Average Error: 0.1 → 0.1
Time: 34.2s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[3 \cdot \left(z \cdot z\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
3 \cdot \left(z \cdot z\right) + x \cdot y
double f(double x, double y, double z) {
        double r37605100 = x;
        double r37605101 = y;
        double r37605102 = r37605100 * r37605101;
        double r37605103 = z;
        double r37605104 = r37605103 * r37605103;
        double r37605105 = r37605102 + r37605104;
        double r37605106 = r37605105 + r37605104;
        double r37605107 = r37605106 + r37605104;
        return r37605107;
}
↓
double f(double x, double y, double z) {
        double r37605108 = 3.0;
        double r37605109 = z;
        double r37605110 = r37605109 * r37605109;
        double r37605111 = r37605108 * r37605110;
        double r37605112 = x;
        double r37605113 = y;
        double r37605114 = r37605112 * r37605113;
        double r37605115 = r37605111 + r37605114;
        return r37605115;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\left(z \cdot z\right) \cdot 3 + x \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \left(z \cdot z\right) + x \cdot y\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

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