Invert emulsion drilling fluids (IEDF) are recognized as the highest-performing fluid systems available, providing invaluable benefits in drilling operations. This study uses conventional and novel algorithms to improve the fitting ability of three and four-parameter rheological models for IEDF. Linear regression (LR), quasi-linear regression (QLR), Gold Search Section (GSS), Generalized Reduced Gradient (GRG), Trust Region (TR), and Gauss-Newton (GN) methods are employed to determine optimal rheological model parameters. The analysis utilizes an extensive field database from five different sources. In optimizing the model parameters, a symmetric mean absolute percentage error-based objective function is used, eliminating the statistical problems experienced in conventional objective functions. Average symmetric mean absolute percentage error (SMAPE) and the number of best fits (NBF) is used for selecting the most appropriate rheological model. In the performance comparison of the models, the ranking index, which is defined as the symmetric mean absolute error percentage and the arithmetic mean of the best fit number, is also used. The symmetry of the error distribution giving the balance between the overestimated and underestimated errors is predicted by the average overestimated and underestimated symmetric percentage errors.