Average Error: 0.1 → 0.1
Time: 9.9s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[3 \cdot \left(y \cdot y\right) + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
3 \cdot \left(y \cdot y\right) + x \cdot x
double f(double x, double y) {
        double r22717733 = x;
        double r22717734 = r22717733 * r22717733;
        double r22717735 = y;
        double r22717736 = r22717735 * r22717735;
        double r22717737 = r22717734 + r22717736;
        double r22717738 = r22717737 + r22717736;
        double r22717739 = r22717738 + r22717736;
        return r22717739;
}
↓
double f(double x, double y) {
        double r22717740 = 3.0;
        double r22717741 = y;
        double r22717742 = r22717741 * r22717741;
        double r22717743 = r22717740 * r22717742;
        double r22717744 = x;
        double r22717745 = r22717744 * r22717744;
        double r22717746 = r22717743 + r22717745;
        return r22717746;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot x + y \cdot \left(y + \left(y + y\right)\right)\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"

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

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