probability.lognormal_pdf

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

Annotations already cover safety (readOnly, idempotent, closed-world), so the description earns credit for adding implementation and output traits: scipy float64 computation, rounding to 10 significant digits, and string return type. It also flags the domain constraint that x must be positive.

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 with the core action first, then parameter meaning, then output format. Every clause adds information; nothing is redundant with the schema or annotations.

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?

Covers parameters, domain constraints, computational method, and return representation, which is more than enough for a single-point density evaluation. Minor gap: no stated behavior for invalid input (x <= 0 or sigma <= 0), though the positivity requirement is declared.

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 carries the full burden and does: it defines x as positive, mu/sigma as the mean and SD of ln X (not of X), sigma positive with defaults 0 and 1. The explicit warning about mu/sigma not being X's moments is exactly the kind of meaning the flat schema cannot convey.

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 precise verb+resource: probability density of the lognormal distribution, with the domain constraint (x positive). An agent can immediately distinguish it from lognormal_cdf/lognormal_ppf siblings by the density-vs-distribution wording.

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 the statistical name (density evaluation at a point), but the description never states when to use this vs lognormal_cdf/lognormal_ppf nor any prerequisites. Adequate but leaves selection to inference from the tool name.

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