Average Error: 0.1 → 0.1
Time: 10.4s
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 r585832 = x;
        double r585833 = r585832 * r585832;
        double r585834 = y;
        double r585835 = r585834 * r585834;
        double r585836 = r585833 + r585835;
        double r585837 = r585836 + r585835;
        double r585838 = r585837 + r585835;
        return r585838;
}
↓
double f(double x, double y) {
        double r585839 = 3.0;
        double r585840 = y;
        double r585841 = r585839 * r585840;
        double r585842 = r585841 * r585840;
        double r585843 = x;
        double r585844 = r585843 * r585843;
        double r585845 = r585842 + r585844;
        return r585845;
}

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 2020042 
(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)))