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

With no annotations, the description carries the full burden of behavioral disclosure. It only restates the equation forms and offers no information about edge cases (e.g., complex roots, singular systems), output format, or whether the operation is pure computation. This leaves significant behavioral uncertainty.

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?

A single sentence with no fluff, front-loaded with the verb and resource types. Every part of the sentence adds meaning and the structure is easily scannable.

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 complexity (9 parameters, one required), the description is notably incomplete. It omits any guidance on parameter selection or the required equation_type value, and while an output schema exists, the missing input semantics create a serious gap for correct invocation.

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 compensate, but it does not. It never explains the required 'equation_type' parameter, its possible values, or how the other parameters map to the three forms. An agent cannot infer which parameters to populate for a given equation type.

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 uses a specific verb ('Solve') and names three distinct mathematical resource types with their exact forms. It clearly distinguishes this tool from siblings like cognitive.solve_arithmetic or cognitive.solve_word_problem by laying out the supported equation categories.

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 clear context on when to use the tool by enumerating the equation forms it handles (linear, quadratic, linear systems). However, it doesn't explicitly mention alternatives or when not to use it, so it stops short of full explicitness.

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