Average Error: 14.9 → 0.3
Time: 2.3s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.12779910323974141 \cdot 10^{59} \lor \neg \left(x \le 4.14978199601705522 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.12779910323974141 \cdot 10^{59} \lor \neg \left(x \le 4.14978199601705522 \cdot 10^{-53}\right):\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

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

\end{array}
double f(double x, double y) {
        double r582620 = x;
        double r582621 = 2.0;
        double r582622 = r582620 * r582621;
        double r582623 = y;
        double r582624 = r582622 * r582623;
        double r582625 = r582620 - r582623;
        double r582626 = r582624 / r582625;
        return r582626;
}
↓
double f(double x, double y) {
        double r582627 = x;
        double r582628 = -5.127799103239741e+59;
        bool r582629 = r582627 <= r582628;
        double r582630 = 4.149781996017055e-53;
        bool r582631 = r582627 <= r582630;
        double r582632 = !r582631;
        bool r582633 = r582629 || r582632;
        double r582634 = y;
        double r582635 = r582627 - r582634;
        double r582636 = r582627 / r582635;
        double r582637 = 2.0;
        double r582638 = r582634 * r582637;
        double r582639 = r582636 * r582638;
        double r582640 = r582627 * r582637;
        double r582641 = r582635 / r582634;
        double r582642 = r582640 / r582641;
        double r582643 = r582633 ? r582639 : r582642;
        return r582643;
}

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

Derivation

  1. Split input into 2 regimes

  2. if x < -5.127799103239741e+59 or 4.149781996017055e-53 < x

    1. Initial program 16.2

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

    3. Applied associate-/l*15.1

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

    5. Applied div-inv15.2

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

    6. Applied times-frac0.5

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

    7. Simplified0.3

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

    if -5.127799103239741e+59 < x < 4.149781996017055e-53

    1. Initial program 13.6

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

    3. Applied associate-/l*0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.12779910323974141 \cdot 10^{59} \lor \neg \left(x \le 4.14978199601705522 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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)))