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

With no annotations, the description carries the full burden. It does disclose the important behavioral constraint that a sign change is required and a quota note ('5 free trial calls per signed wallet'). But it omits what happens on failure (no sign change / non-convergence), the iterations default, and the response shape, which are the behaviors an agent would most want to know.

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 containing the core semantics, followed by a short quota note. Little waste, though the appended emoji pricing tag is slightly tangential to the mathematical purpose.

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 deterministic math tool with no annotations and no output schema, the description covers the core operation and its key precondition. It still leaves gaps on the iterations parameter, expression input format, and failure behavior, so it is adequate but not complete.

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 gives meaningful semantics for three parameters (fn is an expression, a and b are the interval endpoints) that the bare string-typed schema does not. The 'iterations' parameter is never mentioned and no input syntax for fn is provided, so it does not fully compensate for the coverage gap.

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: 'Finds a root of expression fn between a and b by bisection.' The method name and the sign-change precondition let an agent distinguish it from the sibling x402-newton-method without opening the schema. It stops short of explicitly naming the alternative, so it is clear but not sibling-differentiating at the highest level.

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?

The 'requiring a sign change' clause implies a precondition for use, which is useful. However it never states when to choose bisection over another root-finder (e.g. Newton's method) or what happens if the precondition is not met. Usage context is implied rather than explicit.

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