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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so safety is covered. The description adds genuinely useful behavioral context beyond that: exact fraction arithmetic (precision guarantees) and a per-call price plus an alternate HTTPS endpoint. It does not mention rate limits or result format, keeping it below a 5.

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 core operation and ordering convention are front-loaded, the non-commutativity note is a single clarifying clause, and pricing/endpoint details come last. No sentence is wasted.

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 pure two-argument math function with annotations covering safety and no output schema, the description is nearly complete: it defines the operation, operand order, and precision model. The return shape (a four-element array of fraction strings) is not stated, which is a minor gap.

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 coverage is 0%, so the description must carry the load. It does supply key semantics — 'scalar first' defines element order and 'Components are exact fractions' implies the string elements are rational values — but it never states the accepted string syntax (e.g., '1/2' vs '0.5') or clarifies that a and b are each four-element arrays. Partial compensation only.

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 names a specific operation (Hamilton product) on a specific resource (two quaternions) and pins the ordering convention ('scalar first'). The non-commutativity example ('i times j is k, and j times i is minus k') removes any ambiguity about operand order, distinguishing it from siblings like quat_inv and quat_pow.

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 operation is self-evidently a multiplication, so the use case is implied, but there is no explicit when-to-use or when-not guidance and no mention of the quat_* alternatives. An agent must infer that this is the product tool rather than inv/norm/pow/rotate from the name and description alone.

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