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IBM

MCP Math Server

by IBM

machine_epsilon

Determine machine epsilon to assess floating-point precision in numerical computations by finding the smallest value where 1 + ε > 1.

Instructions

Get machine epsilon for floating-point precision. Smallest value where 1 + ε > 1. (Domain: arithmetic, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

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 describes what the tool returns (machine epsilon) but does not cover important behavioral aspects such as the floating-point type (e.g., single or double precision), platform dependencies, error handling, or performance characteristics. The description is minimal and lacks depth for a tool that could have implementation-specific nuances.

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, with the core purpose stated first ('Get machine epsilon for floating-point precision'), followed by a clarifying definition and domain/category tags. Every sentence adds value, and there is no redundant or verbose language. However, the parentheses around the domain/category could be slightly more integrated for optimal structure.

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

Completeness3/5

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

Given the tool's simplicity (zero parameters, no annotations, no output schema), the description is adequate but minimal. It explains what the tool does but lacks details on behavioral traits (e.g., precision type) and usage context. For a tool that returns a fundamental numerical constant, more information on applicability and limitations would enhance completeness, though the current description meets the minimum viable threshold.

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

Parameters4/5

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

The tool has zero parameters, and the input schema has 100% description coverage (though empty). The description does not need to explain parameters, and it appropriately focuses on the tool's output. Since there are no parameters to document, the description's lack of parameter information is not a gap, warranting a score above the baseline.

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

Purpose5/5

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

The description explicitly states the tool's purpose with a specific verb ('Get') and resource ('machine epsilon for floating-point precision'), and provides a clear mathematical definition ('Smallest value where 1 + ε > 1'). It distinguishes itself from sibling tools by focusing on a specific numerical constant rather than general arithmetic operations or other mathematical functions.

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 includes domain and category tags ('Domain: arithmetic, Category: general'), which provide some contextual framing, but it does not offer explicit guidance on when to use this tool versus alternatives. There is no mention of specific use cases, prerequisites, or comparisons to sibling tools that might handle precision-related calculations differently.

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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