probability.normal_cdf

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

Annotations already cover readOnly/idempotent/closed-world, and the description adds real value beyond them: computation is float64 via scipy, the result is rounded to 10 significant digits, and the return is a decimal string. It does not mention numerical edge cases (e.g. extreme sigma or x), which keeps 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, front-loaded with the definition, followed by parameter encoding/return format and a practical pitfall warning. Every sentence contributes, with only minor overlap between the sigma description and the variance warning.

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 and annotations covering the safety profile, the description covers what an agent needs: semantics, input encoding, defaults, and rounding behavior. Nothing critical is missing for a single-purpose statistical function.

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 load, and it does: x and mu are documented as decimal strings with mu defaulting to 0, sigma is constrained to positive standard deviation with default 1, plus an explicit warning not to pass variance. It adds meaningful semantics the bare schema lacks, though x's role as the evaluation point is only implied.

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 gives a precise verb and resource with the explicit mathematical definition P(X ≤ x), which unambiguously separates it from siblings like normal_pdf (density) and normal_ppf (inverse CDF). An agent can select it 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?

There is no explicit when-to-use/when-not guidance or routing to normal_pdf/normal_ppf alternatives; usage is only implied by the embedded formula. The one genuine guideline present is the sigma-vs-variance warning, which is a parameter caveat rather than tool-selection guidance.

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