Average Error: 0.1 → 0.1
Time: 9.2s
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 r23569148 = x;
        double r23569149 = y;
        double r23569150 = r23569148 * r23569149;
        double r23569151 = z;
        double r23569152 = r23569151 * r23569151;
        double r23569153 = r23569150 + r23569152;
        double r23569154 = r23569153 + r23569152;
        double r23569155 = r23569154 + r23569152;
        return r23569155;
}
↓
double f(double x, double y, double z) {
        double r23569156 = x;
        double r23569157 = y;
        double r23569158 = r23569156 * r23569157;
        double r23569159 = z;
        double r23569160 = r23569159 * r23569159;
        double r23569161 = 3.0;
        double r23569162 = r23569160 * r23569161;
        double r23569163 = r23569158 + r23569162;
        return r23569163;
}

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 2019174 
(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)))