verify_sum_difference_formulas

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

No annotations are provided, so the description carries full burden. It mentions 'verification by comparison' but doesn't disclose what the tool actually returns (e.g., boolean result, numeric difference, error message), what happens with invalid inputs, or any computational constraints. For a verification tool with 4 parameters and no annotation coverage, this leaves significant behavioral gaps.

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 (one sentence plus domain/category) with zero wasted words. It's front-loaded with the core purpose and efficiently includes relevant context. Every element earns its place, making it easy to parse quickly.

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 complexity (4 parameters, verification logic), lack of annotations, and no output schema, the description is insufficient. It doesn't explain what constitutes successful verification, what format the result takes, or how the tolerance parameter affects the comparison. For a mathematical verification tool, users need to understand the verification criteria and output format.

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%, meaning none of the 4 parameters (a, b, operation, tolerance) are documented in the schema. The description adds no information about what these parameters represent (e.g., that a and b are angles, operation selects addition/subtraction formulas, tolerance is numerical precision). This fails to compensate for the complete lack of schema documentation.

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: 'Verify sum and difference formulas by comparison with direct calculation.' It specifies the verb ('verify'), resource ('sum and difference formulas'), and method ('comparison with direct calculation'), with domain/category context. However, it doesn't explicitly distinguish this from sibling tools like 'sum_difference_formulas' or 'comprehensive_identity_verification', which prevents a perfect score.

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 mentions the domain (trigonometry) and category (identities), but doesn't indicate whether this is for educational verification, numerical validation, or when other identity verification tools would be more appropriate. No explicit when/when-not statements or named alternatives are provided.

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