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

Annotations already declare readOnly, idempotent, non-destructive, and open-world behavior, so the safety profile is covered. The description adds genuinely useful operational context: cost of $0.001 USDC per successful call and the 'past 15 digits a term is a decimal string' return-format note. However, the a/b/c/d/e parameter narrative describes inputs that the schema does not contain, muddying the behavioral picture.

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 formula is front-loaded and the total length is short with no filler sentences. The price and endpoint sentences are compact, and the range restatement is the only mild redundancy.

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 pure function this is close to sufficient, but with no output schema the description never states what the call returns (the value P(n) as integer or string?) and the phantom a–e inputs leave the calling convention ambiguous.

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% with one parameter, so the description must carry the load. It does explain that n runs 5 to 4096, but that merely restates the schema's min/max, and it then introduces a, b, c, d, e as the five prior terms even though none of those are inputs — leaving the agent unsure what n alone actually supplies.

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 the exact recurrence, P(n) = sum of the previous five terms, which precisely identifies the operation being performed. It is specific enough to separate it from unrelated siblings, though it never explicitly contrasts itself with pentanacci, pentanacci_sum, or pentanacci_mod.

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 statement of when to use this tool versus pentanacci, pentanacci_index, pentanacci_mod, pentanacci_sum, or the parallel tetranacci_step / hexanacci_step tools. The only context given is pricing and an alternate HTTPS endpoint, which is not usage guidance.

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