amplitude_from_coefficients

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 'extracts' amplitude, implying a read-only calculation, but does not specify output format, error handling, mathematical assumptions (e.g., handling of negative coefficients), or performance characteristics. This leaves significant gaps for a tool with undocumented parameters.

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, consisting of a single sentence that directly states the tool's purpose, followed by domain and category tags. There is no wasted verbiage, and every word contributes to understanding the tool's function.

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 mathematical nature, two undocumented parameters, no annotations, and no output schema, the description is insufficient. It lacks details on the calculation method (e.g., amplitude = sqrt(A² + B²)), output format, error cases, or examples, making it incomplete for reliable agent use.

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 two undocumented parameters ('a_coeff' and 'b_coeff'). The description mentions 'trigonometric coefficients A*cos(θ) + B*sin(θ)', which clarifies that 'a_coeff' corresponds to A and 'b_coeff' to B, adding meaningful context. However, it does not explain units, valid ranges, or interpretation, so it only partially compensates for the schema gap.

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: 'Extract amplitude from trigonometric coefficients A*cos(θ) + B*sin(θ).' It specifies the verb ('extract'), resource ('amplitude'), and mathematical context. However, it does not explicitly differentiate from potential sibling tools like 'wave_amplitude_analysis' or other trigonometric tools, which prevents a perfect score.

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 minimal guidance by mentioning the domain ('trigonometry') and category ('wave_analysis'), which implies context. However, it lacks explicit instructions on when to use this tool versus alternatives (e.g., 'wave_amplitude_analysis' or other amplitude-related tools), prerequisites, or examples of appropriate scenarios.

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