Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (0 params, no output schema), the description adequately covers the core purpose. It could mention what the response indicates, but for a health check, 'Check that the API is up' sufficiently implies the result. With annotations covering safety, the description is complete enough.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.