Average Error: 0.1 → 0.1
Time: 11.0s
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 r1125652 = x;
        double r1125653 = y;
        double r1125654 = r1125652 * r1125653;
        double r1125655 = z;
        double r1125656 = r1125655 * r1125655;
        double r1125657 = r1125654 + r1125656;
        double r1125658 = r1125657 + r1125656;
        double r1125659 = r1125658 + r1125656;
        return r1125659;
}
↓
double f(double x, double y, double z) {
        double r1125660 = x;
        double r1125661 = y;
        double r1125662 = r1125660 * r1125661;
        double r1125663 = z;
        double r1125664 = r1125663 * r1125663;
        double r1125665 = r1125662 + r1125664;
        double r1125666 = r1125665 + r1125664;
        double r1125667 = r1125666 + r1125664;
        return r1125667;
}

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)))