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

Annotations already declare readOnly/idempotent/non-destructive, so the safety profile is covered. The description adds real behavioral value by naming the perimeter approximation (Ramanujan), which signals the result is approximate rather than exact — a meaningful disclosure for a computation tool.

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?

Four short front-loaded sentences with no padding, and the formula leads. The trailing pointer to list_bundles is mildly tangential but still useful for discovery.

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 two-parameter deterministic calculator with an output schema already present, the description covers attribution, inputs, and outputs adequately. It even states the return values despite the output schema making that optional, leaving little uncovered.

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 description's 'semi-major a, semi-minor b' merely restates the schema's parameter descriptions. Baseline 3 is appropriate; no syntactic or constraint detail is added beyond the schema.

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 (compute) and resource (ellipse area/perimeter) with the exact formulas, including the approximation method for perimeter (Ramanujan). An agent can immediately distinguish this from generic calculate_area or calculate_perimeter siblings.

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?

Gives clear use contexts ('elliptical fields, tracks, or design') and points to list_bundles for related math calculators. However, it never explicitly excludes or contrasts with the close siblings calculate_area, calculate_perimeter, calculate_sphere, or calculate_cone, so the routing decision is only partially supported.

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