Continual need for high performance in compute-bound scientific applications motivates the study of LUT optimization. LUT optimization replaces a complex expression with an access to pre-computed LUT data containing the expression values. This results in faster expression evaluation and high performance gain. This paper describes a comprehensive methodology for LUT optimization, and show that LUT methods can improve the performance of scientific applications. Mainly two techniques, namely, Anti-symmetric Product Coding (APC) and Odd Multiple Storage (OMS) for achieving LUT optimization are discussed.