Average Error: 0.1 → 0.1
Time: 48.7s
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 r718163 = x;
        double r718164 = y;
        double r718165 = r718163 * r718164;
        double r718166 = z;
        double r718167 = r718166 * r718166;
        double r718168 = r718165 + r718167;
        double r718169 = r718168 + r718167;
        double r718170 = r718169 + r718167;
        return r718170;
}
↓
double f(double x, double y, double z) {
        double r718171 = x;
        double r718172 = y;
        double r718173 = r718171 * r718172;
        double r718174 = z;
        double r718175 = r718174 * r718174;
        double r718176 = r718173 + r718175;
        double r718177 = r718176 + r718175;
        double r718178 = r718177 + r718175;
        return r718178;
}

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 2020047 
(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)))