Most symbolic systems rely on multiple primitives.

Addition, multiplication, exponentials, logarithms — each plays a different role in structuring expressions.

But what happens if you force everything through a single operator?

This idea becomes concrete with the EML operator:

eml(x, y) = exp(x) − ln(y)

In theory, this operator can express all elementary functions.

But theory doesn’t tell us what happens in practice.

The Experiment

I built a small Python framework to explore this idea.

Instead of chasing universality, the focus is on structure:

What changes when symbolic expressions are forced into a single nonlinear primitive?

The framework:

rewrites SymPy expressions into EML trees

evaluates them back into standard form

measures structural complexity (depth, node count, nonlinear nodes)

includes a simple symbolic regression experiment

What Actually Changes?

A few things become immediately obvious:

• expression trees become significantly deeper

• nonlinear structure increases due to…