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

Annotations already declare the full safety profile (readOnly, idempotent, non-destructive, non-open-world), so the description only needs to add behavior beyond that. It notes that roots may be real or complex and that a discriminant and vertex are produced, but says nothing about edge cases such as a=0 (undefined quadratic) or error 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?

Three short sentences, front-loaded with the operation and formula before usage and output notes. The 'Inputs:' clause is largely redundant with the schema and is the one expendable fragment.

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?

An output schema exists, so the description is not obligated to enumerate return values, and annotations cover the safety semantics. What remains thin is the domain constraint on coefficient a and the behavior for degenerate inputs, but otherwise the definition is sufficient to invoke the tool 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 description coverage is 100% and the three coefficients are fully documented in the schema, so baseline is 3. The description's 'Inputs: coefficients a, b, c' merely restates the schema and adds no constraint such as a ≠ 0 or numeric domain limits.

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 gives a specific verb and resource — 'Solve quadratic equation ax²+bx+c=0' — and pins the exact scope with the polynomial formula, so an agent knows precisely what is computed. It does not differentiate itself from the close sibling calculate_equation (a more general equation solver), which is the only missing piece.

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?

'Use for math homework or physics problems' implies a context but gives no when-not guidance and does not route the agent away from calculate_equation or calculate_fraction_operations. The 'See list_bundles' pointer is a soft cross-reference rather than an alternative-selection rule.

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