subfactorial

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

No annotations are provided, so the description carries full burden. It states the calculation purpose but lacks behavioral details: no information on input constraints (e.g., n must be non-negative integer, typical range limits), computational characteristics (e.g., recursion, large-n handling), or output format (e.g., integer result, potential overflow). For a computational tool with zero annotation coverage, this is a significant gap.

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?

Extremely concise and front-loaded: the core purpose is stated in the first phrase, with domain/category tags efficiently appended. Every word earns its place—no redundancy, no unnecessary elaboration. The structure is optimal for quick comprehension.

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 low complexity (single integer parameter, no output schema, no annotations), the description is minimally adequate. It defines the mathematical operation but lacks behavioral context (constraints, performance) and output details. For a basic computational tool, it meets the bare minimum but leaves gaps an agent would need to infer or test.

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 has 0% description coverage, but the description compensates by defining the parameter's meaning: 'n items' in the context of derangements. This clarifies that 'n' represents the number of items for the subfactorial calculation, adding essential semantics beyond the schema's bare integer type. However, it doesn't specify constraints like non-negative values or typical bounds.

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 the specific mathematical operation: 'Calculate subfactorial !n (derangements of n items).' It includes both the mathematical notation (!n) and the combinatorial interpretation (derangements), which precisely distinguishes it from sibling tools like factorial, double_factorial, or other sequence tools. The domain/category tags further clarify its mathematical context.

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 is provided on when to use this tool versus alternatives. The description mentions the domain (arithmetic) and category (basic_sequences), but does not specify scenarios where subfactorial is appropriate compared to similar tools (e.g., factorial for permutations, derangement calculations in combinatorial problems). Usage must be inferred from the mathematical definition alone.

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