Evaluating the Exp-Minus-Log Sheffer Operator for Battery Characterization

Abstract

Odrzywolek (2026) recently introduced the Exp-Minus-Log (EML) operator eml (x, y) = exp(x) - ln(y) and proved constructively that, paired with the constant 1, it generates the entire scientific-calculator basis of elementary functions; in this sense EML is to continuous mathematics what NAND is to Boolean logic. We investigate whether such a uniform single-operator representation can accelerate either the forward simulation or the parameter identification of a six-branch RC equivalent-circuit model (6rc ECM) of a lithium-ion battery cell. We give the analytical EML rewrite of the discretized state-space recursion, derive an exact operation count, and quantify the depth penalty of the master-formula construction used for gradient-based symbolic regression. Our analysis shows that direct EML simulation is slower than the classical exponential-Euler scheme (a ~ 25x instruction overhead per RC branch), but EML-based parametrization offers a structurally complete, gradient-differentiable basis that competes favourably with non-parametric DRT deconvolution and metaheuristic optimisation when the cardinality of RC branches is unknown a priori. We conclude with a concrete recommendation: use EML only on the parametrization side of the 6rc workflow, keeping the classical recursion at runtime.