Evolutionary programming (EP) has been applied with success to many numerical and combinatorial optimization problems in recent years. EP has rather slow convergence rates, however, on some function optimization problems. In this paper, a `fast EP' (FEP) is proposed which uses a Cauchy instead of Gaussian mutation as the primary search operator. The relationship between FEP and classical EP (CEP) is similar to that between fast simulated annealing and the classical version. Both analytical and empirical studies have been carried out to evaluate the performance of FEP and CEP for different function optimization problems. This paper shows that FEP is very good at search in a large neighborhood while CEP is better at search in a small local neighborhood. For a suite of 23 benchmark problems, FEP performs much better than CEP for multimodal functions with many local minima while being comparable to CEP in performance for unimodal and multimodal functions with only a few local minima. This paper also shows the relationship between the search step size and the probability of finding a global optimum and thus explains why FEP performs better than CEP on some functions but not on others. In addition, the importance of the neighborhood size and its relationship to the probability of finding a near-optimum is investigated. Based on these analyses, an improved FEP (IFEP) is proposed and tested empirically. This technique mixes different search operators (mutations). The experimental results show that IFEP performs better than or as well as the better of FEP and CEP for most benchmark problems tested.