root_bisection

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

With no annotations, the description carries the full burden. It discloses the method's requirement (opposite signs), iterative nature (max_iter, tolerance), and return contents ('Dict with the root, convergence flag, iteration table and errors'). It does not detail failure behavior or the meaning of the convergence flag, but the essential behavioral traits are present.

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 description is concise and well-structured: a one-sentence purpose, a requirement, a parameter list, and a return description. No unnecessary content or repetition.

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?

The description covers the main purpose, parameters, and return structure, which is adequate for a 6-parameter tool with no output schema. It does not elaborate on the format of the iteration table or possible error types, leaving some residual ambiguity about the return dict.

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 fully compensates. The Args section explains each of the six parameters with meaningful detail, including examples ('x**2 - 4'), interval endpoints, tolerance, iteration limit, and precision. This adds substantial meaning beyond the schema's bare titles.

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?

The description opens with 'Find a root of f(x) = 0 in [a, b] using the bisection method,' using a specific verb and resource, and clearly identifies the method. This distinguishes it from sibling root-finding tools like Newton, fixed point, and Aitken.

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 description provides a clear precondition: 'Requires f(a) and f(b) to have opposite signs (Bolzano's theorem)' and notes 'b must be > a.' It does not explicitly compare with alternative root-finding tools or state when bisection is preferred, so it falls short of a full 5.

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