solve_equation

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does (solving equations) but lacks details on traits like error handling (e.g., for invalid inputs or complex solutions), performance (e.g., speed or limitations), or output format. This leaves gaps for an AI agent to understand operational behavior.

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 extremely concise and front-loaded, consisting of a single, direct sentence: 'Solve quadratic equations (ax² + bx + c = 0)'. It wastes no words and immediately conveys the core functionality, making it efficient and easy to parse.

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?

Given the tool's moderate complexity (solving equations with 3 parameters) and no annotations or output schema, the description is minimally adequate. It covers the purpose but lacks behavioral details and output information. For a mathematical tool, it should ideally mention result types (e.g., real/complex roots) or error cases, but it meets a basic threshold.

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?

The input schema has 100% description coverage, with clear parameter meanings (coefficients a, b, c). The description adds no additional semantic information beyond what the schema provides, such as constraints (e.g., a ≠ 0) or examples. With high schema coverage, the baseline score of 3 is appropriate, as the description doesn't compensate but doesn't need to heavily.

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 clearly states the tool's purpose: 'Solve quadratic equations (ax² + bx + c = 0)'. It specifies the verb ('solve') and resource ('quadratic equations'), making the function unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'calculate' or 'trigonometry', which might also handle mathematical operations.

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 no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like 'calculate' or 'statistics', nor does it specify contexts or exclusions (e.g., for non-quadratic equations). Usage is implied by the equation form, but explicit alternatives or prerequisites are missing.

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