Describe a mathematical operation

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

Annotations already establish read-only, idempotent, non-destructive behavior. The description adds meaningful behavioral context beyond that: it clarifies the tool returns only schema and example arguments, does not execute operations, and that the returned examples are argument objects intended for later use with math.run. This complements the annotations without contradicting them.

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

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

Three sentences with no wasted words. The first sentence states the core purpose and its read-only nature, the second gives an exclusion condition, and the third explains how to consume the output. Each sentence earns its place and the most important information is front-loaded.

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

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

For a single-parameter tool with a rich enum, full schema coverage, output schema, and comprehensive annotations, this description is complete. It covers what the tool returns, how to select the parameter, when not to use it, and how to feed the result into math.run. Nothing essential is missing for an agent to call it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, and the schema already describes the 'operation' parameter with a full enum and a clear meaning. The description adds contextual usage guidance—that the operation should come from math.search and be unfamiliar—but does not significantly expand the parameter's semantic definition. A baseline of 3 is appropriate when the schema carries the weight.

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

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

The description states a specific verb and resource: 'Get schema and argument examples only for one unfamiliar operation selected by math.search.' It clearly distinguishes this from the sibling math.search and math.run, and even names specific operations it should not be used for, making the tool's scope immediately identifiable.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description explicitly says when to use the tool ('for one unfamiliar operation selected by math.search'), when not to use it ('Do not call this for known integer.machine_arithmetic or combinatorics.count shapes'), and how to use its output ('nest one under math.run.arguments and pass its id as math.run.operation'). This is direct, actionable guidance that leaves little to inference.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.