Average Error: 0 → 0
Time: 10.6s
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 r8725 = x;
        double r8726 = y;
        double r8727 = r8725 + r8726;
        double r8728 = z;
        double r8729 = r8727 + r8728;
        double r8730 = r8726 + r8728;
        double r8731 = r8725 + r8730;
        double r8732 = r8729 - r8731;
        return r8732;
}
↓
double f(double x, double y, double z) {
        double r8733 = x;
        double r8734 = y;
        double r8735 = r8733 + r8734;
        double r8736 = z;
        double r8737 = r8735 + r8736;
        double r8738 = r8734 + r8736;
        double r8739 = r8733 + r8738;
        double r8740 = r8737 - r8739;
        return r8740;
}

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

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

  2. Final simplification0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))