In view of the function transformation to monotone sequence, the sufficient and necessary conditions of monotonic increasing and decreasing function transform are unified to improve the smoothness of the series. The sufficient and necessary conditions which compression transform meets are given, and the necessary and sufficient conditions of reduction the accuracy of error are also given. A conclusion is obtained that the conditions of improving the smoothness and compression transform are consistent, but are contradictory with that of lowering the reduction error. Therefore, the smoothness and reduction accuracy are considered comprehensively during the function transformation to achieve the optimal overall modeling accuracy. Finally, the literature results show the correctness of the proposed conclusion.