permutations

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

With no annotations, the description is the only source of behavioral expectations. It does convey 'exact' arbitrary-precision arithmetic, but it omits return type, error behavior, and how invalid inputs like r > n are handled.

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 a single clear sentence that states the operation, the math formula, and the precision guarantee without unnecessary detail.

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?

The description is self-contained enough for a straightforward computation, but without an output schema or edge-case guidance, an agent may not know how invalid inputs or very large results are returned.

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 nPr notation implies that n is the total number and r is the selection size, and the schema enforces non-negative integers entering the API. However, the description does not explicitly define parameter meaning or expected input relationship.

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 operation ('Compute nPr') and names the mathematical domain. The formula nPr clearly identifies the tool's purpose and helps distinguish it from combination or factorial tools.

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?

There is no guidance on when to use this tool versus related siblings like combinations, nor any mention of prerequisites or constraints such as n >= r.

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