probability.poisson_cdf

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

Beyond the read-only/idempotent annotations, the description adds meaningful behavioral detail: input domains, scipy float64 computation, and a return string rounded to 10 significant digits. It does not describe error behavior for invalid inputs, but the key safety and result-format traits are covered.

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?

The description is compact and front-loaded, with the operation first and then the input/output and tail-probability caveat. Every sentence adds useful information with no repetition.

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 simple two-parameter probability calculator, the description covers the purpose, parameter domains, result precision, and the main tail-computation gotcha. An output schema exists, so it does not need to enumerate return structure further.

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 parameter meaning. It does so for both parameters: k must be a nonnegative integer and lam must be a positive decimal string, which is essential because the schema alone only says integer and 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?

The description states a specific operation and resource: the Poisson cumulative probability P(X ≤ k; λ). It also clarifies the direction of the CDF ('cdf(k) is k or less'), which distinguishes it from the exact-probability pmf sibling.

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 clear usage context for cumulative probabilities, including the important tail rule that 'k or more' must be computed as 1 - cdf(k-1). It does not explicitly name poisson_pmf or other alternatives, so sibling selection is only inferable from the CDF wording.

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