Average Error: 14.4 → 0.7
Time: 9.2s
Precision: 64
\[2 \cdot \frac{x \cdot y}{x - y}\]
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot x}{x - y} = -\infty:\\ \;\;\;\;\left(x \cdot \frac{y}{x - y}\right) \cdot 2\\ \mathbf{elif}\;\frac{y \cdot x}{x - y} \le -3.110153045338136 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \frac{y \cdot x}{x - y}\\ \mathbf{elif}\;\frac{y \cdot x}{x - y} \le -0.0:\\ \;\;\;\;\left(x \cdot \frac{y}{x - y}\right) \cdot 2\\ \mathbf{elif}\;\frac{y \cdot x}{x - y} \le 1.835830023822163 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \frac{y \cdot x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x - y}{y}} \cdot 2\\ \end{array}\]
2 \cdot \frac{x \cdot y}{x - y}
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot x}{x - y} = -\infty:\\
\;\;\;\;\left(x \cdot \frac{y}{x - y}\right) \cdot 2\\

\mathbf{elif}\;\frac{y \cdot x}{x - y} \le -3.110153045338136 \cdot 10^{-292}:\\
\;\;\;\;2 \cdot \frac{y \cdot x}{x - y}\\

\mathbf{elif}\;\frac{y \cdot x}{x - y} \le -0.0:\\
\;\;\;\;\left(x \cdot \frac{y}{x - y}\right) \cdot 2\\

\mathbf{elif}\;\frac{y \cdot x}{x - y} \le 1.835830023822163 \cdot 10^{-28}:\\
\;\;\;\;2 \cdot \frac{y \cdot x}{x - y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{x - y}{y}} \cdot 2\\

\end{array}
double f(double x, double y) {
        double r8684662 = 2.0;
        double r8684663 = x;
        double r8684664 = y;
        double r8684665 = r8684663 * r8684664;
        double r8684666 = r8684663 - r8684664;
        double r8684667 = r8684665 / r8684666;
        double r8684668 = r8684662 * r8684667;
        return r8684668;
}

double f(double x, double y) {
        double r8684669 = y;
        double r8684670 = x;
        double r8684671 = r8684669 * r8684670;
        double r8684672 = r8684670 - r8684669;
        double r8684673 = r8684671 / r8684672;
        double r8684674 = -inf.0;
        bool r8684675 = r8684673 <= r8684674;
        double r8684676 = r8684669 / r8684672;
        double r8684677 = r8684670 * r8684676;
        double r8684678 = 2.0;
        double r8684679 = r8684677 * r8684678;
        double r8684680 = -3.110153045338136e-292;
        bool r8684681 = r8684673 <= r8684680;
        double r8684682 = r8684678 * r8684673;
        double r8684683 = -0.0;
        bool r8684684 = r8684673 <= r8684683;
        double r8684685 = 1.835830023822163e-28;
        bool r8684686 = r8684673 <= r8684685;
        double r8684687 = r8684672 / r8684669;
        double r8684688 = r8684670 / r8684687;
        double r8684689 = r8684688 * r8684678;
        double r8684690 = r8684686 ? r8684682 : r8684689;
        double r8684691 = r8684684 ? r8684679 : r8684690;
        double r8684692 = r8684681 ? r8684682 : r8684691;
        double r8684693 = r8684675 ? r8684679 : r8684692;
        return r8684693;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if (/ (* x y) (- x y)) < -inf.0 or -3.110153045338136e-292 < (/ (* x y) (- x y)) < -0.0

    1. Initial program 54.4

      \[2 \cdot \frac{x \cdot y}{x - y}\]
    2. Using strategy rm
    3. Applied *-un-lft-identity54.4

      \[\leadsto 2 \cdot \frac{x \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]
    4. Applied times-frac2.1

      \[\leadsto 2 \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{y}{x - y}\right)}\]
    5. Simplified2.1

      \[\leadsto 2 \cdot \left(\color{blue}{x} \cdot \frac{y}{x - y}\right)\]

    if -inf.0 < (/ (* x y) (- x y)) < -3.110153045338136e-292 or -0.0 < (/ (* x y) (- x y)) < 1.835830023822163e-28

    1. Initial program 0.5

      \[2 \cdot \frac{x \cdot y}{x - y}\]

    if 1.835830023822163e-28 < (/ (* x y) (- x y))

    1. Initial program 26.3

      \[2 \cdot \frac{x \cdot y}{x - y}\]
    2. Using strategy rm
    3. Applied associate-/l*0.1

      \[\leadsto 2 \cdot \color{blue}{\frac{x}{\frac{x - y}{y}}}\]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x}{x - y} = -\infty:\\ \;\;\;\;\left(x \cdot \frac{y}{x - y}\right) \cdot 2\\ \mathbf{elif}\;\frac{y \cdot x}{x - y} \le -3.110153045338136 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \frac{y \cdot x}{x - y}\\ \mathbf{elif}\;\frac{y \cdot x}{x - y} \le -0.0:\\ \;\;\;\;\left(x \cdot \frac{y}{x - y}\right) \cdot 2\\ \mathbf{elif}\;\frac{y \cdot x}{x - y} \le 1.835830023822163 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \frac{y \cdot x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x - y}{y}} \cdot 2\\ \end{array}\]

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "2*((x*y)/(x-y))"
  (* 2 (/ (* x y) (- x y))))