Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (1 parameter, no output schema, no annotations), the description covers the essential aspects: what it checks, what it returns, and its operational nature. It could have mentioned that the domain must be a public domain or that DNS lookups may be slow, but the information provided is largely sufficient for an agent to select and invoke correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.