1. A computer implemented method of improving similarity distance approximation between data sets, comprising: initializing, using one or more processors, a random number generator with a weighted rain-hash value as a seed, wherein the weighted min-hash value approximates the similarity distance between two or more data sets; uniformly sampling, using the one or more processors, an integer bit value using the random number generator to determine a first number of bits used to represent a single weighted min-hash value; determining, using the one or more processors, an adjusted number of bits to sample based on distance estimate variances of a total number of bits to sample; and varying, using the one or more processors, the determined first number of bits used to represent the single, weighted min-hash value to determine a least number of bits capable of being used to represent the single weighted rain-hash value while achieving a target weighted rain-hash accuracy, wherein the weighted min-hash accuracy specifies a similarity distance approximation between the data sets; and adjusting a number of bits used to represent the single weighted rain-hash value based on the determined least number of bits.