The core idea does seem pretty cool. The paper is annoyingly wordy in a slop-machine-wrote-this way-- the author discloses as much. Lately I have been thinking about how functions (e.g. sin()) are actually implemented (did some baby level numerical integration stuff lately which made me curius.)

Also wonder: is this idea similar to Taylor polynomials?

eg it's obvious that eml(x,1) is exp(x)

So you first find formulas for subtraction, negation, multiplication, division, i, and 2, and then it's easy...

I dunno. The paper strikes me as crank. But what do I know.

"""
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, , and log has always required multiple distinct operations. Here we show that a single binary operator,

eml⁡(x,y)=exp⁡(x)−ln⁡(y),

together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, π, and i; arithmetic operations including +, −, ×, /, and exponentiation as well as the usual transcendental and algebraic functions. For example, ex=eml⁡(x,1), ln⁡x=eml⁡(1,eml⁡(eml⁡(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it [...]
"""

But in these days of machine learning hallucinations, I am a bit critical until an actual mathematician tells me it's correct...

Sorry...