Hyperoperate

Define a tetration as
a(x) = 2^a(x-1)
a(-2) = -∞
a(-1) = 0
Also define a tetration as
f(x,y) = x^f(x,y-1)
f(x,-2) = -∞
f(x,-1) = 0
f(x,0) = 1
For more information, go to writer tool, use math break infinity or defining functions API.
Computing The Last Digits of TetrationL Numbers: https://www.desmos.com/calculator/vdvdvayzts 
Computing 2^(2^16) = 2^65536: Took under one second
Computing 3^(3^27): Took 1.140 seconds
Computing 4^(4^256): Took 10.899 seconds
Computing 5^(5^3125): Takes 130.51 seconds ~ 2.11 minutes
Computing 2^(2^65536): Takes 2884.10 seconds ~ 48.07 minutes
Let define “pentation, repeated tetration” as
g(x,y) = f(x,g(x,y-1))
g(x,0) = 1, g(x,-∞) = 0
For at nearly 100% accurate tetration at base e^1/e, use https://www.desmos.com/calculator/bppslip0j5
However, the graph is still work in progress, we are trying to increase accuracy at tetration of base e^1/e.
The link shows the graph of tetration, base of e^1/e. It shows a = e^1/e, it is based on fact that is nearly 100% accurate. There are still challenges that we need to overcome.
The Superlogarithm function at base e^1/e is also defined in the graph. Let we should define where z(x) = xa, where a is equal to e1/e. The yx is tetration, which is a repeated exponentiation, let x tetrated to y. Let define zi(x) = sloga(x), where slog is the inverse of tetration.