Numerical analysis
Numerical analysis uses machine epsilon to study the effects of rounding error. The actual errors of machine arithmetic are far too complicated to be studied directly, so instead, the following simple model is used. The IEEE arithmetic standard says all floating point operations are done as if it were possible to perform the infinite-precision operation, and then, the result is rounded to a floating point number. Suppose (1) formula_21, formula_25 are floating point numbers, (2) formula_26 is an arithmetic operation on floating point numbers such as addition or multiplication, and (3) formula_27 is the infinite precision operation. According to the standard, the computer calculates: