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IBM

MCP Math Server

by IBM

exp_series

Compute exponential function e^x using Taylor series expansion with specified precision terms for mathematical calculations.

Instructions

Compute exponential function e^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 the full burden of behavioral disclosure. It mentions the method ('Taylor series') and domain ('numerical'), but fails to describe key behaviors such as convergence properties, error handling for large inputs, computational complexity, or output format. For a tool with two parameters and no annotations, this is a significant gap in transparency.

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 core purpose in a single sentence with additional context in parentheses. There is no wasted verbiage, and it efficiently communicates the essential information. However, it could be slightly improved by integrating the parameter semantics or usage guidelines more seamlessly.

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 Taylor series computation with two parameters, no annotations, and no output schema, the description is incomplete. It lacks details on parameter meanings, behavioral traits like accuracy or limitations, and expected output. For a mathematical tool with potential precision issues, more context is needed to ensure correct usage.

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 descriptions. The description does not add any semantic information about the parameters 'x' (the exponent) and 'n' (likely the number of terms in the Taylor series). It fails to explain what these parameters represent, their expected ranges, or how they affect the computation, leaving them undocumented.

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 exponential function e^x using Taylor series'. It specifies the verb ('compute'), resource ('exponential function e^x'), and method ('Taylor series'), making the action unambiguous. However, it does not explicitly differentiate from sibling tools like 'exp' or 'compute_e_series', which might offer alternative methods for computing exponential functions, so it falls short of a perfect score.

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 with 'Domain: numerical, Category: series', which implies it's for numerical inputs and series computations, but it lacks explicit instructions on when to use this tool versus alternatives. For example, it doesn't compare to 'exp' (which might be a direct exponential function) or 'compute_e_series' (which might compute e via series), leaving the agent without clear context for selection among siblings.

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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