Average Error: 15.1 → 0.2
Time: 4.0s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.73735157607842638 \cdot 10^{-55} \lor \neg \left(x \le 2.31015467420133914 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.73735157607842638 \cdot 10^{-55} \lor \neg \left(x \le 2.31015467420133914 \cdot 10^{-42}\right):\\
\;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\

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

\end{array}
double f(double x, double y) {
        double r446838 = x;
        double r446839 = 2.0;
        double r446840 = r446838 * r446839;
        double r446841 = y;
        double r446842 = r446840 * r446841;
        double r446843 = r446838 - r446841;
        double r446844 = r446842 / r446843;
        return r446844;
}
↓
double f(double x, double y) {
        double r446845 = x;
        double r446846 = -1.7373515760784264e-55;
        bool r446847 = r446845 <= r446846;
        double r446848 = 2.310154674201339e-42;
        bool r446849 = r446845 <= r446848;
        double r446850 = !r446849;
        bool r446851 = r446847 || r446850;
        double r446852 = y;
        double r446853 = r446845 - r446852;
        double r446854 = r446845 / r446853;
        double r446855 = 2.0;
        double r446856 = r446855 * r446852;
        double r446857 = r446854 * r446856;
        double r446858 = r446845 * r446855;
        double r446859 = r446853 / r446852;
        double r446860 = r446858 / r446859;
        double r446861 = r446851 ? r446857 : r446860;
        return r446861;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
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 x < -1.7373515760784264e-55 or 2.310154674201339e-42 < x

    1. Initial program 13.7

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

    3. Applied associate-/l*13.3

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

    5. Applied div-inv13.4

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

    6. Applied times-frac0.5

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

    7. Simplified0.4

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

    if -1.7373515760784264e-55 < x < 2.310154674201339e-42

    1. Initial program 17.0

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

    3. Applied associate-/l*0.0

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.73735157607842638 \cdot 10^{-55} \lor \neg \left(x \le 2.31015467420133914 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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)))