Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
↓
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
↓
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
double f(double x, double y, double z) {
        double r8639 = x;
        double r8640 = y;
        double r8641 = r8639 + r8640;
        double r8642 = z;
        double r8643 = r8641 + r8642;
        double r8644 = r8640 + r8642;
        double r8645 = r8639 + r8644;
        double r8646 = r8643 - r8645;
        return r8646;
}
↓
double f(double x, double y, double z) {
        double r8647 = x;
        double r8648 = y;
        double r8649 = r8647 + r8648;
        double r8650 = z;
        double r8651 = r8649 + r8650;
        double r8652 = r8648 + r8650;
        double r8653 = r8647 + r8652;
        double r8654 = r8651 - r8653;
        return r8654;
}

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 simplification0.0

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

Reproduce

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