Solve a specific number with expressions like (e/e+e/e) with no digits

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So this is only for fun really. I'm trying to solve a number with expressions like e/e = 1. This could work for any number really, but I'm trying to solve it only using expressions.

I want to do this using programming. Could be Javascript, Python, etc. I assume brute forcing my way is the best way to do this? Basically I want something like this:

Solve 4000
e/e = 1
(e/e + e/e) = 2
(e/e + e/e)^(e/e + e/e) = 4
(e/e + e/e)^(e/e + e/e + e/e + e/e) = 16

So "just like that" we have 16. If we then do:

((e/e + e/e)^(e/e + e/e + e/e + e/e))^(e/e + e/e + e/e)

We have 4096. If we then do:

((e/e + e/e)^(e/e + e/e + e/e + e/e))^(e/e + e/e + e/e) - ((e/e + e/e)^(e/e + e/e + e/e) * ((e/e + e/e + e/e) * (e/e + e/e + e/e + e/e))

We have.. tadaa, 4000. Basically I just extracted 96 from 4096 by doing 4096 - (12*8). Elegant? No. Fun? Extremely. Would doing this through brute force be possible? Remember, not a single digit was used.