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IBM

MCP Math Server

by IBM

sech

Calculate the hyperbolic secant function (1/cosh) for trigonometric and hyperbolic computations. Use this mathematical tool to process hyperbolic secant values in mathematical workflows.

Instructions

Calculate hyperbolic secant (1/cosh). (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 the calculation but doesn't describe error handling (e.g., for invalid inputs), performance characteristics, or output format. For a mathematical tool with zero annotation coverage, this is a significant gap in transparency about how the tool behaves beyond the basic operation.

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 and front-loaded: 'Calculate hyperbolic secant (1/cosh).' This efficiently states the core purpose. The additional context '(Domain: trigonometry, Category: hyperbolic)' is brief but relevant. There's no wasted text, making it easy to parse quickly.

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 (mathematical function), no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on return values, error conditions, and mathematical assumptions (e.g., input units). For a tool in a server with many siblings, more context is needed to ensure correct usage without trial and error.

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 one parameter 'x' with 0% description coverage, and the tool description doesn't add any parameter-specific information. It doesn't explain what 'x' represents (e.g., a real number, angle in radians/degrees) or constraints. With low schema coverage, the description fails to compensate, but since there's only one parameter, the baseline is adjusted to 3 as it's minimally adequate.

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 tool's purpose: 'Calculate hyperbolic secant (1/cosh).' It specifies the mathematical operation (calculate), the function (hyperbolic secant), and provides the formula (1/cosh). However, it doesn't differentiate from sibling tools like 'sech' vs 'asech' or other hyperbolic functions, which prevents a perfect score.

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 usage context with 'Domain: trigonometry, Category: hyperbolic,' which implies when to use it (trigonometry/hyperbolic contexts). However, it doesn't offer explicit guidance on when to choose this tool over alternatives like 'cosh' or 'asech,' nor does it mention prerequisites or exclusions. This lack of comparative guidance limits its helpfulness.

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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