Moreover, EML is complete in a way that your suggested function isn't: If you take a finite combination of basis functions, can it build periodic functions? Hardy proved over a century ago that real (+,-,/,*,exp,ln) can't do this (and answering the paper's unresolved question about similar real-valued functions in the negative). EML being able to build periodic functions is a lot less surprising for obvious reasons, but still pretty neat.
To represent something like sin(x) with f(x,y) requires infinite steps. Conversely, with eml you get an exact result in around 4 using identities and such.
One could argue that we do Taylor Series approximations on the hardware to represent trigonometric functions, but that highlights the key aspect of the eml approach. You can write a paper with those four steps that describes an exact model, here sin(x). And people can take that paper and optimize the result. This paper is about an auditable grammar that you can compute with.
You can reduce all Boolean logic to NAND, but that doesn't actually mean that semiconductor fabs translate their HDL to NAND gates, because it is possible to build complex gates that directly implement higher level operations in a single gate.
Your "cost of computation" objection can be easily resolved by adding more operators, which makes it boring from a research perspective.
Meanwhile the loss of expressivity can only be compensated by encoding algorithms directly into the expression tree. Your objection that an infinite series is a bad thing rings hollow, since you now introduce the concept of an infinitely sized expression tree. That sounds much more impractical than implementing an algorithm for the exponential and logarithm functions.
You don’t get to make up free ops, claim there is no cost in reality, and hand wave away reality.
There are infinitely many ways to do what the paper did. There’s no gain other than it’s pretty. It loses on every practical front to simply using current ops and architectures.
Conceptual elegance is worth something, isn't it? I don't mean just aesthetic pleasure, as in recreational mathematics, but there's often (not always) value in being able to succinctly describe a wide range of phenomena with a small number of primitives. It could open up new ways of understanding or working that wasn't possible before. Not saying this specific discovery fits the description, but it seems too early to dismiss the idea entirely based on its im/practicality compared to existing solutions.
Aren't there examples in the history of mathematics, where a new idea was criticized for being impractical, then later found to have applications or implications, possibly unexpected even to the person who discovered it?
IIRC a resistor in series to a capacitor does the trick, for exp.
If we’re making sloppy approximations to a tiny range of exp, then I too can do it with a few terms.