Average Error: 0.1 → 0.1
Time: 7.2s
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 r436778 = x;
        double r436779 = r436778 * r436778;
        double r436780 = y;
        double r436781 = r436780 * r436780;
        double r436782 = r436779 + r436781;
        double r436783 = r436782 + r436781;
        double r436784 = r436783 + r436781;
        return r436784;
}
↓
double f(double x, double y) {
        double r436785 = x;
        double r436786 = r436785 * r436785;
        double r436787 = 3.0;
        double r436788 = y;
        double r436789 = r436787 * r436788;
        double r436790 = r436789 * r436788;
        double r436791 = r436786 + r436790;
        return r436791;
}

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

    \[\leadsto \color{blue}{x \cdot x + 3 \cdot \left(y \cdot y\right)}\]
  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 2019212 
(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)))