Average Error: 15.4 → 0.1
Time: 3.1s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1585519.72489239089190959930419921875 \lor \neg \left(x \le 2.18193907154721243421121516618821356559 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1585519.72489239089190959930419921875 \lor \neg \left(x \le 2.18193907154721243421121516618821356559 \cdot 10^{-8}\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 r535640 = x;
        double r535641 = 2.0;
        double r535642 = r535640 * r535641;
        double r535643 = y;
        double r535644 = r535642 * r535643;
        double r535645 = r535640 - r535643;
        double r535646 = r535644 / r535645;
        return r535646;
}
↓
double f(double x, double y) {
        double r535647 = x;
        double r535648 = -1585519.724892391;
        bool r535649 = r535647 <= r535648;
        double r535650 = 2.1819390715472124e-08;
        bool r535651 = r535647 <= r535650;
        double r535652 = !r535651;
        bool r535653 = r535649 || r535652;
        double r535654 = 2.0;
        double r535655 = r535647 * r535654;
        double r535656 = y;
        double r535657 = r535647 - r535656;
        double r535658 = r535655 / r535657;
        double r535659 = r535658 * r535656;
        double r535660 = r535657 / r535656;
        double r535661 = r535655 / r535660;
        double r535662 = r535653 ? r535659 : r535661;
        return r535662;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.4
Target0.4
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1585519.724892391 or 2.1819390715472124e-08 < x

    1. Initial program 17.0

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

    3. Applied associate-/l*15.2

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

    5. Applied associate-/r/0.2

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

    if -1585519.724892391 < x < 2.1819390715472124e-08

    1. Initial program 13.7

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

    3. Applied associate-/l*0.0

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1585519.72489239089190959930419921875 \lor \neg \left(x \le 2.18193907154721243421121516618821356559 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 +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)))