Average Error: 15.3 → 0.2
Time: 4.2s
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 r512996 = x;
        double r512997 = 2.0;
        double r512998 = r512996 * r512997;
        double r512999 = y;
        double r513000 = r512998 * r512999;
        double r513001 = r512996 - r512999;
        double r513002 = r513000 / r513001;
        return r513002;
}
↓
double f(double x, double y) {
        double r513003 = y;
        double r513004 = -2.985649314254737e+16;
        bool r513005 = r513003 <= r513004;
        double r513006 = 2.1640309147455017e-67;
        bool r513007 = r513003 <= r513006;
        double r513008 = !r513007;
        bool r513009 = r513005 || r513008;
        double r513010 = x;
        double r513011 = 2.0;
        double r513012 = r513010 * r513011;
        double r513013 = r513010 - r513003;
        double r513014 = r513013 / r513003;
        double r513015 = r513012 / r513014;
        double r513016 = r513012 / r513013;
        double r513017 = r513016 * r513003;
        double r513018 = r513009 ? r513015 : r513017;
        return r513018;
}

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 +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)))