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IBM

MCP Math Server

by IBM

inverse_hyperbolic_functions

Calculate inverse hyperbolic functions (arcsinh, arccosh, arctanh) for a given number to solve trigonometric and mathematical problems.

Instructions

Calculate all inverse hyperbolic functions for a given x. (Domain: trigonometry, Category: inverse_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. It mentions the domain and category, but doesn't disclose behavioral traits such as what 'all inverse hyperbolic functions' entails (e.g., which functions are included), any constraints (e.g., valid input ranges for x), or the output format. 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.

Conciseness3/5

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

The description is concise with two sentences, but the second sentence ('Domain: trigonometry, Category: inverse_hyperbolic') adds little practical value and feels like metadata rather than helpful guidance. It's front-loaded with the core purpose, but could be more structured to include essential details.

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 tool with no annotations, no output schema, and 0% schema coverage), the description is incomplete. It doesn't explain what 'all inverse hyperbolic functions' means, the return format, or any mathematical constraints, making it inadequate for effective tool use.

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

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It only mentions 'a given x' without explaining what x represents (e.g., a real number, any numeric input) or any semantic details. This adds minimal value beyond the schema, failing to address the coverage gap adequately.

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 all inverse hyperbolic functions for a given x.' It specifies the verb ('calculate') and resource ('inverse hyperbolic functions'), and distinguishes it from siblings like 'asinh' (which calculates only one function). However, it doesn't explicitly differentiate from other inverse hyperbolic siblings (e.g., 'acosh', 'atanh'), which are listed separately, so it's not a perfect 5.

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 with 'Domain: trigonometry, Category: inverse_hyperbolic,' but this is vague and doesn't help the agent decide when to use this tool versus alternatives like 'asinh' or 'acosh'. No explicit when-to-use, when-not-to-use, or alternative tools are mentioned, leaving usage unclear.

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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