Classical petrophysical formulas are fundamental for formation evaluation and reservoir characterization but they often depend on complex empirical constants and nonlinear terms that mostly limit interpretability and slow down computational workflows. The reformulated Archie’s equation eliminates explicit empirical constants, providing a direct relationship between porosity and resistivity. Volume of shale is approximated with a bias-corrected linear form, improving estimates in transitional silty-shale zones, while effective porosity is expressed \(\:{\:{\Phi\:}}_{\text{e}}={\:{\Phi\:}}_{\text{D}}\) \(\:*\) (1-0.95 \(\:{\:\text{V}}_{\text{s}\text{h}}\) ),, reducing overestimation in shaly sands. Simplified M-N plot parameters were also proposed, including \(\:M\) ≈ 0.7 * ( \(\:{\Delta\:}t\) − 189) − 0.3 * ( \(\:{\:\rho\:}_{b}\:\) - 1) and \(\:N\) ≈ \(\:\varPhi\:N\) - 0.25 * ( \(\:{\:\rho\:}_{b}\) - 1), enabling faster lithology analysis. Validation was performed using both a synthetic dataset with controlled parameter distributions, noise injection, and realistic cross-correlations and real well log data from the Sakesar Formation (Balkassar OXY-1, Potwar Basin, Pakistan). Results show that concise formulas achieve strong agreement with traditional equations for volume of shale (R² ≈ 0.997; RMSE = 0.0135) and effective porosity (R² ≈ 0.998; RMSE = 0.0008), while water saturation requires a single calibration factor to match Archie’s response in carbonate settings. Symbolic complexity metrics confirm that concise formulas substantially reduce node count and expression depth compared to traditional counterparts. These concise expressions are especially valuable for rapid workflows such as logging-while-drilling (LWD) and automated interpretation, demonstrating the potential of AI-driven symbolic regression to modernize petrophysical analysis by bridging empirical knowledge with efficient, interpretable alternatives.
