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

Annotations already declare readOnlyHint, idempotentHint, non-destructive and closed-world, so the safety profile is fully covered. The description adds almost nothing behavioral beyond that, and the fragment 'Returns: {factorial}' is an unclear placeholder that only mentions one of three outputs.

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 sentences, front-loaded with the operations, no padding. The trailing 'Returns: {factorial}' is slightly noisy/ambiguous but does not bloat the text.

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?

An output schema exists, so return values need not be described. The description covers all three computations and the schema enforces the n<=170 bound, leaving little an agent needs to call it correctly.

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 100%, so the schema already documents n and r. The description adds marginal meaning by tying r to P(n,r) and C(n,r), which is the baseline expectation when the schema does the heavy lifting.

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?

States a specific verb ('Calculate') and names three concrete operations (factorial, permutations P(n,r), combinations C(n,r)), which is far more precise than a generic math tool. It does not explicitly differentiate itself from math siblings like calculate_gcd_lcm or calculate_logarithm, so it stops 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 or when-not-to-use guidance. The 'See list_bundles for related math calculators' pointer is a discovery aid, not a routing rule that helps an agent choose this tool over the many sibling math calculators.

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