Re: EML: All elementary functions from a single operator

I kept scanning the paper for a table showing how to express each elementary function in terms of eml. I never found one. After that, my interest evaporated. It’s cute, I suppose; useful, I'm not convinced.
The “phylogenetic” tree of the elementary functions is a typesetting tour de force, but isn’t the English language already sufficiently weirded?
It might be amusing to see whether Maxima can simplify various arcane expressions in eml back to their elementary forms. And what about expressing the principal branches? That looks like a nightmare.


--Barton
________________________________
From: Stavros Macrakis <[email protected]>
Sent: Wednesday, April 15, 2026 1:17 PM
To: <[email protected]> <[email protected]>
Subject: [Maxima-discuss] EML: All elementary functions from a single operator

Caution: Non-NU Email

The physicist Andrzej Odrzywołek (adiunkt at Jagiellonian University),  announced<https://urldefense.com/v3/__https://arxiv.org/html/2603.21852v2__;!!PvXuogZ4sRB2p-tU!CA_SQ_a-ptqXUR52sYmTFsZPoqM1rv8G8RRMpX7n0iMb36Rdj7JVWac5EfgBxFPePSiC6rswnszt5fE$>:


 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://urldefense.com/v3/__https://www.theregister.com/2026/04/14/two_button_calculator/__;!!PvXuogZ4sRB2p-tU!CA_SQ_a-ptqXUR52sYmTFsZPoqM1rv8G8RRMpX7n0iMb36Rdj7JVWac5EfgBxFPePSiC6rsw8-BevUA$>.

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]<mailto:[email protected]>

https://arxiv.org/html/2603.21852v2#S0.SSx1.p1.7<https://urldefense.com/v3/__https://arxiv.org/html/2603.21852v2*S0.SSx1.p1.7__;Iw!!PvXuogZ4sRB2p-tU!CA_SQ_a-ptqXUR52sYmTFsZPoqM1rv8G8RRMpX7n0iMb36Rdj7JVWac5EfgBxFPePSiC6rsw0XFuLag$>

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