The forms and constant terms of heat transfer correlations can be determined simultaneously with symbolic regression with prescribed precision. In this paper, a genetic programming (GP) technique developed by Silva is adopted as the tool of symbolic regression. However, the test results indicate that when the undetermined functions contain constant terms, symbolic regression results based on the code of Silva usually have increasing sizes. It is difficult to employ them for practical applications when the correlations are not concisely enough. In order to solve this problem, some new function modules are inserted into the GP of Silva, including (a) a function structure simplification module, (b) a constants optimization module, (c) an expansion rate reduction module with self-swap genetic operator, and (d) a small term search intensity enhancement module with intro-new genetic operator. The statistical performance demonstrates that all of these four new modules are beneficial to improve performance of symbolic regression, especially when the constants optimization module is added. Furthermore, when different modules are added simultaneously, the improvements are more remarkable. Finally, applications of deriving heat transfer correlations for a shell-and-tube heat exchanger with continuous helical baffles and a single-row heat exchanger with helically finned tubes are performed. The results indicate that heat transfer correlations obtained in this paper are proven to be better than the power-law-based correlations.