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

Annotations already declare readOnlyHint=true, destructiveHint=false, and openWorldHint=false, so the safety profile is covered. The description adds a concrete transformation example but says nothing about failure modes (irreducible or malformed expressions) or the required input syntax, which is worth noting given the notation mismatch (description shows 'x² - 5x + 6', schema shows 'x**2 - 5*x + 6').

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 front-loaded sentence plus an illustrative example, with no filler. The operation and its result shape are conveyed in minimal space.

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?

An output schema exists, so return values need not be described, and the single parameter is well documented. What's missing is the disambiguation an agent needs among ~150 calculator siblings and any statement about error behavior for unfactorable input.

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?

Only one parameter exists and schema coverage is 100%, so the baseline is 3. The description's example implies the accepted expression form, but its unicode/caret notation differs from the schema's '**' syntax, so it does not reliably add meaning 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 ('Factor polynomials') and reinforces it with a concrete input→output example, so an agent knows exactly what operation this performs. It does not, however, distinguish itself from closely related siblings such as calculator_expand, calculator_simplify, or calculator_polynomial.

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?

There is no guidance on when to use this tool versus the inverse operation (calculator_expand) or a general simplifier (calculator_simplify), nor any note about valid input class or what happens with irreducible polynomials. Usage must be inferred entirely from the tool name.

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