Evaluation using the monomial form of a degree-"n" polynomial requires at most "n" additions and ("n"2 + "n")/2 multiplications, if powers are calculated by repeated multiplication and each monomial is evaluated individually. (This can be reduced to "n" additions and 2"n" − 1 multiplications by evaluating the powers of "x" iteratively.) If numerical data are represented in terms of digits (or bits), then the naive algorithm also entails storing approximately 2"n" times the number of bits of "x" (the evaluated polynomial has approximate magnitude "xn", and one must also store "xn" itself). By contrast, Horner's method requires only "n" additions and "n" multiplications, and its storage requirements are only "n" times the number of bits of "x". Alternatively, Horner's method can be computed with "n" fused multiply–adds. Horner's method can also be extended to evaluate the first "k" derivatives of the polynomial with "kn" additions and multiplications.