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IBM

MCP Math Server

by IBM

linear_interpolate

Calculate intermediate values between two known points using linear interpolation for numerical data estimation.

Instructions

Perform linear interpolation between two points (Domain: numerical, Category: interpolation)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xYes
x0Yes
y0Yes
x1Yes
y1Yes
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 states the operation but doesn't disclose behavioral traits: it doesn't explain the interpolation formula (y = y0 + (x - x0)*(y1 - y0)/(x1 - x0)), error handling (e.g., division by zero if x0 = x1), output format, or numerical precision. For a mathematical tool with 5 parameters, 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 a single, efficient sentence that directly states the tool's function. It's appropriately sized for a simple mathematical operation, with no wasted words. However, it could be more front-loaded by immediately specifying it's for 1D interpolation, but overall it's concise and well-structured.

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 tool's complexity (mathematical interpolation with 5 parameters), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the interpolation formula, parameter roles, constraints, or return value. For a tool in a server with many mathematical functions, more context is needed to use it correctly without trial and error.

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 adds minimal semantics: it implies parameters are numerical points for interpolation but doesn't explain what x, x0, y0, x1, y1 represent (e.g., x is the input value, (x0,y0) and (x1,y1) are the two points). It doesn't clarify constraints like x0 ≠ x1 or ordering. The description fails to compensate for the lack of schema coverage.

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 linear interpolation between two points'. It specifies the domain (numerical) and category (interpolation), making the verb+resource explicit. However, it doesn't distinguish from sibling tools like 'bilinear_interpolate' or 'linear_interpolate_sequence', which would require mentioning it's for 1D interpolation between exactly two points.

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 doesn't mention sibling tools like 'bilinear_interpolate' (for 2D) or 'linear_interpolate_sequence' (for multiple points), nor does it specify prerequisites or typical use cases. The agent must infer usage from the name and parameters alone.

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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