probability.f_pdf

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

Annotations already cover safety (readOnly, idempotent, closed-world), so the bar is lower. The description adds real context beyond them: scipy float64 computation, rounding to 10 significant digits, string return, and the dfn/dfd non-commutativity warning, all of which shape correct interpretation.

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?

Two dense sentences, front-loaded with purpose then parameters then the return/rounding detail. No filler, though the parameter listing could be scannable.

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, return values needn't be explained, yet the description still notes the rounded-string return. Combined with parameter meanings and the dfn/dfd caveat, an agent has what it needs to call it correctly.

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 coverage is 0% (bare titles), so the description must compensate, and it does: x must be ≥0, dfn/dfd are positive decimal strings meaning numerator/denominator df, and their order matters. It doesn't specify string format edge cases, 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 (compute probability density) and resource (F distribution), which cleanly distinguishes it from siblings like f_cdf and f_ppf. It doesn't explicitly name those alternatives, but the function is unambiguous.

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?

Usage is implied by 'probability density,' but the description never states when to use this density function versus the cumulative (f_cdf) or quantile (f_ppf) siblings. The swap-dfn/dfd note is a behavioral caveat, not routing guidance.

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