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 of behavioral disclosure. It only states what the tool calculates without describing output format (e.g., radians vs. degrees), error handling (e.g., for invalid inputs), or mathematical properties (e.g., range of output values). For a mathematical function tool with zero annotation coverage, this leaves significant behavioral 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, with no wasted words. The first phrase directly states the tool's purpose, and the parenthetical adds minimal but relevant context. Every sentence (effectively one) earns its place.

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, lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not address key contextual aspects like output format (radians/degrees), mathematical constraints, or how it differs from sibling tools. The description alone is insufficient for reliable tool invocation.

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 a single parameter 'value' of type 'number'. The description adds no information about this parameter's meaning (e.g., that it represents the tangent value, expected range, or units). It does not compensate for the lack of schema documentation, leaving the parameter's semantics unclear beyond its basic type.

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 as 'Calculate arctangent (inverse tangent)' with a specific mathematical verb ('calculate') and resource ('arctangent'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools like 'atan2' or 'atan_degrees', which handle related but distinct calculations.

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 mentions 'Domain: trigonometry, Category: inverse_functions', but this is generic context rather than explicit usage instructions. There is no mention of when to prefer 'atan' over 'atan2' (for two-argument arctangent) or 'atan_degrees' (for degree output), which are directly relevant sibling tools.

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