probability.lognormal_ppf

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

Annotations already establish readOnly/idempotent/closed-world, and the description goes beyond them by disclosing the computation backend (scipy float64) and the output form (a string rounded to 10 significant digits). It says nothing about error behavior when q falls outside (0,1), which leaves one useful behavioral detail unstated.

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 sentences, front-loaded with the definition and formula, then constraints, then the return format and a final caveat. No sentence is redundant.

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?

For a three-parameter pure-computation tool with a documented output schema, the description covers the definition, the domain constraints, the parameter meaning, and the return format. Only the out-of-range failure mode is unaddressed, which is minor.

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% — the schema offers only titles 'Q', 'Mu', 'Sigma' — so the description must carry all meaning, and it does: q ∈ (0,1), mu and sigma as the mean and standard deviation of ln X, sigma > 0, defaults 0 and 1. The explicit warning against passing X's statistics is a genuine semantic clarification the schema cannot provide.

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?

It states a specific operation (quantile of the lognormal distribution) along with the exact formula exp(μ + σΦ⁻¹(q)), which pins the semantics precisely. The formula also distinguishes it from siblings like normal_ppf and lognormal_cdf without needing to name them.

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 supplies concrete applicability constraints — q must be strictly between 0 and 1, sigma must be positive — and calls out the common misuse of putting X's own statistics into mu/sigma instead of those of ln X. It never explicitly routes the agent to a sibling (e.g., normal_ppf for a normal quantile), so a small gap remains.

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