Average Error: 0.1 → 0.1
Time: 13.1s
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 r35796870 = x;
        double r35796871 = r35796870 * r35796870;
        double r35796872 = y;
        double r35796873 = r35796872 * r35796872;
        double r35796874 = r35796871 + r35796873;
        double r35796875 = r35796874 + r35796873;
        double r35796876 = r35796875 + r35796873;
        return r35796876;
}
↓
double f(double x, double y) {
        double r35796877 = 3.0;
        double r35796878 = y;
        double r35796879 = r35796878 * r35796878;
        double r35796880 = r35796877 * r35796879;
        double r35796881 = x;
        double r35796882 = r35796881 * r35796881;
        double r35796883 = r35796880 + r35796882;
        return r35796883;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))