Average Error: 15.4 → 0.8
Time: 1.6s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.9668118683841495 \cdot 10^{107} \lor \neg \left(x \le 1.3220637101071684 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.9668118683841495 \cdot 10^{107} \lor \neg \left(x \le 1.3220637101071684 \cdot 10^{-86}\right):\\
\;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\

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

\end{array}
double f(double x, double y) {
        double r476737 = x;
        double r476738 = 2.0;
        double r476739 = r476737 * r476738;
        double r476740 = y;
        double r476741 = r476739 * r476740;
        double r476742 = r476737 - r476740;
        double r476743 = r476741 / r476742;
        return r476743;
}
↓
double f(double x, double y) {
        double r476744 = x;
        double r476745 = -8.96681186838415e+107;
        bool r476746 = r476744 <= r476745;
        double r476747 = 1.3220637101071684e-86;
        bool r476748 = r476744 <= r476747;
        double r476749 = !r476748;
        bool r476750 = r476746 || r476749;
        double r476751 = 2.0;
        double r476752 = r476744 * r476751;
        double r476753 = y;
        double r476754 = r476744 - r476753;
        double r476755 = r476752 / r476754;
        double r476756 = r476755 * r476753;
        double r476757 = r476744 / r476753;
        double r476758 = 1.0;
        double r476759 = r476757 - r476758;
        double r476760 = r476752 / r476759;
        double r476761 = r476750 ? r476756 : r476760;
        return r476761;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.4
Target0.4
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 2 regimes

  2. if x < -8.96681186838415e+107 or 1.3220637101071684e-86 < x

    1. Initial program 16.1

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

    3. Applied associate-/l*15.3

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

    5. Applied associate-/r/0.9

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

    if -8.96681186838415e+107 < x < 1.3220637101071684e-86

    1. Initial program 14.7

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

    3. Applied associate-/l*0.7

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

    5. Applied div-sub0.7

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

    6. Simplified0.7

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.9668118683841495 \cdot 10^{107} \lor \neg \left(x \le 1.3220637101071684 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 +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)))