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IBM

MCP Math Server

by IBM

compute_golden_ratio_fibonacci

Calculate the golden ratio (φ) by approximating the limit of consecutive Fibonacci numbers. Input the number of terms to compute the ratio F(n+1)/F(n).

Instructions

Compute golden ratio using Fibonacci sequence: φ = lim(n→∞) F(n+1)/F(n) (Domain: arithmetic, Category: mathematical_constants)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
termsYes
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 states the tool computes the golden ratio but does not explain how it handles the 'terms' parameter (e.g., whether it approximates the limit or computes up to a given term), potential precision issues, or error handling for invalid inputs. For a computational tool with zero annotation coverage, this is a significant gap, warranting a score of 2.

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, stating the purpose and formula in a single sentence. The additional domain and category tags are minimal and do not detract from clarity. However, the lack of parameter details or usage guidelines means it could be more informative without sacrificing brevity, so it scores a 4.

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 of a mathematical computation tool with no annotations, no output schema, and low parameter coverage, the description is incomplete. It fails to explain the computation method, parameter semantics, or expected output format, leaving critical gaps for the agent. This inadequacy results in a score of 2.

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 one parameter 'terms' with 0% description coverage, and the tool description does not mention it at all. This leaves the parameter's meaning, valid range, and impact on the computation undocumented. With low schema coverage and no compensation in the description, the score is 2, as the agent lacks essential information to use the tool correctly.

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 computes the golden ratio using the Fibonacci sequence, specifying the mathematical formula φ = lim(n→∞) F(n+1)/F(n). It distinguishes itself from sibling tools like 'golden_ratio' or 'golden_ratio_cf' by explicitly mentioning the Fibonacci method. However, it does not fully differentiate from 'compute_golden_ratio_continued_fraction' in terms of when to choose one over the other, keeping it at a 4.

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 like 'compute_golden_ratio_continued_fraction' or 'golden_ratio'. It lacks context on prerequisites, such as the range or constraints for the 'terms' parameter, and does not mention any performance considerations or limitations. This absence of usage instructions results in a score of 2.

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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