stirling_second

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the calculation but does not describe any behavioral traits such as input constraints (e.g., n and k must be non-negative integers, k ≤ n), computational complexity, error handling, or output format. For a mathematical function with two parameters, this leaves significant gaps in understanding how the tool behaves.

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 extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category information is efficiently appended. Every word earns its place, making it easy to parse quickly.

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 (a combinatorial function with two parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is insufficient. It does not explain the mathematical definition, typical use cases, input constraints, or what the output represents (e.g., an integer count). For effective agent use, more context is needed.

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, so the description must compensate. It mentions 'S(n,k)' which implies n and k are parameters, but does not explain their meanings (e.g., n is the number of elements, k is the number of non-empty subsets). This adds minimal semantic value beyond the schema's parameter names, resulting in a baseline score for inadequate compensation.

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 tool's purpose: 'Calculate Stirling number of the second kind S(n,k).' It specifies the verb ('Calculate'), resource ('Stirling number of the second kind'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'stirling_first' or 'stirling_second_row', which are closely related combinatorial functions.

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 provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('combinatorial_numbers'), but does not specify typical use cases, prerequisites, or comparisons with sibling tools like 'stirling_first' (which calculates the first kind) or 'stirling_second_row' (which might compute a row of these numbers).

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