probability.exponential_cdf

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

Annotations already cover the safety profile (readOnly, idempotent, closed-world), and the description adds real behavioral detail beyond them: scipy float64 computation and a return value rounded to 10 significant digits as a string. That precision/rounding behavior is exactly the kind of thing annotations can't express.

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 formula and followed by constraints and a common-error warning. No filler, though the return-format sentence arguably duplicates the output schema.

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?

The output schema covers return values, and the description still adds precision/rounding and the full input-domain constraints, so an agent can call it correctly. Only minor gap is the unstated string format for x.

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 burden and mostly does: it constrains x to ≥ 0, rate to a positive decimal string, and warns against supplying the mean. It falls just short of specifying that x is also a decimal string (only rate is called out as a string).

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 (compute) and resource (exponential distribution CDF) plus the exact formula P(X ≤ x) = 1 - e^(-λx). This unambiguously separates it from exponential_pdf and exponential_ppf siblings, which share the resource but differ in the operation.

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 gives input-domain constraints (x ≥ 0, rate > 0) and a useful warning not to pass the mean 1/λ as rate, but never names when to use this vs exponential_pdf/exponential_ppf. Usage is implied by the formula rather than stated with alternatives.

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