Average Error: 0.1 → 0.1
Time: 12.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
double f(double x, double y, double z) {
        double r443769 = x;
        double r443770 = y;
        double r443771 = r443769 * r443770;
        double r443772 = z;
        double r443773 = r443772 * r443772;
        double r443774 = r443771 + r443773;
        double r443775 = r443774 + r443773;
        double r443776 = r443775 + r443773;
        return r443776;
}
↓
double f(double x, double y, double z) {
        double r443777 = x;
        double r443778 = y;
        double r443779 = r443777 * r443778;
        double r443780 = z;
        double r443781 = r443780 * r443780;
        double r443782 = r443779 + r443781;
        double r443783 = r443782 + r443781;
        double r443784 = r443783 + r443781;
        return r443784;
}

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

Target

Original0.1
Target0.1
Herbie0.1
\[\left(3 \cdot z\right) \cdot z + y \cdot x\]

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))