verify_hyperbolic_identity

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 identity and domain but does not explain how the verification works (e.g., numerical computation with tolerance), what the output looks like (e.g., boolean or detailed result), or any error handling. This leaves significant gaps in understanding the tool's behavior.

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 concise, consisting of a single sentence that states the identity and includes domain/category context. It is front-loaded with the core purpose. However, the parenthetical note could be integrated more smoothly, but overall, it avoids unnecessary verbosity.

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 verification tool with 2 parameters, no annotations, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral details, or output format, making it inadequate for an AI agent to fully understand how to invoke and interpret results from this tool.

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 2 parameters (x and tolerance) with 0% schema description coverage, meaning no parameter details are provided in the schema. The description does not add any information about these parameters, such as what 'x' represents (e.g., a real number) or how 'tolerance' affects the verification. This fails to compensate for the lack of schema 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: verifying the hyperbolic identity cosh²(x) - sinh²(x) = 1. It specifies the mathematical operation (verification) and the identity involved. However, it does not distinguish this tool from sibling tools like 'verify_identity' or 'comprehensive_identity_verification', which might handle similar mathematical verifications.

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 guidance by mentioning the domain (trigonometry) and category (hyperbolic), but it does not explicitly state when to use this tool versus alternatives like 'verify_identity' or other hyperbolic function tools. There is no information on prerequisites, limitations, or specific use cases beyond the identity verification.

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