Average Error: 15.3 → 0.2
Time: 1.7s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -29856493142547368 \lor \neg \left(y \le 2.1640309147455017 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -29856493142547368 \lor \neg \left(y \le 2.1640309147455017 \cdot 10^{-67}\right):\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

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

\end{array}
double f(double x, double y) {
        double r544654 = x;
        double r544655 = 2.0;
        double r544656 = r544654 * r544655;
        double r544657 = y;
        double r544658 = r544656 * r544657;
        double r544659 = r544654 - r544657;
        double r544660 = r544658 / r544659;
        return r544660;
}
↓
double f(double x, double y) {
        double r544661 = y;
        double r544662 = -2.985649314254737e+16;
        bool r544663 = r544661 <= r544662;
        double r544664 = 2.1640309147455017e-67;
        bool r544665 = r544661 <= r544664;
        double r544666 = !r544665;
        bool r544667 = r544663 || r544666;
        double r544668 = x;
        double r544669 = 2.0;
        double r544670 = r544668 * r544669;
        double r544671 = r544668 - r544661;
        double r544672 = r544671 / r544661;
        double r544673 = r544670 / r544672;
        double r544674 = r544670 / r544671;
        double r544675 = r544674 * r544661;
        double r544676 = r544667 ? r544673 : r544675;
        return r544676;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Split input into 2 regimes

  2. if y < -2.985649314254737e+16 or 2.1640309147455017e-67 < y

    1. Initial program 15.3

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

    3. Applied associate-/l*0.4

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

    if -2.985649314254737e+16 < y < 2.1640309147455017e-67

    1. Initial program 15.3

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

    3. Applied associate-/l*16.1

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

    5. Applied associate-/r/0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -29856493142547368 \lor \neg \left(y \le 2.1640309147455017 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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)))