Roundoff error arises from rounding results of floating-point operations during the algorithm. Input error is error in the input to the algorithm from prior calculations or measurements. We describe roundoff error first, and then input error.
Machine epsilon bounds the roundoff in individual floating-point operations.
It may be loosely defined as the largest relative error in any floating-point operation that neither overflows nor underflows. See section 4.1.1 and Table 4.1 for a discussion of common values of machine epsilon. Since underflow is almost always less significant than roundoff, we will not consider it further. Then one simply replaces by in the error bounds.