probability.chi_square_pdf

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

Annotations already declare readOnly, idempotent, and closed-world, so safety is covered. The description adds real behavioral detail beyond them: scipy float64 computation, rounding to 10 significant digits, and string return type. It stops short of describing error behavior for out-of-domain inputs, which keeps it from a 5.

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?

Three tight sentences, front-loaded with the purpose, followed by constraints, then the disambiguation. No filler and nothing repeated from structured fields.

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 two-parameter scalar function with an output schema and read-only annotations, the description covers purpose, domain constraints, numeric precision, and the sibling alternative. Nothing needed to invoke it correctly is missing.

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 0 percent with only 'X' and 'Df' titles, so the description carries the burden and largely does: it states x must be ≥ 0 and df must be a positive decimal string, covering both parameters' domain and type. It could be slightly more explicit that x is the evaluation point, but the compensation is substantial.

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 gives a specific verb and resource ('카이제곱분포의 확률밀도를 구한다') and immediately distinguishes itself from the sibling chi_square_cdf by stating it returns a density, not a probability. An agent can route correctly without opening the schema.

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?

It explicitly names the alternative and the condition that selects it: '밀도값이지 확률이 아니므로 누적확률은 chi_square_cdf 를 쓴다.' Combined with the domain constraints (x ≥ 0, df > 0), the agent knows both when to call this tool and when not to.

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