Average Error: 0.1 → 0.1
Time: 11.9s
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 r379907 = x;
        double r379908 = y;
        double r379909 = r379907 * r379908;
        double r379910 = z;
        double r379911 = r379910 * r379910;
        double r379912 = r379909 + r379911;
        double r379913 = r379912 + r379911;
        double r379914 = r379913 + r379911;
        return r379914;
}
↓
double f(double x, double y, double z) {
        double r379915 = x;
        double r379916 = y;
        double r379917 = r379915 * r379916;
        double r379918 = z;
        double r379919 = r379918 * r379918;
        double r379920 = r379917 + r379919;
        double r379921 = r379920 + r379919;
        double r379922 = r379921 + r379919;
        return r379922;
}

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 2019305 
(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)))