probability.chi_square_cdf

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

Annotations already declare readOnly, idempotent, closed-world behavior. The description adds genuinely new operational detail: inputs are decimal strings, computation is via scipy float64, output is a string rounded to 10 significant digits. That discloses output format and precision beyond the annotations.

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, each earning its place: the computation, the domain/format constraints, and the p-value relationship. The main purpose is front-loaded.

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?

An output schema exists, yet the description still conveys return type and precision, and it covers both parameters' domains. For a two-parameter probability function, 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 parameter meaning, and it does: it defines x as a non-negative decimal string and df as a positive decimal string. Only minor gaps (e.g., edge behavior at x=0, extremely large df) remain.

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 the specific computation: cumulative probability P(X ≤ x) of the chi-square distribution. This clearly distinguishes it from siblings like probability.chi_square_pdf and probability.chi_square_ppf without ambiguity.

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?

Adds useful context by noting that hypothesis-test p-values are the right-tail complement (1 minus this value), guiding the agent toward chi_square_ppf for that task. It does not explicitly name the alternative tool, so it stops short of full when/when-not routing.

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