Average Error: 0.1 → 0.1
Time: 17.6s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + \left(3 \cdot y\right) \cdot y\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
x \cdot x + \left(3 \cdot y\right) \cdot y
double f(double x, double y) {
        double r395891 = x;
        double r395892 = r395891 * r395891;
        double r395893 = y;
        double r395894 = r395893 * r395893;
        double r395895 = r395892 + r395894;
        double r395896 = r395895 + r395894;
        double r395897 = r395896 + r395894;
        return r395897;
}
↓
double f(double x, double y) {
        double r395898 = x;
        double r395899 = r395898 * r395898;
        double r395900 = 3.0;
        double r395901 = y;
        double r395902 = r395900 * r395901;
        double r395903 = r395902 * r395901;
        double r395904 = r395899 + r395903;
        return r395904;
}

Error

Bits error versus x

Bits error versus y

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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

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

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"
  :precision binary64

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

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