Average Error: 0.1 → 0.1
Time: 19.3s
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 r608835 = x;
        double r608836 = y;
        double r608837 = r608835 * r608836;
        double r608838 = z;
        double r608839 = r608838 * r608838;
        double r608840 = r608837 + r608839;
        double r608841 = r608840 + r608839;
        double r608842 = r608841 + r608839;
        return r608842;
}
↓
double f(double x, double y, double z) {
        double r608843 = x;
        double r608844 = y;
        double r608845 = r608843 * r608844;
        double r608846 = z;
        double r608847 = r608846 * r608846;
        double r608848 = r608845 + r608847;
        double r608849 = r608848 + r608847;
        double r608850 = r608849 + r608847;
        return r608850;
}

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 2020047 
(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)))