Average Error: 15.5 → 0.2
Time: 1.8s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.5251409834127483 \cdot 10^{52} \lor \neg \left(y \le 1.226684745187438 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.5251409834127483 \cdot 10^{52} \lor \neg \left(y \le 1.226684745187438 \cdot 10^{-25}\right):\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

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

\end{array}
double f(double x, double y) {
        double r479850 = x;
        double r479851 = 2.0;
        double r479852 = r479850 * r479851;
        double r479853 = y;
        double r479854 = r479852 * r479853;
        double r479855 = r479850 - r479853;
        double r479856 = r479854 / r479855;
        return r479856;
}
↓
double f(double x, double y) {
        double r479857 = y;
        double r479858 = -2.5251409834127483e+52;
        bool r479859 = r479857 <= r479858;
        double r479860 = 1.226684745187438e-25;
        bool r479861 = r479857 <= r479860;
        double r479862 = !r479861;
        bool r479863 = r479859 || r479862;
        double r479864 = x;
        double r479865 = 2.0;
        double r479866 = r479864 * r479865;
        double r479867 = r479864 - r479857;
        double r479868 = r479867 / r479857;
        double r479869 = r479866 / r479868;
        double r479870 = r479864 / r479867;
        double r479871 = r479857 * r479865;
        double r479872 = r479870 * r479871;
        double r479873 = r479863 ? r479869 : r479872;
        return r479873;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.5251409834127483e+52 or 1.226684745187438e-25 < y

    1. Initial program 17.4

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

    3. Applied associate-/l*0.1

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

    if -2.5251409834127483e+52 < y < 1.226684745187438e-25

    1. Initial program 13.7

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

    3. Applied associate-/l*14.3

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
    4. Using strategy rm

    5. Applied div-inv14.4

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

    6. Applied times-frac0.4

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

    7. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.5251409834127483 \cdot 10^{52} \lor \neg \left(y \le 1.226684745187438 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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)))