단위·차원 검사

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

Annotations already declare readOnlyHint=true and openWorldHint=false, so safety is covered; the description adds genuinely new behavior: what a match returns, that mismatches explain which dimensions differ, that units carrying values also yield a numeric result, and that errors name the offending input so it can be fixed and retried. Return-value shape is only sketched ('matches; otherwise explanation'), which keeps it from 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?

Front-loaded with the two-mode split, then compact labeled examples; nearly every line carries information. The tradeoff is a slight telegraphic terseness (schema-style literals instead of prose) that may slow a first read but wastes no 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?

With five optional parameters, two operating modes, and no output schema, the description must carry mode selection and result shape — and it does both via examples plus the failure/explanation note. The remaining gap is precedence when conflicting parameter combinations are given, which matters for a zero-required-parameter tool.

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 the baseline is 3; the description earns extra by showing how expr/units/expect compose in a realistic call and by clarifying that the 'units' map values may embed magnitudes ('20 m'), a semantic the schema's 'Unit per variable, optionally with value' only hints at. It also constrains the symbol vocabulary (m, kg, N, J, km/h, m/s^2, dimensionless "1"), which the schema does not.

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 two concrete operations — dimension checking of a formula and unit conversion — with worked JSON examples that make the resource ('units/dimensions of a physics/engineering formula') unmistakable. It does not, however, distinguish itself from the sibling verify_math, which an agent could plausibly confuse with this tool for formula checking.

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 clearly delineates the two invocation modes by showing which parameter set selects which ('Check: {expr, units, expect}' vs 'Convert: {value, to}'), which is the main usage decision. It stops short of stating when to prefer verify_math or plot_function instead, and doesn't say what happens if both expr and value are supplied.

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