EML operator demo

Odrzywołek (arXiv:2603.21852) showed that a single binary operator eml(x, y) = exp(x) − ln(y) plus the constant 1 can build every elementary function — the continuous analogue of NAND. These demos let you check the claim by hand.

① Same operator, 12 functions

Pick any function from the dropdown. Itʼs built entirely out of eml and 1. The green ✓ confirms the tree evaluates to the same value as Math.*.

functioninput x=

depth 3 · K 7 · paper K 7

eml tree → 0.91629073

Math reference → 0.91629073

✓ values match — this eml tree really is ln(x)

RPN program (7 tokens)

1,1,x,E,1,E,E

② Three-symbol calculator

A pocket calculator with only 1, x, and EML is Turing-complete over the elementary functions. Load a preset to see the paperʼs RPN programs run.

Only three symbols exist: 1, x, and EML. Load a preset to see the paperʼs programs, or build your own.

input x=

program (0 tokens)

empty

stack (top → bottom)

empty

result

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