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@divbyzero@mathstodon.xyz

Post #1967911

2026-04-14 00:32 UTC

This is so cool! Given only the "exponential minus log" function, elm(x,y)=exp(x)-ln(y), and the constant 1, you can perform +, -, x, ÷, exp, ln, trig, powers, roots, etc. You can also obtain e and π! See https://arxiv.org/pdf/2603.21852 and https://arxiv.org/src/2603.21852v2/anc/SupplementaryInformation.pdf

Replies (5)

  • @danielmclaury@mathstodon.xyz 2026-04-14 03:31

    @divbyzero@mathstodon.xyz I was surprised by this statement, and then I read more carefully and saw that this is not f(x) = exp(x) - log(x), but rather f(x, y) = exp(x) - log(y), and at that point it's totally obvious. By setting y = 1 you recover the exponential function. By setting x = 0 you get 1 - log(y), which you can play around with a bit to extract log(y). And then you have exponentials and logs and subtraction and that's obviously enough to give you everything.

    Open ##2324823

  • @targetdrone@mastodon.social 2026-04-15 04:55

    @divbyzero@mathstodon.xyz Looks like the basis for constructing ever more elaborate slide rules.

    Open ##2324825

  • @Elizafox@social.treehouse.systems 2026-04-15 09:43

    @divbyzero@mathstodon.xyz this is a result that naturally falls out of exp-log constructions that have been known since Euler. The symbolic regression angle is interesting and novel. It’s less clear how this may be an improvement over existing exp-log circuits.

    Open ##2324826

  • @riley@toot.cat 2026-04-15 10:23

    @divbyzero@mathstodon.xyz Your table is cheating. If you can do the 'minus' part outside the 'eml', you really shouldn't define it to begin with, and just start from 'exp, ln, and basic arithmetics' as your building blocks.

    Open ##2324828

  • @cliffordheath@mastodon.social 2026-04-15 23:50

    @divbyzero@mathstodon.xyz What I find most exciting about this math discovery is that any calculation converted into this form will have a single simplest (canonical) representation which will be findable with lexical subsitutions. So it can simplify any expression to its simplest form. Every expression is canonically identified by an even-numbered sequence of binary digits. 1=1, 0=E(). This gives every possible calculation exactly one number which identifies it.

    Open ##2324829