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

Annotations already establish readOnly, idempotent, non-destructive, open-world behavior, so the safety profile is covered. The description adds two genuinely useful facts beyond that — the boolean return value (no output schema exists) and the 1-credit cost — but says nothing about edge-case behavior such as how negative or very large numbers are handled.

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 definition before the return contract and the cost note, with no filler. The parenthetical example is slightly redundant with the definition but earns its place by disambiguating the rule.

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 annotations and no output schema, the definition covers purpose, return value, and cost adequately. The only missing piece is what happens for invalid input (negatives), which is partly covered by the schema but not by the description.

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 100%, so the single 'num' parameter is already fully documented, including the 'must be non-negative' constraint. The description's example illustrates the concept but adds no syntax or format detail beyond the schema, so baseline 3 applies.

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 predicate with its exact mathematical condition and an inline worked example (153 = 1³ + 5³ + 3³), which removes any ambiguity about what 'sum of cubes' means. An agent can trivially distinguish it from neighbors like is_prime, is_perfect_square, or is_power_of_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?

The predicate nature implies usage clearly, but the description gives no explicit when-to-use or when-not-to-use guidance and never points to sibling tools (e.g., is_armstrong_number-style overlaps such as is_power or is_perfect_square) that an agent might confuse it with. Adequate but leaves routing to inference.

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