calculate_factorial_permutation

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

No annotations are provided, so the description must cover behavioral traits. It mentions the calculations but does not disclose output format for permutations/combinations, constraints like n>=r, or potential issues. The return is described as '{factorial}' which is incomplete and possibly misleading.

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?

Two sentences, no fluff. First sentence defines purpose directly, second provides a pointer to related tools. Efficient and well-structured.

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 (three distinct calculations) and the presence of an output schema, the description is somewhat sparse. It does not clarify the output for permutations/combinations or handle edge cases, but the output schema may compensate.

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% so parameters are well-defined in schema. The description adds that n is for all calculations and r is for P and C, but does not explain the required relationship (n >= r) or provide additional constraints beyond schema.

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 clearly states it calculates factorial, permutations, and combinations, specifying P(n,r) and C(n,r). However, it does not explicitly differentiate from other similar math calculators among the many siblings, though the mention of 'list_bundles' suggests grouping.

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?

No explicit guidance on when to use this tool versus alternatives. The only hint is to see list_bundles for related calculators, but no criteria for selection or exclusions.

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