'atan2' or the mathematical context for choosing between trigonometric functions. There's only a basic functional statement without usage context.

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