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IBM

MCP Math Server

by IBM

hyperbolic_functions

Calculate hyperbolic sine, cosine, tangent, and other hyperbolic functions for any input value x to solve trigonometry problems involving hyperbolic functions.

Instructions

Calculate all hyperbolic functions for a given x simultaneously. (Domain: trigonometry, Category: hyperbolic)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xYes
Behavior2/5

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 that it calculates 'all hyperbolic functions simultaneously', which implies a batch operation, but it does not disclose details like what specific functions are included, the output format, error handling for invalid inputs, or computational constraints. 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.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise with two sentences that directly state the purpose and context. It is front-loaded with the main action and avoids unnecessary details, though it could be slightly more informative without losing efficiency.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of calculating multiple hyperbolic functions, no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on what functions are computed, the return structure, error conditions, or usage examples, making it inadequate for effective tool selection and invocation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

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 mentions 'a given x' but does not add meaning beyond the schema (e.g., valid ranges, units, or examples). Since schema coverage is low, the description should compensate more but only provides basic context, resulting in a baseline score due to the single parameter.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the verb ('calculate') and resource ('all hyperbolic functions for a given x simultaneously'), making the purpose specific and understandable. However, it does not explicitly distinguish this tool from sibling tools like 'sinh', 'cosh', 'tanh', etc., which calculate individual hyperbolic functions, so it doesn't fully differentiate from siblings.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

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 specify when to use this tool versus alternatives like individual hyperbolic function tools (e.g., 'sinh', 'cosh') or other mathematical tools. No explicit when/when-not or alternative recommendations are provided.

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

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