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

With no annotations, the description carries the full behavioral burden. It does add genuinely useful context by naming the implementation (Math.hypot, implying floating-point output) and by disclosing that calls require a signed wallet with 5 free trials — a real auth/payment constraint. However, it says nothing about the return value, error behavior, or that the string-typed parameters must parse as numbers.

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 puts the operation first, and the pricing clause is compact. The redundant 'Distance2d:' prefix restating the tool name is minor waste, but the whole definition is appropriately sized for a simple math tool.

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 trivial pure-math tool this is close to complete — the computation is fully specified. With no output schema, however, the description should say what comes back (a number, presumably in input units), and the odd optionality and string typing of the four coordinates are left unexplained.

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, and it partially does by pairing the parameters as (x1, y1) and (x2, y2), clarifying each string's coordinate role. It does not explain that the strings should contain numeric values, nor why all four are optional, leaving a real gap at 0% schema coverage.

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 Euclidean distance between two 2D points — and the explicit 'Euclidean' + '2d' qualifiers separate it from manhattan-distance, chebyshev-distance, and distance3d siblings. It does not name those siblings directly, so an agent still has to infer the distinction, but the purpose itself 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?

There is no when-to-use guidance: nothing says to prefer this over x402-manhattan-distance, x402-chebyshev-distance, x402-distance3d, or x402-geo-distance when a metric choice is available. The only added sentence is a pricing/trial note, 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.