Proof that float multiplication is not associative

test.cc

#include <iostream>
#include <random>

using namespace std;

int main() {
  random_device dev;
  default_random_engine engine(dev());
  uniform_int_distribution<int> dist(0, 99999999);
  int x, y, z, count = 0;
  double dx, dy, dz;
  for (;;) {
    ++count;
    dx = x = dist(engine);
    dy = y = dist(engine);
    dz = z = dist(engine);
    if (dx * dy * dz != dz * dy * dx) {
      cout.precision(17);
      cout << x << ',' << y << ',' << z << " after " << count << " iterations." << endl;
      cout << "dx * dy * dz = " << dx * dy * dz << endl;
      cout << "dz * dy * dx = " << dz * dy * dx << endl;
      return 0;
    }
  }
}

Sample run:

98263439,98702733,16852388 after 1013 iterations.
dx * dy * dz = 1.6344912011976766e+23
dz * dy * dx = 1.6344912011976762e+23