Average Error: 0.1 → 0.1
Time: 17.1s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
double f(double x, double y, double z) {
        double r313837 = x;
        double r313838 = y;
        double r313839 = r313837 * r313838;
        double r313840 = z;
        double r313841 = r313840 * r313840;
        double r313842 = r313839 + r313841;
        double r313843 = r313842 + r313841;
        double r313844 = r313843 + r313841;
        return r313844;
}
↓
double f(double x, double y, double z) {
        double r313845 = x;
        double r313846 = y;
        double r313847 = r313845 * r313846;
        double r313848 = z;
        double r313849 = r313848 * r313848;
        double r313850 = r313847 + r313849;
        double r313851 = r313850 + r313849;
        double r313852 = r313851 + r313849;
        return r313852;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))