Swamping
Beginner
When a small number added to a big total disappears, because the total can’t store enough digits to notice it.
Novice
In floating-point addition the smaller number is shifted to line up with the larger one; if the difference in size exceeds the mantissa width, the small number is shifted out entirely and lost. Long sums in a narrow accumulator suffer from this.
Expert
Loss of addends whose magnitude is below the accumulator’s ulp: roughly when the sum exceeds the addend by more than . Worse for long reductions and non-zero-mean data. Mitigated by wider accumulators, chunked (pairwise) summation and stochastic rounding.