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

With no annotations, the description carries the full burden, but it does disclose the return values (r and r²), the equal-length input constraint, and a payment/auth signal ('5 free trial calls per signed wallet'). It does not state error behavior on unequal or non-numeric inputs, nor that the operation is a pure read with no side effects.

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?

The computational purpose is front-loaded in a single efficient sentence with no padding. The trailing emoji pricing clause is mildly promotional noise, but it does convey billing context rather than being pure filler.

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 compute tool with no annotations, no output schema, and 0% parameter documentation, the description leaves key gaps: the a/b vs x/y mapping, input format (comma-separated strings? JSON?), and behavior on invalid input are all unspecified.

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 there are four undeclared string params (a, b, x, y). The description says 'two equal-length numeric arrays,' which does not explain why four parameters exist or which names map to which input, leaving the caller to guess whether a/b and x/y are pairs or aliases.

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?

Names a specific verb and resource — 'Computes the Pearson correlation of two equal-length numeric arrays' — and even states the outputs (r and r squared). However, it offers no differentiation from close siblings like x402-correlation-coefficient, x402-autocorrelation, or x402-spearman-rank, which an agent could easily confuse with this one.

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, no exclusion criteria, and no mention of sibling alternatives such as x402-correlation-coefficient or x402-spearman-rank for non-linear rank correlation. The only extra sentence is a promotional note about free trial calls, which is not usage guidance.

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