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

Annotations already declare readOnly/idempotent/non-destructive/openWorld, so the safety profile is covered. The description adds genuinely useful operational context beyond the annotations: a per-call price ($0.001 USDC, x402 on Solana) and an equivalent HTTPS endpoint. It stops short of describing the response shape or failure modes, which keeps it at 4 rather than 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 definition and examples are front-loaded, and the pricing/endpoint details come last where they belong. The single slightly wasteful sentence is 'n runs from 1 to 1000000,' which duplicates the schema minimum/maximum.

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 one-parameter boolean predicate with no output schema, the description supplies definition, examples, domain, cost, and an alternate transport — enough to call it correctly. The remaining ambiguity is the exact digit-counting convention for written factorizations, partially but not fully resolved by the examples.

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 compensate, and it does only partially: it repeats the 1–1000000 range already encoded in the schema and gives illustrative values of n (125, 128, 1, 16, 12) that implicitly clarify what n means. It never explicitly says n is the integer being tested for frugality, leaving a small inference gap.

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 states a specific boolean predicate ('whether the written factorization uses fewer digits than n') and backs it with concrete yes/no examples (125, 128 vs 1, 16, 12), which makes the concept graspable without opening the schema. It does not differentiate itself from the nearby sibling frugal_count (which presumably counts such numbers up to n), so an agent could still hesitate between the two.

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?

There is no when-to-use guidance and no mention of alternatives such as frugal_count, equidigital, or extravagant, despite those siblings sharing the same domain vocabulary. The only scoping information ('n runs from 1 to 1000000') is a restatement of the schema bounds rather than usage guidance.

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