Average Error: 14.9 → 0.3
Time: 2.5s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.12779910323974141 \cdot 10^{59} \lor \neg \left(x \le 4.14978199601705522 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.12779910323974141 \cdot 10^{59} \lor \neg \left(x \le 4.14978199601705522 \cdot 10^{-53}\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 r429540 = x;
        double r429541 = 2.0;
        double r429542 = r429540 * r429541;
        double r429543 = y;
        double r429544 = r429542 * r429543;
        double r429545 = r429540 - r429543;
        double r429546 = r429544 / r429545;
        return r429546;
}
↓
double f(double x, double y) {
        double r429547 = x;
        double r429548 = -5.127799103239741e+59;
        bool r429549 = r429547 <= r429548;
        double r429550 = 4.149781996017055e-53;
        bool r429551 = r429547 <= r429550;
        double r429552 = !r429551;
        bool r429553 = r429549 || r429552;
        double r429554 = 2.0;
        double r429555 = r429547 * r429554;
        double r429556 = y;
        double r429557 = r429547 - r429556;
        double r429558 = r429555 / r429557;
        double r429559 = r429558 * r429556;
        double r429560 = r429557 / r429556;
        double r429561 = r429555 / r429560;
        double r429562 = r429553 ? r429559 : r429561;
        return r429562;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
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 < -5.127799103239741e+59 or 4.149781996017055e-53 < x

    1. Initial program 16.2

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

    3. Applied associate-/l*15.1

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

    5. Applied associate-/r/0.3

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

    if -5.127799103239741e+59 < x < 4.149781996017055e-53

    1. Initial program 13.6

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

    3. Applied associate-/l*0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.12779910323974141 \cdot 10^{59} \lor \neg \left(x \le 4.14978199601705522 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 +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)))