Average Error: 0.1 → 0.1
Time: 7.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(3 \cdot z\right) \cdot z + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(3 \cdot z\right) \cdot z + x \cdot y
double f(double x, double y, double z) {
        double r26045856 = x;
        double r26045857 = y;
        double r26045858 = r26045856 * r26045857;
        double r26045859 = z;
        double r26045860 = r26045859 * r26045859;
        double r26045861 = r26045858 + r26045860;
        double r26045862 = r26045861 + r26045860;
        double r26045863 = r26045862 + r26045860;
        return r26045863;
}
↓
double f(double x, double y, double z) {
        double r26045864 = 3.0;
        double r26045865 = z;
        double r26045866 = r26045864 * r26045865;
        double r26045867 = r26045866 * r26045865;
        double r26045868 = x;
        double r26045869 = y;
        double r26045870 = r26045868 * r26045869;
        double r26045871 = r26045867 + r26045870;
        return r26045871;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3 \cdot {z}^{2} + x \cdot y}\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(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)))