Average Error: 0.1 → 0.1
Time: 3.5s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[z \cdot \left(z + \left(z + z\right)\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
z \cdot \left(z + \left(z + z\right)\right) + x \cdot y
double f(double x, double y, double z) {
        double r308815 = x;
        double r308816 = y;
        double r308817 = r308815 * r308816;
        double r308818 = z;
        double r308819 = r308818 * r308818;
        double r308820 = r308817 + r308819;
        double r308821 = r308820 + r308819;
        double r308822 = r308821 + r308819;
        return r308822;
}
↓
double f(double x, double y, double z) {
        double r308823 = z;
        double r308824 = r308823 + r308823;
        double r308825 = r308823 + r308824;
        double r308826 = r308823 * r308825;
        double r308827 = x;
        double r308828 = y;
        double r308829 = r308827 * r308828;
        double r308830 = r308826 + r308829;
        return r308830;
}

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. Using strategy rm

  3. Applied associate-+l+0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

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

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