There’s a fun paper showing that you can define all elementary functions using just two primitive operations: the constant 1, and the binary function eml(x, y) := e^x - log(y).

https://arxiv.org/abs/2603.21852

That’s a neat little result, which makes for some fun games.

What’s the simplest expression you can find that evaluates to your favourite constant?

The best I have found for 2 is:

eml(1, eml(eml(eml(1, eml(eml(1, eml(1, eml(1, 1))), 1)), eml(1, 1)), 1))