atan2

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

No annotations are provided, so the description carries full burden. While it mentions 'full quadrant determination' (which hints at the tool's behavior with respect to quadrant signs), it doesn't disclose important behavioral traits like: what coordinate system is assumed, whether inputs can be zero/negative, what output range/units are used (radians vs degrees), or error handling. The description is insufficient for a mathematical function with potential edge cases.

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 - just one sentence plus a parenthetical. It's front-loaded with the core purpose. However, the parenthetical '(Domain: trigonometry, Category: inverse_functions)' adds minimal value and could be considered somewhat redundant given the tool name and obvious mathematical context.

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 that there are no annotations and no output schema, the description is incomplete. For a mathematical function tool, users need to know: output units (radians implied but not stated), behavior with special inputs (like x=0), and mathematical properties. The description mentions 'full quadrant determination' which is helpful, but doesn't provide enough context for reliable use, especially compared to the extensive sibling tool list that includes similar trigonometric functions.

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, providing only parameter names (y, x) and types. The description adds no parameter semantics whatsoever - it doesn't explain what y and x represent (typically Cartesian coordinates), their relationship, or any constraints. However, since this is a standard mathematical function with well-known parameters, the baseline of 3 is appropriate despite the lack of explicit parameter 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: 'Calculate two-argument arctangent for full quadrant determination.' It specifies the mathematical operation (arctangent) and its key feature (full quadrant determination). However, it doesn't explicitly differentiate from its sibling 'atan2_degrees', which appears to be a similar tool with degree output.

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 minimal usage guidance. The parenthetical '(Domain: trigonometry, Category: inverse_functions)' gives some context about the mathematical domain, but offers no explicit guidance on when to use this tool versus alternatives like 'atan' (single-argument arctangent) or 'atan2_degrees'. There's no mention of specific use cases or prerequisites.

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