Average Error: 15.0 → 0.5
Time: 1.4s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.0904944677460728 \cdot 10^{64} \lor \neg \left(x \le 2.86704485106370398 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.0904944677460728 \cdot 10^{64} \lor \neg \left(x \le 2.86704485106370398 \cdot 10^{-84}\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 r509244 = x;
        double r509245 = 2.0;
        double r509246 = r509244 * r509245;
        double r509247 = y;
        double r509248 = r509246 * r509247;
        double r509249 = r509244 - r509247;
        double r509250 = r509248 / r509249;
        return r509250;
}
↓
double f(double x, double y) {
        double r509251 = x;
        double r509252 = -4.090494467746073e+64;
        bool r509253 = r509251 <= r509252;
        double r509254 = 2.867044851063704e-84;
        bool r509255 = r509251 <= r509254;
        double r509256 = !r509255;
        bool r509257 = r509253 || r509256;
        double r509258 = 2.0;
        double r509259 = r509251 * r509258;
        double r509260 = y;
        double r509261 = r509251 - r509260;
        double r509262 = r509259 / r509261;
        double r509263 = r509262 * r509260;
        double r509264 = r509251 / r509260;
        double r509265 = 1.0;
        double r509266 = r509264 - r509265;
        double r509267 = r509259 / r509266;
        double r509268 = r509257 ? r509263 : r509267;
        return r509268;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
Target0.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -4.090494467746073e+64 or 2.867044851063704e-84 < x

    1. Initial program 15.7

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

    3. Applied associate-/l*14.3

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

    5. Applied associate-/r/0.6

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

    if -4.090494467746073e+64 < x < 2.867044851063704e-84

    1. Initial program 14.3

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

    3. Applied associate-/l*0.4

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

    5. Applied div-sub0.4

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

    6. Simplified0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.0904944677460728 \cdot 10^{64} \lor \neg \left(x \le 2.86704485106370398 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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)))