Average Error: 15.4 → 0.3
Time: 1.7s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -95380968.4142476171 \lor \neg \left(x \le 1.64772115240192995 \cdot 10^{69}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -95380968.4142476171 \lor \neg \left(x \le 1.64772115240192995 \cdot 10^{69}\right):\\
\;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\

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

\end{array}
double f(double x, double y) {
        double r498281 = x;
        double r498282 = 2.0;
        double r498283 = r498281 * r498282;
        double r498284 = y;
        double r498285 = r498283 * r498284;
        double r498286 = r498281 - r498284;
        double r498287 = r498285 / r498286;
        return r498287;
}
↓
double f(double x, double y) {
        double r498288 = x;
        double r498289 = -95380968.41424762;
        bool r498290 = r498288 <= r498289;
        double r498291 = 1.64772115240193e+69;
        bool r498292 = r498288 <= r498291;
        double r498293 = !r498292;
        bool r498294 = r498290 || r498293;
        double r498295 = 2.0;
        double r498296 = r498288 * r498295;
        double r498297 = y;
        double r498298 = r498288 - r498297;
        double r498299 = r498296 / r498298;
        double r498300 = r498299 * r498297;
        double r498301 = r498298 / r498297;
        double r498302 = r498296 / r498301;
        double r498303 = r498294 ? r498300 : r498302;
        return r498303;
}

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
Target0.3
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 < -95380968.41424762 or 1.64772115240193e+69 < x

    1. Initial program 18.4

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

    3. Applied associate-/l*16.2

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

    5. Applied associate-/r/0.1

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

    if -95380968.41424762 < x < 1.64772115240193e+69

    1. Initial program 13.0

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

    3. Applied associate-/l*0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -95380968.4142476171 \lor \neg \left(x \le 1.64772115240192995 \cdot 10^{69}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(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)))