double_factorial

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

No annotations are provided, so the description carries full burden. It mentions the mathematical operation but doesn't disclose important behavioral aspects: what happens with negative or non-integer inputs (though schema says integer), whether there are computational limits, error handling, or performance characteristics. The formula implies the operation but lacks implementation details an agent would need.

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 appropriately concise with two sentences: one defining the operation and one providing domain/category tags. It's front-loaded with the core purpose. The mathematical formula is efficiently expressed. However, the domain/category tags add little value and could be considered extraneous.

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 no annotations, 0% schema coverage, and no output schema, the description is incomplete. It explains what the tool does mathematically but doesn't cover parameter semantics, return values, error conditions, or practical usage context. For a mathematical function with potential edge cases (like negative inputs), this leaves significant gaps for an agent.

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 description coverage is 0%, so the description must compensate. It only mentions 'n' indirectly in the formula without explaining what values are valid (e.g., non-negative integers typically for double factorial). No information about parameter constraints, defaults, or examples is provided beyond what's inferable from the mathematical notation.

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 calculates the double factorial of a number and provides the mathematical formula (n!! = n × (n-2) × ...). It distinguishes itself from the sibling 'factorial' tool by specifying the double factorial operation. However, it doesn't explicitly contrast with other mathematical operations in the sibling list beyond the formula.

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. With many sibling tools for mathematical calculations (like factorial, power, etc.), there's no indication of appropriate contexts, edge cases, or comparisons to similar tools. The domain/category tags are generic and don't offer practical usage direction.

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