Average Error: 0.0 → 0.0
Time: 1.6s
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 r731 = x;
        double r732 = y;
        double r733 = r731 + r732;
        double r734 = z;
        double r735 = r733 + r734;
        double r736 = r732 + r734;
        double r737 = r731 + r736;
        double r738 = r735 - r737;
        return r738;
}
↓
double f(double x, double y, double z) {
        double r739 = x;
        double r740 = y;
        double r741 = r739 + r740;
        double r742 = z;
        double r743 = r741 + r742;
        double r744 = r740 + r742;
        double r745 = r739 + r744;
        double r746 = r743 - r745;
        return r746;
}

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 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))