xy = eml(eml(1, eml(eml(eml(eml(1, eml(eml(1, eml(1, x)), 1)), eml(1, eml(eml(1, eml(y, 1)), 1))), 1), 1)), 1)

From Table 4, I think addition is slightly more complicated?

More on topic:

> No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations.

I was taught that these were all hypergeometric functions. What distinction is being drawn here?

It's one of those facts that tends to blow minds when it's first encountered, I can see why one would name a company after it.

Although you also need to encode where to put the input.

The real question is what emoji to use for eml when written out.

This is a function from ℝ² to ℝ. It can't be its own inverse; what would that mean?

Elementary functions such as exponentiation, logarithms and trigonometric functions are the standard vocabulary of STEM education. Each comes with its own rules and a dedicated button on a scientific calculator;

What?

and 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

Yeah, this is done by using tables and series. His method does not actually facilitate the computation of these functions.

There is no such things as "continuous mathematics". Maybe he meant to say continuous function?

The whole thing comes off a gibberish or rediscovering something that already exists.

    e^ix = cos x + i sin x

    e^-ix = cos -x + i sin -x
          = cos x - i sin x

   e^ix + e^-ix = 2 cos x
   cos x = (e*ix - e^-ix) / 2

Multiplication, division, addition and subtraction are all straightforward. So are hyperbolic trig functions. All other trig functions can be derived as per above.

You can find this link on the right side of the arxiv page:

https://arxiv.org/src/2603.21852v2/anc/SupplementaryInformat...