Average Error: 0.1 → 0.1
Time: 12.7s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[x \cdot y + \left(z \cdot z\right) \cdot 3\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
x \cdot y + \left(z \cdot z\right) \cdot 3
double f(double x, double y, double z) {
        double r506101 = x;
        double r506102 = y;
        double r506103 = r506101 * r506102;
        double r506104 = z;
        double r506105 = r506104 * r506104;
        double r506106 = r506103 + r506105;
        double r506107 = r506106 + r506105;
        double r506108 = r506107 + r506105;
        return r506108;
}
↓
double f(double x, double y, double z) {
        double r506109 = x;
        double r506110 = y;
        double r506111 = r506109 * r506110;
        double r506112 = z;
        double r506113 = r506112 * r506112;
        double r506114 = 3.0;
        double r506115 = r506113 * r506114;
        double r506116 = r506111 + r506115;
        return r506116;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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)))