Average Error: 15.0 → 0.8
Time: 5.9s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -5.79766759371720844 \cdot 10^{-68}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -6.832690604332275 \cdot 10^{-308}:\\ \;\;\;\;\frac{1}{\frac{x - y}{\left(x \cdot 2\right) \cdot y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 1.0974670677454873 \cdot 10^{-305}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.5491712206131216 \cdot 10^{-36}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \end{array}\]
\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 -5.79766759371720844 \cdot 10^{-68}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

\mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -6.832690604332275 \cdot 10^{-308}:\\
\;\;\;\;\frac{1}{\frac{x - y}{\left(x \cdot 2\right) \cdot y}}\\

\mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 1.0974670677454873 \cdot 10^{-305}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

\mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.5491712206131216 \cdot 10^{-36}:\\
\;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\

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

\end{array}
double f(double x, double y) {
        double r2835 = x;
        double r2836 = 2.0;
        double r2837 = r2835 * r2836;
        double r2838 = y;
        double r2839 = r2837 * r2838;
        double r2840 = r2835 - r2838;
        double r2841 = r2839 / r2840;
        return r2841;
}
↓
double f(double x, double y) {
        double r2842 = x;
        double r2843 = 2.0;
        double r2844 = r2842 * r2843;
        double r2845 = y;
        double r2846 = r2844 * r2845;
        double r2847 = r2842 - r2845;
        double r2848 = r2846 / r2847;
        double r2849 = -5.7976675937172084e-68;
        bool r2850 = r2848 <= r2849;
        double r2851 = r2847 / r2845;
        double r2852 = r2844 / r2851;
        double r2853 = -6.832690604332275e-308;
        bool r2854 = r2848 <= r2853;
        double r2855 = 1.0;
        double r2856 = r2847 / r2846;
        double r2857 = r2855 / r2856;
        double r2858 = 1.0974670677454873e-305;
        bool r2859 = r2848 <= r2858;
        double r2860 = 2.5491712206131216e-36;
        bool r2861 = r2848 <= r2860;
        double r2862 = r2845 / r2847;
        double r2863 = r2844 * r2862;
        double r2864 = r2861 ? r2848 : r2863;
        double r2865 = r2859 ? r2852 : r2864;
        double r2866 = r2854 ? r2857 : r2865;
        double r2867 = r2850 ? r2852 : r2866;
        return r2867;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
Target0.3
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ (* (* x 2.0) y) (- x y)) < -5.7976675937172084e-68 or -6.832690604332275e-308 < (/ (* (* x 2.0) y) (- x y)) < 1.0974670677454873e-305

    1. Initial program 34.7

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

    3. Applied associate-/l*0.9

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

    if -5.7976675937172084e-68 < (/ (* (* x 2.0) y) (- x y)) < -6.832690604332275e-308

    1. Initial program 0.8

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

    3. Applied clear-num1.0

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

    if 1.0974670677454873e-305 < (/ (* (* x 2.0) y) (- x y)) < 2.5491712206131216e-36

    1. Initial program 0.7

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

    if 2.5491712206131216e-36 < (/ (* (* x 2.0) y) (- x y))

    1. Initial program 27.3

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

    3. Applied *-un-lft-identity27.3

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

      \[\leadsto \color{blue}{\left(x \cdot 2\right)} \cdot \frac{y}{x - y}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -5.79766759371720844 \cdot 10^{-68}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -6.832690604332275 \cdot 10^{-308}:\\ \;\;\;\;\frac{1}{\frac{x - y}{\left(x \cdot 2\right) \cdot y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 1.0974670677454873 \cdot 10^{-305}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.5491712206131216 \cdot 10^{-36}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))