Average Error: 0.1 → 0.1
Time: 17.6s
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 r27733809 = x;
        double r27733810 = y;
        double r27733811 = r27733809 * r27733810;
        double r27733812 = z;
        double r27733813 = r27733812 * r27733812;
        double r27733814 = r27733811 + r27733813;
        double r27733815 = r27733814 + r27733813;
        double r27733816 = r27733815 + r27733813;
        return r27733816;
}
↓
double f(double x, double y, double z) {
        double r27733817 = x;
        double r27733818 = y;
        double r27733819 = r27733817 * r27733818;
        double r27733820 = z;
        double r27733821 = r27733820 * r27733820;
        double r27733822 = r27733819 + r27733821;
        double r27733823 = r27733822 + r27733821;
        double r27733824 = r27733823 + r27733821;
        return r27733824;
}

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 2019172 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

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