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IBM

MCP Math Server

by IBM

ln_series

Compute natural logarithm ln(1+x) using Taylor series expansion for precise numerical calculations.

Instructions

Compute natural logarithm ln(1+x) using Taylor series (Domain: numerical, Category: series)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xYes
nYes
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries full burden. It mentions using Taylor series but doesn't disclose important behavioral aspects: convergence properties (e.g., works best for |x| < 1), accuracy dependence on parameter 'n', computational complexity, error handling for invalid inputs, or what happens when the series diverges. For a numerical approximation tool with no annotation coverage, this is a significant gap.

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 very concise - a single sentence with parenthetical domain/category information. It's front-loaded with the core purpose. However, the extreme brevity comes at the cost of completeness, making it more under-specified than optimally concise.

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 a mathematical approximation tool with 2 required parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain the mathematical context (Taylor series approximation), parameter roles, convergence conditions, accuracy trade-offs, or return format. The 'Domain: numerical, Category: series' hint is insufficient for proper tool selection and 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?

Schema description coverage is 0%, so the schema provides no parameter documentation. The description doesn't explain what 'x' and 'n' represent beyond implying they're numerical. It doesn't clarify that 'x' is the argument to ln(1+x) or that 'n' is the number of Taylor series terms. For a tool with two required parameters and zero schema coverage, the description adds minimal semantic value.

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: 'Compute natural logarithm ln(1+x) using Taylor series.' It specifies the mathematical function (natural logarithm with argument 1+x) and the computational method (Taylor series). However, it doesn't explicitly differentiate from sibling tools like 'ln' or 'ln_series' alternatives that might exist, though the method specification helps somewhat.

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 usage guidance. It mentions 'Domain: numerical, Category: series' which gives some context about input type and mathematical category, but offers no explicit guidance on when to use this tool versus alternatives like the standard 'ln' tool or other approximation methods. No prerequisites, limitations, or comparison to siblings are provided.

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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