Changing tolerance at fixed echo depth isolates the deterministic gate rule. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Two metre tolerance rejects a sixteen metre echo
The echo depth is 16 m and the target is 12 m, so the difference is 4 m. Tolerance 2 m rejects it.
16−12=4>2
Four metre tolerance accepts the endpoint
With tolerance 4 m, the same 4 m difference lands exactly on the accepted endpoint.
16−12=4≤4
Six metre tolerance also accepts the echo
Widening tolerance to 6 m still accepts the same echo. This does not claim clinical image quality; it only shows the gate rule.