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

With no annotations, the description carries the full burden, and it does disclose what the computation does and returns (eigenvalue nature, stationary point, path ending at recommended_settings). It omits operational behavior such as the role of api_key/auth, how n_steps or max_radius affect the trace, and goal direction handling, which keeps it short of a 5.

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?

Two tight paragraphs: the first gives method and when-to-use, the second gives input/output contract. No waste, though the last sentence is somewhat long and partly duplicates what the output schema already conveys.

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 9-parameter, zero-required, compute-heavy tool with an output schema, the description covers the critical invocation modes and the return shape. The gaps are the undocumented secondary parameters and auth behavior, which an agent could stumble on.

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 coverage is 0%, so the description must compensate. It explains model, data, and response well, but leaves goal, api_key, n_steps, include_ci, max_radius, and factor_columns entirely undocumented; the remaining titles/defaults are only weakly self-explanatory. Partial compensation, not full.

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 method (ridge / steepest-ascent path of a quadratic RSM) with citations, and clearly distinguishes it from fit_rsm (which produces the model) and the plain-optimum siblings by framing it as the tool for saddle/out-of-region cases. An agent can identify the resource, method, and scope without opening the 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 exact triggering condition — 'when the unconstrained optimum is a saddle or sits outside the studied region' — and offers two explicit invocation paths ('Pass a fitted model ... OR raw data + response to auto-fit one'). This is a genuinely routing-quality guideline.

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