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

With no annotations, the description does useful work: it discloses the computation is pure CPU and instant, and that results are exact big-integer values accompanied by a digit count. However, it says nothing about error behavior for negative or out-of-range n, nor clarifies whether the digit count is part of the return payload or a separate field.

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 compact sentences with the core action front-loaded and no filler. The phrase "and its digit count" is slightly ambiguous in placement, which keeps it from a 5.

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?

For a one-parameter, no-annotations, no-output-schema tool, the description covers the key expectations: exactness, speed, and the extra digit-count output. A sentence on invalid input handling would make it fully complete.

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% and the single parameter n is documented with its 0-1000 range in the schema itself. The description adds no further meaning about n (e.g., how large inputs affect runtime or output size), so baseline 3 applies.

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 names a specific verb and resource ("Compute the factorial of a number") and adds the distinguishing trait of exact big-integer precision plus a digit count. It does not explicitly distinguish itself from near-neighbors like fibonacci, prime, or math_eval, so it falls short of a 5.

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 when-to-use guidance, no mention of when to prefer this over evaluate_math/math_eval for large factorials, and no discussion of the 0-1000 boundary or what happens outside it. Usage is only implied by the tool name.

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