This paper presents the optimized methodology of the table-lookup-and-addition methods to approximate the elementary functions. Compared to the previously published methods including SBTM, STAM and their improved method in the paper [1], our method uses three small look-up tables to replace the biggest look-up tables in the previous methods and shortens the number of address bits to some look-up tables in the previous methods to reduce the memory requirements significantly. For example, when both our method and the method in the paper [1] require the least number of bits, the compression ratio can reach to 1.57 using 16 bits operand for function 1/x. The data in this paper have been validated by using a set of C programs; and the designs have been synthesized with EDA tools.