Average Error: 0.1 → 0.1
Time: 6.8s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot y + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left(3 \cdot y\right) \cdot y + x \cdot x
double f(double x, double y) {
        double r8764654 = x;
        double r8764655 = r8764654 * r8764654;
        double r8764656 = y;
        double r8764657 = r8764656 * r8764656;
        double r8764658 = r8764655 + r8764657;
        double r8764659 = r8764658 + r8764657;
        double r8764660 = r8764659 + r8764657;
        return r8764660;
}
↓
double f(double x, double y) {
        double r8764661 = 3.0;
        double r8764662 = y;
        double r8764663 = r8764661 * r8764662;
        double r8764664 = r8764663 * r8764662;
        double r8764665 = x;
        double r8764666 = r8764665 * r8764665;
        double r8764667 = r8764664 + r8764666;
        return r8764667;
}

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

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

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 
(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)))