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IBM

MCP Math Server

by IBM

digit_frequency

Count how many times each digit appears in a number to analyze digit distribution patterns. Supports different number bases for flexible mathematical analysis.

Instructions

Count frequency of each digit in a number. (Domain: arithmetic, Category: digital_operations)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
baseNo
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. It states what the tool does but does not disclose behavioral traits such as how it handles negative numbers, non-integer inputs, or large values, nor does it describe the output format (e.g., a dictionary of digit frequencies). For a tool with no annotations, this leaves significant gaps in understanding its behavior.

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 extremely concise and front-loaded: 'Count frequency of each digit in a number.' The domain and category tags are efficiently appended without redundancy. Every word serves a purpose, and there is no wasted text, making it highly efficient.

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 moderate complexity (2 parameters, no output schema, no annotations), the description is incomplete. It lacks details on parameter meanings, output format, edge cases (e.g., handling of zero or negative numbers), and behavioral context. While concise, it does not provide enough information for an agent to use the tool effectively without additional inference.

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?

The input schema has 0% description coverage, with parameters 'n' (integer) and 'base' (integer, default 10) undocumented. The description mentions 'digit' and 'number' but does not explain that 'n' is the input number or that 'base' allows counting digits in different numeral systems (e.g., binary or hexadecimal). It adds minimal semantic value beyond the schema, failing to compensate for the low 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: 'Count frequency of each digit in a number.' It specifies the verb ('count'), resource ('frequency of each digit'), and target ('a number'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'digit_count' or 'digit_sum', which could have overlapping domains, 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 guidance with the domain and category tags ('Domain: arithmetic, Category: digital_operations'), which imply a mathematical context. However, it lacks explicit instructions on when to use this tool versus alternatives (e.g., 'digit_count' for total digits or 'digit_sum' for sum of digits), and does not mention prerequisites or exclusions, offering only implied usage.

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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