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

With no annotations, the description carries the full burden. It does add real behavioral value by disclosing the exact computational method and the payment/trial model, but says nothing about the return value (boolean vs. numeric), edge cases (negative, non-integer, zero), or error behavior.

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 and compact: the definition lands first, then the method. The 'Is Triangular:' prefix duplicates the tool name and the trailing promo with emoji is not agent-relevant, but the body is otherwise waste-free.

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 predicate with no output schema and no annotations, the description covers what it computes but omits what it returns and how malformed input is handled. Adequate, with a clear gap around output semantics.

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% and the sole 'value' parameter is typed as a string with no description. The formula '1+8n' implies an integer is expected, but the description never reconciles that with the string type, nor states range or negative-number handling.

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 — 'Checks whether value is a triangular number' — and even names the test used ('1+8n for a perfect square'). Among the dense sibling list of number-predicate tools (is-prime, is-pronic, is-perfect), this is immediately distinguishable from the name and first clause alone.

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?

No when-to-use guidance and no mention of the adjacent predicates (is-square-free, is-pronic, triangular-series) an agent might confuse this with. The only extra sentence is promotional ('5 free trial calls per signed wallet'), not usage direction.

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