math.polynomial_horner

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

The annotations already declare readOnly, idempotent, and closed-world behavior, so the bar is lower. The description still adds real behavioral value: it uses Decimal arithmetic and never goes through float, so results are exact rather than floating-point approximations; and it returns the degree as well as the value. It does not state limits on coefficient count or error behavior for malformed Decimal strings.

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?

The description is four short sentences, and it leads with what the tool computes before moving to parameter conventions. Every sentence carries information, including the ascending-order warning. It is slightly repetitive about ordering across two sentences.

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 numeric evaluator with an output schema, this is complete enough. It covers arithmetic mode (Decimal, no float), input ordering conventions, the x format, and which return values to expect (value plus degree); all remaining details are documented by the schema.

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 full burden, and it mostly does: it defines the coefficient ordering as descending, gives a worked example ([1, 0, -4] is x²-4), and says x is a Decimal string. It does not explicitly state that each coefficient item is also a Decimal string, leaving that detail to be inferred from the schema's item 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 states a specific verb and resource: evaluate polynomial P(x) using Horner's method in Decimal precision. An agent can immediately tell what the tool computes. It does not differentiate itself from sibling math.polynomial_roots, which is the nearest alternative, so it falls short of a 5.

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?

Usage is only implied: it is an evaluator for a polynomial at a point, as opposed to the root-finder. The description adds a practical warning that passing coefficients in ascending order evaluates a different polynomial, which is helpful usage guidance. However, it never says when to choose this tool over math.polynomial_roots or symbolic-based alternatives.

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