Distance functions are the main tools to measure similarity of two sequences and to search the closest sequences to given query sequence. Several well known distance functions, however, have asymptotical time complexity of O(mn) which cannot be fully afforded by systems that deal with large volumes of data. These distance functions, including Edit distance on Real sequences (EDR) [5], have pruning methods to reduce execution time by dismissing false candidates as early as possible. In this paper, we propose the Histogram Distance on Fixed Reference (HDFR) ordering, with various reference histogram construction methods, to improve the filtering power of the pruning methods in EDR. Experiments show that a decrease in EDR execution time is observed after HDFR is applied. While we base our experiments on EDR, HDFR can also be applied to other distance functions with appropriate pruning methods.