pell_number

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a Pell number, implying a read-only operation, but does not address potential constraints like input range (e.g., n must be non-negative), performance considerations (e.g., recursion depth for large n), or error handling. For a tool with zero annotation coverage, this leaves significant gaps in understanding its 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?

The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose. Every word earns its place, with no redundant information. The parenthetical domain and category are brief and add context without verbosity.

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?

Given the tool's low complexity (single integer parameter) and lack of annotations or output schema, the description is minimally adequate. It explains what the tool does but lacks details on usage, behavioral traits, or parameter constraints. For a simple arithmetic tool, this might suffice, but it leaves gaps that could hinder an agent's ability to use it correctly in all scenarios.

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?

The input schema has 0% description coverage, with a single parameter 'n' of type integer. The description adds minimal semantics by specifying 'nth' in 'Calculate the nth Pell number P_n', indicating 'n' is an index. However, it does not explain valid ranges (e.g., n >= 0) or the meaning of 'P_n', which is insufficient to fully compensate for the low schema coverage. The baseline is 3 due to the single parameter, but the description adds only marginal value.

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 clearly states the tool's purpose: 'Calculate the nth Pell number P_n.' It specifies the verb ('Calculate'), resource ('Pell number'), and parameter ('nth'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'pell_sequence' or 'pell_lucas_number', which is why it scores 4 instead of 5.

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 description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('recursive_sequences'), but this is too vague to help an agent choose between similar tools like 'pell_sequence' or 'pell_lucas_number'. There are no explicit when/when-not instructions or named alternatives.

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