coth

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 discloses 'singularity handling' which is a key behavioral trait beyond basic calculation, indicating robustness for edge cases. However, it lacks details on error handling, precision, or output format, leaving gaps in behavioral understanding.

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 a single, efficient sentence that front-loads the core purpose ('Calculate hyperbolic cotangent') and adds value with the formula and singularity handling. The domain/category tags are concise and informative, with no wasted words.

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 low complexity (single input, no nested objects) and lack of annotations/output schema, the description is minimally adequate. It covers the core operation and a key behavioral trait (singularity handling), but does not address return values, error conditions, or mathematical constraints (e.g., domain restrictions beyond singularities), leaving room for improvement.

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 1 parameter with 0% description coverage, and the description does not explicitly mention parameters. However, for a single-parameter mathematical function where the parameter's role is implicit (input value 'x'), the description's focus on the operation and singularity handling provides adequate context. The baseline for 0 parameters would be 4, but here the single parameter's semantics are reasonably inferred.

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 explicitly states the verb ('Calculate'), the resource ('hyperbolic cotangent'), and provides the mathematical formula ('1/tanh'), which clearly distinguishes it from sibling tools like 'cot' (regular cotangent) or 'tanh' (hyperbolic tangent). The domain/category tags further contextualize it within trigonometry/hyperbolic 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 mentions 'singularity handling' which implies usage when input values might cause division by zero, but it does not specify when to use this tool versus alternatives like 'acoth' (inverse hyperbolic cotangent) or other hyperbolic functions. No explicit guidance on when-not-to-use or prerequisites is provided.

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