Average Error: 0.0 → 0
Time: 4.6s
Precision: 64
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
↓
\[0\]
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
↓
0
double f(double x, double y, double z) {
        double r8788 = x;
        double r8789 = y;
        double r8790 = r8788 + r8789;
        double r8791 = z;
        double r8792 = r8790 + r8791;
        double r8793 = r8789 + r8791;
        double r8794 = r8788 + r8793;
        double r8795 = r8792 - r8794;
        return r8795;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r8796 = 0.0;
        return r8796;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))