Average Error: 0.1 → 0.1
Time: 8.5s
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 r418738 = x;
        double r418739 = y;
        double r418740 = r418738 * r418739;
        double r418741 = z;
        double r418742 = r418741 * r418741;
        double r418743 = r418740 + r418742;
        double r418744 = r418743 + r418742;
        double r418745 = r418744 + r418742;
        return r418745;
}
↓
double f(double x, double y, double z) {
        double r418746 = x;
        double r418747 = y;
        double r418748 = r418746 * r418747;
        double r418749 = z;
        double r418750 = r418749 * r418749;
        double r418751 = r418748 + r418750;
        double r418752 = r418751 + r418750;
        double r418753 = r418752 + r418750;
        return r418753;
}

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 2019195 
(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)))