probability.gamma_cdf

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

Annotations already declare readOnlyHint, idempotentHint and openWorldHint=false, so the safety profile is covered. The description adds real context beyond that: computation is done in scipy float64 and the result is returned as a string rounded to 10 significant digits, plus the scale-vs-rate inversion trap. It stops short of stating error behavior for out-of-range input.

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 dense sentences: definition first, then parameter constraints, then numerical precision and the rate/scale pitfall last. No filler, and the most decision-relevant pitfall is not buried.

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 pure statistical function with an existing output schema, the description covers the operation, all parameter domains, the numeric backend and precision, and the single most likely caller error. Nothing further is needed to invoke 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 0%, so the description must carry the full load, and it does: x is constrained to ≥ 0, shape(k) must be positive, scale(θ) defaults to 1 and must be a positive decimal string, and its meaning (reciprocal of rate) is spelled out. Every one of the three parameters gets semantics the schema alone does not provide.

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 and resource ('감마분포의 누적확률 P(X ≤ x)를 구한다'), naming the exact statistical quantity computed. That makes it trivially distinguishable from the sibling gamma_pdf (density) and gamma_ppf (inverse) without opening any 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?

The description gives domain constraints (x ≥ 0, shape positive, scale positive) and a genuinely useful usage warning that scale is the reciprocal of rate, so rate must not be passed directly. However, it never says when to choose this over gamma_pdf/gamma_ppf, so routing between the three gamma tools is left to inference from the name.

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