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IBM

MCP Math Server

by IBM

collatz_stopping_time

Calculate the number of steps required for a positive integer to reach 1 using the Collatz conjecture iterative sequence.

Instructions

Calculate the Collatz stopping time (number of steps to reach 1). (Domain: arithmetic, Category: iterative_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
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 states what the tool calculates but doesn't disclose behavioral traits like input constraints (e.g., n must be positive integer), computational complexity, error handling, or output format. For a mathematical 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 efficiently structured in a single sentence with domain/category context. However, the domain/category annotations could be considered redundant since they don't add operational value for tool selection.

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 no annotations, 0% schema coverage, no output schema, and a single parameter tool, the description is inadequate. It doesn't explain what the stopping time represents, input constraints, output format, or edge cases. For a mathematical calculation tool, more context is needed.

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%, and the description provides no parameter information beyond what's implied by the tool name. The single parameter 'n' is completely undocumented in both schema and description, leaving its meaning and constraints unclear.

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 specific verb ('Calculate') and resource ('Collatz stopping time'), with additional domain/category context. It distinguishes from sibling tools like 'collatz_sequence' (which generates the full sequence) and 'collatz_max_value' (which finds the maximum value).

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?

No guidance is provided on when to use this tool versus alternatives. While the purpose is clear, there's no mention of when this calculation is appropriate compared to other Collatz-related tools or mathematical sequence tools in the extensive sibling list.

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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