The polar method differs from the basic method in that it is a type of rejection sampling. It discards some generated random numbers, but can be faster than the basic method because it is simpler to compute (provided that the random number generator is relatively fast) and is more numerically robust. Avoiding the use of expensive trigonometric functions improves speed over the basic form. It discards of the total input uniformly distributed random number pairs generated, i.e. discards uniformly distributed random number pairs per Gaussian random number pair generated, requiring input random numbers per output random number.