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IBM

MCP Math Server

by IBM

geom_manhattan_distance

Calculate Manhattan distance between two 2D points for geometry problems using taxicab metric.

Instructions

Calculate Manhattan (taxicab) distance between two 2D points (Domain: geometry, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
p1Yes
p2Yes
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 states the tool calculates a distance, implying a read-only operation, but does not address potential behaviors like error handling (e.g., invalid point formats), computational limits, or output format. The description is too sparse to fully inform the agent about how the tool behaves beyond its basic function.

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. There is no wasted verbiage, and the domain/category tags are efficiently appended. However, the brevity comes at the cost of completeness, as it omits necessary details for full understanding.

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 (a mathematical calculation with 2 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not explain parameter formats, expected output, or any behavioral nuances. For a tool that requires precise input formatting to avoid errors, this leaves significant gaps in contextual understanding.

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 2 parameters (p1, p2) with 0% description coverage, meaning the schema provides no details on their format or meaning. The description only mentions 'two 2D points' without specifying how points should be represented (e.g., as strings like 'x,y'). It adds minimal semantic value, failing to compensate for the lack of schema documentation, which is critical for proper tool invocation.

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: 'Calculate Manhattan (taxicab) distance between two 2D points.' It specifies the verb ('calculate'), resource ('Manhattan distance'), and domain/context ('geometry'). However, it does not explicitly differentiate from sibling tools like 'geom_distance' or 'geom_distance_3d', which likely compute Euclidean distances, 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: it mentions the domain ('geometry') and category ('general'), but offers no explicit advice on when to use this tool versus alternatives (e.g., 'geom_distance' for Euclidean distance). There is no mention of prerequisites, constraints, or typical scenarios, leaving the agent with little contextual direction.

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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