EML: All elementary functions from a single operator

The physicist Andrzej Odrzywołek (*adiunkt* at Jagiellonian University),
announced <https://arxiv.org/html/2603.21852v2>:

 a single binary operator, eml(x,y)=exp(x)-ln(y),  together with the
constant 1, generates the standard repertoire of a scientific calculator.

and compared *eml* to the Sheffer stroke (*nand*) as a universal operator,
in fact he calls it *EML Sheffer*. The intermediate results are in general
complex.

This has gotten some attention in the press, e.g., in *The Register
<https://www.theregister.com/2026/04/14/two_button_calculator/>*.

Let's assume that his central claim is true -- it doesn't seem implausible,
although I wonder whether his use of the principal branch runs into
problems.

Still, as far as I can tell, this has little interest for mathematics or
symbolic calculation. He claims two applications for it:

   1. analog computing "pure-EML form could possibly be implemented
   efficiently in FPGA or analog circuits."
   2. discovering closed-form expressions from data

For analog computing, the combination of *exp *and *log *in the formulas
means that intermediate results may have a large range of magnitudes, and
accuracy will be hard. EML requires complex arithmetic; he has no concrete
proposal on how to implement that in analog circuits -- perhaps as
magnitude/phase in an AC circuit? And even something as simple as *x*y* is
a 12-node network.

For discovering closed-form expressions from data points ("symbolic
regression"), he proposes using gradient-based optimizers (like Adam) to
train trees to recover closed-form expressions from numerical data, and
gives some examples. I am skeptical, because (a) it's not clear to me that
having one operator and deep trees is better than having many operators and
shallower trees; (b) combining *exp* and *log *is going to create
expressions that have large dynamic range and unstable behavior which I'd
think would be unsuitable for gradient-based optimization.

He also claims

 all the above difficulties (edge cases) are not much different from those
usually encountered in every kind of floating-point or symbolic computation.


Comments?

Does anyone see any value in this?

              -s

All elementary functions from a single operator
Andrzej Odrzywołek
Institute of Theoretical Physics, Jagiellonian University, 30-348 Krakow,
Poland
E-mail: [email protected]

https://arxiv.org/html/2603.21852v2#S0.SSx1.p1.7

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