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

No annotations are provided, so the description carries the full burden. It correctly conveys a read-only computation and adds a genuinely useful behavioral fact — the 5-free-call trial per signed wallet implies a paid, wallet-authenticated endpoint. However it omits output characteristics (a probability in [0,1]) and any rate/limit detail beyond the trial.

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?

A single front-loaded sentence states the operation, followed by a short commercial note. Nothing is padded, though the emoji and trial clause are tangential to tool selection.

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?

The tool is a simple single-parameter math function with no output schema, so the description need not explain return values. Still, with no annotations and an entirely undocumented parameter, an agent lacks the input-format detail needed to call it confidently; the payment constraint is the one piece of useful added context.

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% and the sole parameter 'x' is a bare string with no description. The description only says 'at x', adding no meaning about valid input format, numeric parsing, or domain. With one undocumented parameter, the description does not compensate for the schema gap.

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 and resource: 'Returns the standard normal cumulative distribution at x'. The word 'standard' implies the mean=0, sd=1 case, which distinguishes it conceptually from the sibling x402-normal-cdf, but the description never explicitly names or contrasts that sibling.

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 when-to-use guidance and no mention of alternatives, despite close siblings like x402-normal-cdf, x402-normal-pdf, and x402-normal-quantile. The only extra sentence is a pricing note, not usage context.

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