math.ifft

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

Beyond the readOnly/idempotent annotations, it discloses the size ceiling (65536), the 1e-9 imaginary-tolerance error behavior for real_output=true, and that the return shape itself changes (string list vs {real, imag} pairs). These are exactly the runtime traits an agent cannot infer from annotations or schema.

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?

Four dense sentences, each contributing a distinct fact (purpose, size limit, flag behavior, input completeness constraint), with the core purpose front-loaded. No filler or restatement of the name.

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 two-parameter transform tool with an output schema, the description covers the input contract, size limit, error mode, and output variants, so nothing needed to call it correctly is missing. Return-value structure being described is a bonus rather than a redundancy.

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 0%, so the description must carry the load and it does: bins is defined as the ordered, complete N-length magnitude/phase list, and real_output's default, error threshold, and output-shape consequence are all spelled out. Only the string encoding of bin values is left implicit.

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 names a specific verb and resource in the inverse direction: reconstruct time-domain samples from an fft bin list of {magnitude, phase_rad} with 1/N normalization. That makes the inverse relationship to math.fft unambiguous without the agent needing to inspect either schema.

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?

It states the operational precondition that bins must contain all N entries in order, and warns that supplying a partial list reconstructs a different signal, which is genuine when-to-use-in-this-way guidance. It also gives a rule for choosing real_output (true for real signals, false when imaginary components are expected), but it never explicitly names math.fft as the forward-direction alternative.

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