probability.beta_cdf

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

Annotations already declare readOnly/idempotent/closed-world, and the description adds genuinely new behavioral detail: scipy float64 computation, rounding to 10 significant digits, and string return type. It does not cover failure behavior for out-of-range inputs, keeping it from a 5.

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: definition first, then input/output contract, then a gotcha. No filler and front-loaded with the core purpose.

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 annotations covering the safety profile and an output schema present, the description covers everything else needed: domain of each input, numeric precision, return type, and the symmetry caveat. Nothing essential 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?

Schema description coverage is 0%, so the description must carry all parameter meaning, and it does: x constrained to [0,1], alpha and beta as positive decimal strings, plus the α/β swap warning. It adds no per-parameter detail beyond that (e.g., no precision limits), so not a 5.

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+resource ('베타분포의 누적확률') and even gives the exact definitional formula P(X ≤ x) = I_x(α, β), which unambiguously distinguishes it from beta_pdf and beta_ppf by mathematical form.

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?

Provides domain constraints (x in [0,1], α and β positive) and a note that swapping α/β changes the result, which implicitly tells the agent this is the CDF not the PDF/PPF, but it never explicitly says when to choose this over probability.beta_pdf or probability.beta_ppf.

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