No, you have a chaotic system. Each iteration depends on the bitwise details of the previous iteration.
It is possible to calculate the algebraic iteration to any given number of steps in terms of the original inputs, getting out more complicated formulas each step, but the rounding that takes place at each individual step turns out to be important to the long-term outcome, and the algebraic formulas for multiple steps will not reproduce that round-off the same way.
Example: after two iterations, the new y is
w21/(exp(3 - 8/(exp(- w21/(exp(-x) + 1) - 6/(exp(-z) + 1) - 4) + 1)) + 1) + 6/(exp(3 - 8/(exp(- w21/(exp(-x) + 1) - 6/(exp(-z) + 1) - 4) + 1)) + 1) + 4
where those are the initial x, z values in the formula.
Your system immediately loses its original y coordinate, by the way: the original y coordinate plays no role in the system.