\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -1.390909119607474 \cdot 10^{-45} \lor \neg \left(x \le 7.09985068380016666 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \left(y \cdot \frac{1}{x - y}\right)\\ \end{array}\]

\frac{\left(x \cdot 2\right) \cdot y}{x - y}

↓

\begin{array}{l}
\mathbf{if}\;x \le -1.390909119607474 \cdot 10^{-45} \lor \neg \left(x \le 7.09985068380016666 \cdot 10^{-27}\right):\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2\right) \cdot \left(y \cdot \frac{1}{x - y}\right)\\

\end{array}

double f(double x, double y) {
        double r489824 = x;
        double r489825 = 2.0;
        double r489826 = r489824 * r489825;
        double r489827 = y;
        double r489828 = r489826 * r489827;
        double r489829 = r489824 - r489827;
        double r489830 = r489828 / r489829;
        return r489830;
}

↓

double f(double x, double y) {
        double r489831 = x;
        double r489832 = -1.390909119607474e-45;
        bool r489833 = r489831 <= r489832;
        double r489834 = 7.099850683800167e-27;
        bool r489835 = r489831 <= r489834;
        double r489836 = !r489835;
        bool r489837 = r489833 || r489836;
        double r489838 = y;
        double r489839 = r489831 - r489838;
        double r489840 = r489831 / r489839;
        double r489841 = 2.0;
        double r489842 = r489838 * r489841;
        double r489843 = r489840 * r489842;
        double r489844 = r489831 * r489841;
        double r489845 = 1.0;
        double r489846 = r489845 / r489839;
        double r489847 = r489838 * r489846;
        double r489848 = r489844 * r489847;
        double r489849 = r489837 ? r489843 : r489848;
        return r489849;
}

Original	14.8
Target	0.4
Herbie	0.2

Derivation

Split input into 2 regimes
if x < -1.390909119607474e-45 or 7.099850683800167e-27 < x
1. Initial program 14.4
  \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied associate-/l*13.0
  \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
4. Using strategy rm
5. Applied div-inv13.2
  \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(x - y\right) \cdot \frac{1}{y}}}\]
6. Applied times-frac0.4
  \[\leadsto \color{blue}{\frac{x}{x - y} \cdot \frac{2}{\frac{1}{y}}}\]
7. Simplified0.3
  \[\leadsto \frac{x}{x - y} \cdot \color{blue}{\left(y \cdot 2\right)}\]
if -1.390909119607474e-45 < x < 7.099850683800167e-27
1. Initial program 15.4
  \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied *-un-lft-identity15.4
  \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]
4. Applied times-frac0.0
  \[\leadsto \color{blue}{\frac{x \cdot 2}{1} \cdot \frac{y}{x - y}}\]
5. Simplified0.0
  \[\leadsto \color{blue}{\left(x \cdot 2\right)} \cdot \frac{y}{x - y}\]
6. Using strategy rm
7. Applied div-inv0.2
  \[\leadsto \left(x \cdot 2\right) \cdot \color{blue}{\left(y \cdot \frac{1}{x - y}\right)}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.390909119607474 \cdot 10^{-45} \lor \neg \left(x \le 7.09985068380016666 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \left(y \cdot \frac{1}{x - y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +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)))

Error

Try it out

Target

Derivation

`if x < -1.390909119607474e-45 or 7.099850683800167e-27 < x`

`if -1.390909119607474e-45 < x < 7.099850683800167e-27`

Reproduce

In
Out