Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[3 \cdot \left(z \cdot z\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
3 \cdot \left(z \cdot z\right) + x \cdot y
double f(double x, double y, double z) {
        double r23082543 = x;
        double r23082544 = y;
        double r23082545 = r23082543 * r23082544;
        double r23082546 = z;
        double r23082547 = r23082546 * r23082546;
        double r23082548 = r23082545 + r23082547;
        double r23082549 = r23082548 + r23082547;
        double r23082550 = r23082549 + r23082547;
        return r23082550;
}
↓
double f(double x, double y, double z) {
        double r23082551 = 3.0;
        double r23082552 = z;
        double r23082553 = r23082552 * r23082552;
        double r23082554 = r23082551 * r23082553;
        double r23082555 = x;
        double r23082556 = y;
        double r23082557 = r23082555 * r23082556;
        double r23082558 = r23082554 + r23082557;
        return r23082558;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\left(z \cdot z\right) \cdot 3 + x \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \left(z \cdot z\right) + x \cdot y\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))