[2603.21852] All elementary functions from a single binary operator

A research paper introduces a single binary operator eml(x,y)=exp(x)-ln(y) that, combined with the constant 1, can generate all elementary functions used in scientific computing — including sin, cos, sqrt, log, arithmetic operations, and transcendental functions. Analogous to how NAND/NOR gates suffice for all Boolean logic, this EML operator provides a universal primitive for continuous mathematics. Discovered via exhaustive search, every expression in EML form becomes a binary tree of identical nodes with a trivially simple grammar (S -> 1 | eml(S,S)). The paper also demonstrates that this uniform structure enables gradient-based symbolic regression using EML trees as trainable circuits with the Adam optimizer, allowing exact recovery of closed-form elementary functions from numerical data at shallow tree depths.