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

With no annotations, the description carries the full burden, and it does disclose the return value (Pearson r) and the equal-length numeric precondition, plus a payment note ('5 free trial calls per signed wallet'). It says nothing about output format, error handling for mismatched lengths, or NaN behavior, so the disclosure is only partial.

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 that names the tool and its purpose with no filler; the payment/trial tag is the only slightly extraneous element.

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 4-parameter tool with no annotations, no output schema, and zero schema coverage, the description is too thin: two of four parameters are undocumented and the input encoding is unstated. A caller cannot confidently construct a valid invocation from this text alone.

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% and the tool takes 4 parameters, so the description must compensate. It maps x and y to 'two equal-length numeric arrays' but leaves a and b completely unexplained, and it never says how the arrays are passed (comma-separated string, JSON, etc.) since the schema types them as strings.

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 Pearson correlation coefficient' — plus the operands (two equal-length numeric arrays x and y). It is clear what it computes, though it never contrasts itself with the sibling x402-correlation or x402-spearman-rank, so sibling differentiation is absent.

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?

The only usage signal is the implicit precondition that the inputs must be equal-length numeric arrays. There is no guidance on when to pick this over x402-correlation, x402-covariance, or x402-spearman-rank, and no when-not-to-use note.

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