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

With no annotations, the description carries the full disclosure burden. It usefully discloses the certification method, strict error box, and real-only output, but says nothing about failure modes (no real roots, degenerate input), multiplicity handling, or determinism.

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?

Three tight sentences with the core behavior front-loaded; the coefficient convention and exclusions are placed after the main statement. The 'instead of letting a language model estimate roots' line is slightly promotional but still earns its place as a usage cue.

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?

There is no output schema, so the description must describe the return value; it only implies a list of roots with error boxes and never specifies the structure (e.g., intervals vs. points) or ordering. Adequate for a simple two-param tool, but the return contract is left partly implicit.

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 100%, so both parameters are already documented, and the description's coefficient-ordering example duplicates the schema text verbatim. The optional tolerance parameter is never mentioned in the description, so no value is added beyond the schema.

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?

States a specific verb and resource ('All real roots of a polynomial') plus the method guarantee ('Krawczyk-certified with a strict error box'), which an agent can distinguish from generic solvers like solve/verify. It also explicitly bounds scope by excluding complex roots.

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?

Gives a clear when-to-use directive ('Use it instead of letting a language model estimate roots') and states the exclusion (complex roots not returned). It does not contrast against the plausible sibling tools solve or verify, so the routing guidance is incomplete.

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