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matheusbgodoi

SciMath MCP

propagate_uncertainty

Read-onlyIdempotent

Propagate independent standard uncertainties through an expression, returning nominal value, standard uncertainty, relative uncertainty, and coverage interval. Supports optional units and output unit conversion.

Instructions

Propagate independent standard uncertainties through an expression. Each measurement has value, uncertainty, and optional unit. Returns nominal value, standard uncertainty, relative uncertainty, and a coverage interval; use output_unit when the result is dimensionful.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
precisionNo
angle_unitNoradians
expressionYes
output_unitNo
measurementsYes
coverage_factorNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
unitNoOutput unit, when dimensionful.
exactNoExact symbolic result when available.
resultYesPrimary result; strings preserve mathematical precision.
detailsNo
warningsNo
operationYesOperation actually performed.
approximateNoNumerical approximation at the requested precision.
normalized_inputNoCanonical input used by the computation engine.
Behavior3/5

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

The annotations already declare the tool read-only, idempotent, and non-destructive. The description adds the behavioral assumption of independent uncertainties and the note that output_unit is needed for dimensionful results. It does not contradict any annotations, but it also doesn't disclose potential limitations or edge cases.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is two sentences and front-loads the core function. It avoids redundancy and every clause contributes to understanding.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Despite the presence of an output schema, the description is not fully complete. It lacks details on how to structure the expression, how measurements map to variable names, and the role of coverage_factor and precision. These are essential for an agent to invoke the tool correctly.

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?

With 0% schema description coverage, the description must compensate. It explains that each measurement consists of value, uncertainty, and optional unit, and it gives guidance on output_unit. However, it leaves parameters like expression, precision, angle_unit, and coverage_factor without semantic explanation.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's function: propagating independent standard uncertainties through an expression. It specifies the key resource (uncertainty propagation) and distinguishes it from sibling tools like calculate or statistics.

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 does not provide any guidance on when to use this tool versus alternatives. It neither names sibling tools nor explains the circumstances that call for uncertainty propagation over other calculations. The only instruction ('use output_unit when the result is dimensionful') is parameter-specific, not about tool selection.

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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