atan2

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the output is in radians, which is useful context, but fails to describe other key behaviors: it does not specify the range of output (e.g., typically -π to π), handling of edge cases like (0,0), or error conditions. For a mathematical function with no annotation coverage, this leaves significant gaps in understanding its operation.

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, consisting of a single, clear sentence in Chinese. It efficiently conveys the core purpose without any wasted words, making it easy to parse and understand quickly.

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 mathematical function with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It covers the basic purpose and output unit but misses critical details: behavioral traits (e.g., output range, error handling), parameter semantics, and usage context. For a tool in a server with many siblings, this leaves the agent poorly equipped to use it correctly.

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 description adds minimal meaning beyond the input schema. It clarifies that parameters represent coordinates (x, y) for angle calculation, but with 0% schema description coverage and 2 parameters, it does not compensate fully. It lacks details on parameter roles (e.g., y is numerator, x is denominator in atan2(y,x)) or units. Since schema coverage is low, the description provides some value but is insufficient for complete parameter understanding.

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: '计算从x轴到点(x,y)的角度（返回弧度）' which translates to 'calculate the angle from the x-axis to the point (x, y) (returns radians).' It specifies the verb (calculate), resource (angle), and output unit (radians). However, it does not explicitly differentiate from sibling tools like 'atan' or 'complex_argument,' which might have overlapping trigonometric or angular functions.

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. It lacks context on scenarios where atan2 is preferred over other trigonometric functions (e.g., for handling quadrant-specific angles or avoiding division by zero). No exclusions or prerequisites are mentioned, leaving usage unclear relative to siblings.

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