probability.f_cdf

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

Annotations already cover the safety profile (readOnlyHint, idempotentHint, openWorldHint=false). The description adds real behavioral context beyond that: the computation is done via scipy float64 and the result is rounded to 10 significant digits and returned as a string. It does not discuss error behavior for out-of-domain inputs.

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 with no filler: the purpose and formula come first, then the input/return contract, then the p-value relation. Slightly better placement of the parameter constraints alongside the purpose would make it ideal.

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?

With an output schema present, the description need not explain return structure, yet it still discloses the precision contract, which is useful. The main remaining gap is domain-error behavior for invalid x or non-positive degrees of freedom, which is only implicitly covered by the stated constraints.

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 parameter burden, and it does: x is constrained to ≥ 0, dfn is the numerator degrees of freedom, dfd the denominator, both positive decimal strings. Only the string formatting convention (e.g. plain decimal vs scientific notation) remains unstated.

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 verb and resource with the exact quantity computed: the cumulative probability P(X ≤ x) of the F distribution. This formula makes it distinguishable from siblings like probability.f_pdf and probability.f_ppf 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?

It notes that a test's p-value is the right tail, 1 minus this value, which hints at how the tool fits into hypothesis testing. However, it never names f_ppf or f_pdf as alternatives, and it gives no explicit when-to-use or when-not guidance.

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