Average Error: 15.4 → 0.1
Time: 2.9s
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 r525561 = x;
        double r525562 = 2.0;
        double r525563 = r525561 * r525562;
        double r525564 = y;
        double r525565 = r525563 * r525564;
        double r525566 = r525561 - r525564;
        double r525567 = r525565 / r525566;
        return r525567;
}
↓
double f(double x, double y) {
        double r525568 = x;
        double r525569 = -1585519.724892391;
        bool r525570 = r525568 <= r525569;
        double r525571 = 2.1819390715472124e-08;
        bool r525572 = r525568 <= r525571;
        double r525573 = !r525572;
        bool r525574 = r525570 || r525573;
        double r525575 = 2.0;
        double r525576 = r525568 * r525575;
        double r525577 = y;
        double r525578 = r525568 - r525577;
        double r525579 = r525576 / r525578;
        double r525580 = r525579 * r525577;
        double r525581 = r525578 / r525577;
        double r525582 = r525576 / r525581;
        double r525583 = r525574 ? r525580 : r525582;
        return r525583;
}

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 
(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)))