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

Annotations already establish readOnlyHint and idempotentHint, so the safety profile is covered; the description adds real value beyond that by disclosing that every formula reproduces its own reference example before being listed and that each result carries its limits. The licensing/scope disclaimer is also behaviorally relevant context an agent would not otherwise know. It stops short of describing result shape or failure behavior for invalid formula codes.

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?

Four compact sentences, front-loaded with the action and followed by the discovery pointer, a trust guarantee, and the scope caveat. Little waste, though the parenthetical formula list is longer than needed and the scope disclaimer could be tightened.

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 no output schema, the description appropriately signals that results carry their own limits, and the discover_capabilities pointer resolves the main unknown for a 0%-coverage two-parameter tool. The remaining gap is the structure of the nested `inputs` object, which an agent must infer from the discovery 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 description coverage is 0% and the nested `inputs` object is entirely undocumented, so the description must carry the load. It does partially compensate by telling the agent that formula codes and input names come from discover_capabilities, which is the single most useful piece of parameter context here, but it says nothing about how the `inputs` object maps to a given formula's arguments or about the `^f[a-z2-9]{5}$` code format.

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 opens with a specific verb and resource ("Run one of our built-in physics formulas ... on YOUR inputs") and enumerates the formula families (sound speed, echo range, drop shock, field magnitude, thermal, timing). It clearly conveys a computation tool rather than a lookup or verification tool, though it does not explicitly differentiate itself from close siblings like verify_math_or_tolerance or verify_trig_expression.

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 gives one concrete prerequisite: use discover_capabilities to find formula codes and input names, which is genuinely actionable. It also bounds scope with "Planning and math verification check only — not a licensed professional engineering review," but it never states when an agent should pick this over verify_math_or_tolerance, verify_trig_expression, or run_chain, which are the most likely alternatives.

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