Average Error: 14.9 → 0.7
Time: 2.0s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.92710084194865545 \cdot 10^{143} \lor \neg \left(y \le 0.075799955277164155\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.92710084194865545 \cdot 10^{143} \lor \neg \left(y \le 0.075799955277164155\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 r519278 = x;
        double r519279 = 2.0;
        double r519280 = r519278 * r519279;
        double r519281 = y;
        double r519282 = r519280 * r519281;
        double r519283 = r519278 - r519281;
        double r519284 = r519282 / r519283;
        return r519284;
}
↓
double f(double x, double y) {
        double r519285 = y;
        double r519286 = -3.9271008419486554e+143;
        bool r519287 = r519285 <= r519286;
        double r519288 = 0.07579995527716415;
        bool r519289 = r519285 <= r519288;
        double r519290 = !r519289;
        bool r519291 = r519287 || r519290;
        double r519292 = x;
        double r519293 = 2.0;
        double r519294 = r519292 * r519293;
        double r519295 = r519292 - r519285;
        double r519296 = r519295 / r519285;
        double r519297 = r519294 / r519296;
        double r519298 = r519292 / r519295;
        double r519299 = r519285 * r519293;
        double r519300 = r519298 * r519299;
        double r519301 = r519291 ? r519297 : r519300;
        return r519301;
}

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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.9271008419486554e+143 or 0.07579995527716415 < y

    1. Initial program 18.7

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

    3. Applied associate-/l*0.1

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

    if -3.9271008419486554e+143 < y < 0.07579995527716415

    1. Initial program 12.5

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

    3. Applied associate-/l*12.1

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

    5. Applied div-inv12.2

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

    6. Applied times-frac1.3

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

    7. Simplified1.1

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.92710084194865545 \cdot 10^{143} \lor \neg \left(y \le 0.075799955277164155\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +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)))