Average Error: 0.1 → 0.1
Time: 4.1s
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 r622928 = x;
        double r622929 = y;
        double r622930 = r622928 * r622929;
        double r622931 = z;
        double r622932 = r622931 * r622931;
        double r622933 = r622930 + r622932;
        double r622934 = r622933 + r622932;
        double r622935 = r622934 + r622932;
        return r622935;
}
↓
double f(double x, double y, double z) {
        double r622936 = x;
        double r622937 = y;
        double r622938 = r622936 * r622937;
        double r622939 = z;
        double r622940 = r622939 * r622939;
        double r622941 = r622938 + r622940;
        double r622942 = r622941 + r622940;
        double r622943 = r622942 + r622940;
        return r622943;
}

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 2020100 +o rules:numerics
(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)))