How can I get an approximate answer to this simple exponentiation algorithm so the end result fits in memory?

I ve a loop applying

y_tmp=y
y=x
x=y_tmp+((x+c[i])^5)%21888242871839275222246405745257275088548364400416034343698204186575808495617

219 times, where `x` and `y` are longint inputs and `c` is a static array of 220 255-bit integers. I would like to find an input `y` given an input and an ouput `x`.

A would be possibility is to not apply the modulus and this would allows plotting a curve without applying the modulus with varying `y` as input (since applying the modulus at the end is the same and in my case I can get the non reduced output for which I want to find a `y` value). But of course the problem is doing so means the end result to be drawn on `x` don t fit in any computer memory.

What alternative strategy can I use to get an approximation while minimizing the amount of memory needed to plot the final result?