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IBM

MCP Math Server

by IBM

golden_section_search

Optimize univariate functions by finding minima or maxima within a specified interval using the golden section search algorithm.

Instructions

Perform golden section search for univariate function optimization (Domain: numerical, Category: optimization)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
fYes
aYes
bYes
toleranceNo
max_iterationsNo
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 states the tool performs optimization but doesn't disclose behavioral traits like convergence criteria (implied by 'tolerance' and 'max_iterations' in schema), output format, error handling, or performance characteristics. The description adds minimal context beyond the name, leaving key operational details unspecified.

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 a single, efficient sentence that front-loads the core purpose. It avoids redundancy and wastes no words, though it could be more informative. The structure is clear but minimalistic.

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 (numerical optimization with 5 parameters), lack of annotations, 0% schema coverage, and no output schema, the description is inadequate. It doesn't explain what the tool returns, how it behaves, or how to interpret results. For a tool with significant parameter and behavioral complexity, this leaves too many gaps for effective use.

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

Parameters1/5

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

The schema description coverage is 0%, meaning none of the 5 parameters (f, a, b, tolerance, max_iterations) are documented in the schema. The description adds no information about parameter meanings, expected formats (e.g., 'f' as a string representing a function), or usage constraints. This leaves parameters entirely unexplained, failing to compensate for the schema gap.

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: 'Perform golden section search for univariate function optimization.' It specifies the verb ('perform'), resource ('golden section search'), and domain/category ('univariate function optimization'). However, it doesn't explicitly differentiate from sibling tools like 'gradient_descent' or 'coordinate_descent' which are also optimization methods, though the 'univariate' qualifier provides some implicit distinction.

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 no guidance on when to use this tool versus alternatives. It mentions the domain ('numerical') and category ('optimization'), but doesn't specify scenarios where golden section search is preferred over other optimization methods (e.g., for unimodal functions, when derivatives are unavailable). There's no mention of prerequisites or limitations.

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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