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IBM

MCP Math Server

by IBM

acsch

Calculate the inverse hyperbolic cosecant of a number with domain validation for trigonometric applications.

Instructions

Calculate inverse hyperbolic cosecant with domain validation. (Domain: trigonometry, Category: inverse_hyperbolic)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xYes
Behavior3/5

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 discloses 'domain validation' as a behavioral trait, which is useful beyond basic calculation. However, it lacks details on error handling, input constraints (e.g., valid ranges for 'x'), output format, or performance characteristics. This leaves gaps in understanding how the tool behaves in edge cases.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

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

The description is extremely concise and front-loaded: a single sentence that directly states the tool's function and key feature ('domain validation'). There is no wasted text, and it efficiently communicates the core purpose without unnecessary elaboration.

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 (a mathematical function with domain validation), no annotations, no output schema, and low parameter coverage, the description is incomplete. It hints at behavior but lacks details on inputs, outputs, errors, or usage context. For a tool that likely has specific mathematical constraints, more information is needed to ensure correct invocation.

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?

The input schema has 1 parameter with 0% description coverage, and the description does not add any semantic information about the parameter 'x'. It does not explain what 'x' represents (e.g., a real number, domain restrictions), its units, or how domain validation applies. This fails to compensate for the low schema coverage, leaving the parameter poorly documented.

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 inverse hyperbolic cosecant with domain validation.' It specifies the verb ('calculate'), resource ('inverse hyperbolic cosecant'), and an important behavioral aspect ('domain validation'). However, it does not explicitly differentiate from sibling tools like 'acsch' (which might be similar) or other inverse hyperbolic functions, though the domain/category hints at context.

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: it mentions domain validation and categorizes the tool under 'trigonometry' and 'inverse_hyperbolic', which implies usage in mathematical contexts. However, it does not specify when to use this tool versus alternatives (e.g., other inverse hyperbolic functions like 'asinh' or 'acosh'), nor does it provide explicit when-not-to-use instructions or prerequisites.

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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