Machining processes have emerged as an important requirement in product design concepts, manufacturing applications, and the overall functional aspects of the product. For machining a component, it is important to understand the characteristics of work material in order to choose the appropriate cutting tool and to fix a set of machining parameters to achieve optimum output. This article presents the details of experiments conducted for machining Inconel 718, by turning process, with two different coated carbide tool inserts (KC5525 and HK150), with an objective of optimizing the process. Furthermore, four different analytical models were developed, validated, and compared to exhibit their performance in establishing the input–output relationship. A set of input machining parameters were chosen to yield a higher material removal rate (MRR), coupled with a moderate surface finish. Experimental data were generated for the chosen set of input parameters and the resultant output parameter and the machining performance of the two tool inserts was compared. With the above experimental data, Analytical models were developed, using genetic programming (GP), artificial neural networks (ANN), adaptive neuro‐fuzzy inference system (ANFIS) and the mathematical regression models with an objective of minimizing the surface roughness while turning Inconel‐718. The effect of machining parameters on the surface roughness was evaluated and the optimum machining condition for minimizing the surface roughness was determined; further the order of influencing input parameters was brought out. Prediction accuracy of the four models was established and the above models were validated, using the different set of experimental data. Comparison of performance of the four models is discussed, extent of prediction accuracy of each model is brought out and the advantages, disadvantages, and limitations of the four models are outlined in this article. This shall be a reference to the machinists to choose appropriate cutting parameters to meet the surface finish requirements demanded by the product designers.