watch_beat_math

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

No annotations are supplied, so the description carries the full disclosure burden. It identifies the computed quantities but never states that this is a pure, side-effect-free calculation with no external data or permissions required, nor does it note that lift_angle influences the result. For a low-risk calculator this is acceptable, but it leaves the behavioral profile to inference.

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 with the outputs enumerated compactly. No filler, no repetition of the tool name, nothing that could be cut without losing information.

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 usefully enumerates the return values (Hertz, ticks per second, daily rate deviation), which is exactly what an agent needs. The remaining shortfall is that lift_angle's effect and the expected units/range of rate_sec_day are not clarified beyond 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 100%, so bph, lift_angle, and rate_sec_day are already documented with examples and a default. The description adds only the framing that rate_sec_day relates to the daily rate deviation output; it does not explain how lift_angle changes the computation or how the parameters interact. Baseline 3 is appropriate.

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 (Calculate) plus a precise domain resource (mechanical watch movement escapement frequency) and names the exact outputs (Hertz, ticks per second, daily rate deviation). The sibling tools are all unrelated calculators (bullion_melt, specific_gravity, beam_deflection, fossil_age_overlap), so there is no ambiguity to resolve.

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: an agent can infer it applies when converting a beat rate (BPH) into frequency/rate figures. There is no explicit statement of when to use it, no preconditions, and no mention of whether bph must be a standard value. With no sibling in the same domain, the lack of routing guidance is a minor but real gap.

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