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

No annotations exist, so the description carries the full behavioral burden, yet it discloses almost nothing: no output unit (radians vs degrees), no edge-case behavior for atan2(0,0) or negative real values, no auth or error semantics. The '5 free trial calls per signed wallet' note is the only behavioral detail and is generic monetization boilerplate.

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 delivers the computation and formula, followed only by the trial-call tagline. Efficient, though the marketing emoji note is not definitional content.

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?

A pure-math tool with no output schema, so the description should specify the return unit and boundary behavior; it does neither. With zero annotation and zero schema coverage, an agent cannot reliably predict what this returns for edge inputs.

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 must compensate. It does add real value by revealing that 'a' is an alias for 'real' and 'b' for 'imag', but it never clarifies whether all four are required, how the aliases interact, or which takes precedence — leaving half the ambiguity unresolved.

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 — 'Computes the argument angle of a complex number' — and even gives the underlying formula atan2(imag, real), which separates it from siblings like x402-complex-magnitude or x402-complex-conjugate. The 'real/a and imag/b' alias phrasing introduces mild ambiguity but the core purpose is unambiguous.

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?

No statement of when to use this versus the many sibling complex-number tools (magnitude, conjugate, add/sub/mul/div), and no prerequisites or input conventions. Usage must be inferred from the formula alone.

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