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

Annotations already declare readOnlyHint=true, destructiveHint=false, and openWorldHint=false, so the safety profile is covered. The description adds nothing beyond that — no constraint that x values must be distinct, that x and y must be the same length, or what happens for out-of-range targets.

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?

Seven words with zero waste and the core information front-loaded, but it is under-specified rather than genuinely concise — economy achieved by omitting content an agent needs, not by tight writing.

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?

An output schema exists, so return values needn't be explained, but for a 4-parameter numerical tool with three required arrays/scalar inputs the description omits the pairing and validation rules that determine a correct call. It is too thin for the tool's complexity.

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 100%, so baseline is 3. The description does add one useful gloss by clarifying that the 'polynomial' method means Lagrange (the schema only says 'linear or polynomial'), but it says nothing about how x/y/target relate.

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 fragment 'Linear or Lagrange polynomial interpolation' names the resource and both supported methods, so an agent can tell it apart from calculator_linear_regression or calculator_polynomial. However it has no verb and no scope statement (e.g., single target point vs. curve fitting), leaving the purpose only partially pinned down.

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 at all: no mention that x/y must be sample pairs, no routing away from nearby siblings like calculator_newton_raphson, calculator_numerical_solve, or calculator_linear_regression. The agent must infer the context entirely from the name.

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