probability.exponential_pdf

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

Annotations already declare readOnlyHint, idempotentHint, and closed-world scope, so safety is covered. The description adds genuinely useful behavior beyond that: computation via scipy float64 and a return value rounded to 10 significant digits, plus the warning that supplying the mean as rate yields a wrong result.

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 tightly packed sentences: formula first, then input constraints, then the misuse warning. No filler, and the most identifying information is front-loaded.

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 math function with an output schema and full annotation coverage, this is complete: domain constraints, input semantics, numeric precision, and the main pitfall are all addressed. Nothing an agent needs 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?

With 0% schema description coverage, the description must carry both parameters and mostly does: it defines x as a non-negative value and rate as a positive decimal string representing λ (explicitly not the mean). The one small gap is that it does not restate that x is itself a decimal string, though the schema type conveys that.

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 ('지수분포의 확률밀도', exponential PDF) and supplies the exact formula f(x; λ)=λe^(-λx), which unambiguously separates it from siblings like exponential_cdf and exponential_ppf. An agent can identify the correct tool 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 clearly states the domain constraint (x must be ≥ 0) and the critical input rule that rate must be λ, not the mean 1/λ, which prevents the most likely misuse. It does not explicitly route to exponential_cdf/exponential_ppf for cumulative or inverse cases, so sibling disambiguation is left partly implicit.

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