Find an exact mathematical operation

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

Annotations already declare readOnlyHint=true, idempotentHint=true, and destructiveHint=false, but the description adds valuable behavioral context beyond these: 'Ranking is deterministic lexical retrieval,' 'Omit arguments to browse; follow next_cursor with the same filters to continue,' and 'capability_id: exact inspect (SUMMARY / CONTRACT / FULL views).' It also clarifies that matches are not recommendations and that checker tools are separate IDs, preventing false expectations. No contradiction with annotations.

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?

The description is well-structured with Forms, bullets, and examples, and the first sentence front-loads the core purpose. It is longer than minimal because the tool has multiple modes, but almost every sentence earns its place. Some redundancy with schema text (e.g., limit default, cursor reuse) prevents a top score for conciseness.

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?

Given the tool's complexity—8 optional parameters, two distinct modes, pagination, and an output schema—the description is complete enough for an agent to select and invoke it correctly. It covers discovery vs. exact inspection, filtering, browsing, continuation, and the relationship to separate checker tools. The presence of an output schema means return-value details are already handled elsewhere.

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?

The input schema already provides 100% coverage with descriptive text for every parameter, so the baseline is 3. The description adds meaningful extra context by linking query, domain, limit, and cursor behavior, giving concrete examples, and explaining the capability_id inspection modes. This is helpful but not essential given the schema is already thorough, so a 4 is appropriate rather than 5.

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 opens with a specific verb-resource pairing: 'Search or inspect installed math tools by desired outcome or exact ID.' It clearly distinguishes the two modes (query-based discovery vs. capability_id inspection) and, in context of the sibling math.run, separates searching/inspecting from executing. This is a precise, non-tautological purpose statement.

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 states when to use the tool: 'Use when a task may benefit from exact computation, search, structural analysis, or a separate checker tool—even if shell code could also calculate the answer.' It also gives behavioral exclusions, such as 'Ranking is deterministic lexical retrieval; matches are not recommendations' and 'Checker tools are separate IDs..., not a switch on producers,' which helps the agent avoid misuse. The two named examples further clarify realistic invocation patterns.

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