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

Annotations already cover the safety profile (readOnly, non-destructive, closed-world), so the bar is lower. The description adds genuinely new behavioral context: the two-tier payment model (daily free allowance, then $0.31 USDC on Base via x402) and that no account or API key is required. That is exactly the kind of auth/cost context annotations cannot express, though it still omits anything about computation or failure behavior.

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 opening sentence is duplicated verbatim ("Real relationship, or two autocorrelated series drifting together." twice), wasting the most prominent position. The example request in the description also duplicates the input schema's example, and payment text is interleaved before any statement of what the tool does.

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?

With no output schema, the description carries the burden of explaining return values, and it says nothing about what comes back (correlation coefficient, p-value, spuriousness verdict). It also omits length/type constraints on the series, leaving the agent unable to predict or interpret results beyond billing details.

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 reported at 100%, so the baseline is 3. The description adds only an example invocation, and the schema 'descriptions' are themselves just repeated example arrays, so neither source explains what x and y represent, that they are equal-length numeric series, or any constraints. No meaning beyond the schema is added.

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?

The description frames the tool rhetorically ("Real relationship, or two autocorrelated series drifting together") rather than stating a concrete verb+resource such as "test whether the correlation between two series is spurious." The name 'correlation' plus the framing imply the purpose, but an agent gets no clean statement of what is computed or returned. It also does nothing to distinguish itself from statistical siblings like deflatedsharpe, multipletest, or clusteredt.

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, when-not-to-use, or alternative-tool guidance at all. The only operational text is pricing/allowance mechanics (free 250/day, then $0.31), which tells the agent about billing, not about when this tool is the right choice over its many statistical siblings.

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