Average Error: 0.1 → 0.1
Time: 2.9s
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 r530923 = x;
        double r530924 = y;
        double r530925 = r530923 * r530924;
        double r530926 = z;
        double r530927 = r530926 * r530926;
        double r530928 = r530925 + r530927;
        double r530929 = r530928 + r530927;
        double r530930 = r530929 + r530927;
        return r530930;
}
↓
double f(double x, double y, double z) {
        double r530931 = x;
        double r530932 = y;
        double r530933 = r530931 * r530932;
        double r530934 = z;
        double r530935 = r530934 * r530934;
        double r530936 = r530933 + r530935;
        double r530937 = r530936 + r530935;
        double r530938 = r530937 + r530935;
        return r530938;
}

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 2019356 
(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)))