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

With no annotations, the description carries the full burden. Disclosing the exact formula is genuinely useful behavioral information for a pure-math tool, and '5 free trial calls per signed wallet' hints at a quota/auth requirement. However it never states that the operation is side-effect-free, what happens when a equals b (division by zero), or how numeric strings 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?

The formula is front-loaded and the whole thing is one compact sentence. The promotional emoji/free-trial clause is filler relative to the tool's purpose, costing a point but not much length.

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 3-param math tool with no output schema and no annotations, the formula is the essential content and it is present. Missing is any statement of the return value/format and edge-case behavior, which leaves the agent slightly under-informed about calling it correctly.

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 0% and the three parameters have no descriptions, so the description must compensate. The formula does assign roles to all three names (value, a, b), which is more than the schema provides, but it never clarifies that a is the lower bound and b the upper bound, that inputs are numeric strings, or the a==b edge case.

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 (computes) plus the exact formula, so the agent knows this is the inverse of interpolation. It is distinguishable from x402-lerp by the formula, but the description never names the sibling it contrasts with, so an agent scanning the huge x402-* family must infer the distinction.

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 exclusions, and no mention of alternatives such as x402-lerp, x402-interpolate, or x402-map-to-range. The agent is left to guess when inverse lerp is the right choice.

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