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 does disclose a genuine behavioral trait beyond the schema — the metered '5 free trial calls per signed wallet' payment/auth model — but says nothing about the approximation used, precision, units, or how invalid axis values are handled.

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 with the core operation first, followed by the pricing note. No filler or repetition; it could still be slightly tighter by separating the trial clause.

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 simple two-parameter math tool with no output schema and no annotations, the definition is adequate to invoke but incomplete: it never states what is returned (value, units, precision) or that the string-typed inputs must be numeric. A result-format hint would close the gap.

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 maps the two parameters to their meaning ('semi-major and semi-minor axes'), which is useful, but both are declared as strings with no required marking, and the description gives no units, numeric format, or validity constraints.

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 circumference of an ellipse from semi-major and semi-minor axes. The scope is unambiguous and distinct from the geometry siblings (e.g. x402-ellipse-area, x402-ellipsoid-volume), though the description doesn't explicitly name a sibling to differentiate against.

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 guidance on when to use this tool versus alternatives such as x402-ellipse-area or a general units/geometry tool, and no prerequisites described beyond the free-trial note. The agent must infer applicability purely from the resource name.

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