Average Error: 0.1 → 0.1
Time: 18.7s
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 r1034834 = x;
        double r1034835 = y;
        double r1034836 = r1034834 * r1034835;
        double r1034837 = z;
        double r1034838 = r1034837 * r1034837;
        double r1034839 = r1034836 + r1034838;
        double r1034840 = r1034839 + r1034838;
        double r1034841 = r1034840 + r1034838;
        return r1034841;
}
↓
double f(double x, double y, double z) {
        double r1034842 = x;
        double r1034843 = y;
        double r1034844 = r1034842 * r1034843;
        double r1034845 = z;
        double r1034846 = r1034845 * r1034845;
        double r1034847 = r1034844 + r1034846;
        double r1034848 = r1034847 + r1034846;
        double r1034849 = r1034848 + r1034846;
        return r1034849;
}

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 2019303 
(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)))