 To illustrate the savings of an FFT, consider the count of complex multiplications and additions for N=4096 data points.Evaluating the DFT's sums directly involves "N"2 complex multiplications and "N"("N" − 1) complex additions, of which formula_12 operations can be saved by eliminating trivial operations such as multiplications by 1, leaving about 30 million operations.On the other hand, the radix-2 Cooley–Tukey algorithm, for "N" a power of 2, can compute the same result with only ("N"/2)log2("N") complex multiplications (again, ignoring simplifications of multiplications by 1 and similar) and "N" log2("N") complex additions, in total about 30,000 operations - a thousand times less than with direct evaluation.