Average Error: 14.9 → 0.6
Time: 11.3s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -3.302272323166789625129135265296185343759 \cdot 10^{-28}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -5.298932597959136209382922379774980860889 \cdot 10^{-305}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -0.0:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.187968701250411981151631046847998371838 \cdot 10^{-44}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -3.302272323166789625129135265296185343759 \cdot 10^{-28}:\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\

\mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -5.298932597959136209382922379774980860889 \cdot 10^{-305}:\\
\;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\

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

\mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.187968701250411981151631046847998371838 \cdot 10^{-44}:\\
\;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\

\end{array}
double f(double x, double y) {
        double r365730 = x;
        double r365731 = 2.0;
        double r365732 = r365730 * r365731;
        double r365733 = y;
        double r365734 = r365732 * r365733;
        double r365735 = r365730 - r365733;
        double r365736 = r365734 / r365735;
        return r365736;
}
↓
double f(double x, double y) {
        double r365737 = x;
        double r365738 = 2.0;
        double r365739 = r365737 * r365738;
        double r365740 = y;
        double r365741 = r365739 * r365740;
        double r365742 = r365737 - r365740;
        double r365743 = r365741 / r365742;
        double r365744 = -3.3022723231667896e-28;
        bool r365745 = r365743 <= r365744;
        double r365746 = r365740 / r365742;
        double r365747 = r365739 * r365746;
        double r365748 = -5.298932597959136e-305;
        bool r365749 = r365743 <= r365748;
        double r365750 = -0.0;
        bool r365751 = r365743 <= r365750;
        double r365752 = 2.187968701250412e-44;
        bool r365753 = r365743 <= r365752;
        double r365754 = r365737 / r365740;
        double r365755 = 1.0;
        double r365756 = r365754 - r365755;
        double r365757 = r365739 / r365756;
        double r365758 = r365753 ? r365743 : r365757;
        double r365759 = r365751 ? r365747 : r365758;
        double r365760 = r365749 ? r365743 : r365759;
        double r365761 = r365745 ? r365747 : r365760;
        return r365761;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.3
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (* x 2.0) y) (- x y)) < -3.3022723231667896e-28 or -5.298932597959136e-305 < (/ (* (* x 2.0) y) (- x y)) < -0.0

    1. Initial program 40.2

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity40.2

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

    4. Applied times-frac0.3

      \[\leadsto \color{blue}{\frac{x \cdot 2}{1} \cdot \frac{y}{x - y}}\]

    5. Simplified0.3

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

    if -3.3022723231667896e-28 < (/ (* (* x 2.0) y) (- x y)) < -5.298932597959136e-305 or -0.0 < (/ (* (* x 2.0) y) (- x y)) < 2.187968701250412e-44

    1. Initial program 0.7

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

    if 2.187968701250412e-44 < (/ (* (* x 2.0) y) (- x y))

    1. Initial program 24.7

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
    2. Using strategy rm

    3. Applied associate-/l*0.5

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]

    4. Simplified0.5

      \[\leadsto \frac{x \cdot 2}{\color{blue}{\frac{x}{y} - 1}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -3.302272323166789625129135265296185343759 \cdot 10^{-28}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -5.298932597959136209382922379774980860889 \cdot 10^{-305}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -0.0:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.187968701250411981151631046847998371838 \cdot 10^{-44}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))