probability.gamma_pdf

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

Annotations already declare readOnly/idempotent, and the description adds meaningful context: scipy float64 computation with rounding to 10 significant figures and a string return type. That discloses the numerical behavior and output precision an agent needs.

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: purpose and formula first, then parameter constraints, then the rate/scale pitfall. No wasted text and front-loaded with the definition.

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?

Even though an output schema exists, the description explains the precision/rounding and return type, and fully documents all three otherwise-undocumented parameters. An agent has everything needed 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 coverage is 0%, so the description carries the full burden and does so well: x ≥ 0, shape positive, scale is a positive decimal string defaulting to 1, plus the crucial rate-vs-scale warning that the schema cannot convey.

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 (구한다), the exact resource (감마분포 확률밀도) and gives the formula f(x; k, θ). The '확률밀도' term clearly separates it from gamma_cdf and gamma_ppf siblings.

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?

Gives a critical exclusion — scale is the reciprocal of rate, so passing rate directly is wrong — which is exactly the kind of guidance that prevents misuse. It does not, however, explicitly name gamma_cdf/gamma_ppf as the alternatives when a cumulative or quantile value is wanted.

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