complex_polar

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 conversion action but lacks details on output format (e.g., whether r and θ are returned as separate values or in a string), error handling (e.g., for invalid inputs), or computational behavior (e.g., precision, units for θ). This is a significant gap for a tool with no structured annotations.

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—a single sentence that directly states the tool's function without unnecessary words. It's front-loaded with the core purpose, making it efficient and easy to parse. Every part of the sentence earns its place by conveying essential information.

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 complexity of mathematical conversion, lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address output details, error cases, or usage context, leaving gaps that could hinder an AI agent's ability to invoke the tool correctly. For a tool with these characteristics, more information is needed.

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, but the description doesn't add any parameter semantics beyond the schema's property names (real, imag). It doesn't explain what these parameters represent (e.g., real and imaginary parts of a complex number) or their expected formats. With low schema coverage, the description fails to compensate adequately, resulting in a baseline score.

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: converting complex numbers to polar form (r∠θ). It specifies the verb 'convert' and the resource 'complex numbers', making it understandable. However, it doesn't explicitly differentiate from sibling tools like complex_magnitude or complex_argument, which might handle related calculations, so it doesn't reach the highest 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 no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like complex_magnitude (which might compute only the magnitude) or complex_argument (which might compute only the angle), nor does it specify any prerequisites or context for usage. This leaves the agent without clear direction on tool selection.

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