Average Error: 15.3 → 0.2
Time: 3.7s
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 r551003 = x;
        double r551004 = 2.0;
        double r551005 = r551003 * r551004;
        double r551006 = y;
        double r551007 = r551005 * r551006;
        double r551008 = r551003 - r551006;
        double r551009 = r551007 / r551008;
        return r551009;
}
↓
double f(double x, double y) {
        double r551010 = y;
        double r551011 = -2.985649314254737e+16;
        bool r551012 = r551010 <= r551011;
        double r551013 = 2.1640309147455017e-67;
        bool r551014 = r551010 <= r551013;
        double r551015 = !r551014;
        bool r551016 = r551012 || r551015;
        double r551017 = x;
        double r551018 = 2.0;
        double r551019 = r551017 * r551018;
        double r551020 = r551017 - r551010;
        double r551021 = r551020 / r551010;
        double r551022 = r551019 / r551021;
        double r551023 = r551019 / r551020;
        double r551024 = r551023 * r551010;
        double r551025 = r551016 ? r551022 : r551024;
        return r551025;
}

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)))