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

With readOnlyHint/idempotentHint already covering the safety profile, the description adds genuinely new behavioral context: the call is paid ($0.001 USDC per successful call via x402 on Solana) and mirrored over HTTPS at a specific POST endpoint. That payment/auth dimension is invisible in the annotations and matters before invoking.

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?

Front-loaded with the exact quantity and three concrete examples before any constraints or pricing. The pricing/HTTPS sentence is bulkier than the math content but is functional information, not filler.

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?

No output schema exists, and the worked examples (3/7 ends at 231, 1/2 ends at 2) effectively communicate the return value — a single integer. Input domain, validity constraint, cost, and alternate transport are all covered, leaving nothing an agent needs missing.

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%, so the description must carry weight here. It does contribute the real semantic constraint that the fraction must be proper (a < b), which is not encoded in the schema, plus effective ranges a,b ∈ [1,30] / b ≥ 2 — although those bounds are already duplicated from the schema's minimum/maximum fields.

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-and-resource: returns the last denominator in the greedy Egyptian expansion of a/b, with worked examples (3/7 → 231) that pin down the exact quantity. It is clearly distinguishable from egyptian_first / egyptian_length by the word 'last', though it never names those 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?

Usage is implied through the constraint 'the fraction must be proper' and the worked examples, which tell an agent the valid input region. There is no explicit statement of when to prefer this over egyptian_greedy, egyptian_first, or egyptian_sum, so the agent must infer routing from the sibling names.

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