\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]

↓

\[0\]

double f(double x, double y, double z) {
        double r8091 = x;
        double r8092 = y;
        double r8093 = r8091 + r8092;
        double r8094 = z;
        double r8095 = r8093 + r8094;
        double r8096 = r8092 + r8094;
        double r8097 = r8091 + r8096;
        double r8098 = r8095 - r8097;
        return r8098;
}

↓

double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r8099 = 0.0;
        return r8099;
}

\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)

↓

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 0.0
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
Simplified0
\[\leadsto \color{blue}{0}\]
Final simplification0
\[\leadsto 0\]

Reproduce

herbie shell --seed 2019102 
(FPCore (x y z)
  :name "Commute and associate"
  (- (+ (+ x y) z) (+ x (+ y z))))