Average Error: 15.1 → 0.3
Time: 1.6s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.30256252647234854 \cdot 10^{-30} \lor \neg \left(x \le 1.16647711379078738 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.30256252647234854 \cdot 10^{-30} \lor \neg \left(x \le 1.16647711379078738 \cdot 10^{-74}\right):\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

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

\end{array}
double code(double x, double y) {
	return ((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((x <= -3.3025625264723485e-30) || !(x <= 1.1664771137907874e-74))) {
		VAR = ((double) (((double) (x / ((double) (x - y)))) * ((double) (y * 2.0))));
	} else {
		VAR = ((double) (((double) (x * 2.0)) * ((double) (y / ((double) (x - y))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.4
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 < -3.3025625264723485e-30 or 1.1664771137907874e-74 < x

    1. Initial program 14.1

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

    3. Applied associate-/l*13.1

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
    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-frac0.6

      \[\leadsto \color{blue}{\frac{x}{x - y} \cdot \frac{2}{\frac{1}{y}}}\]

    7. Simplified0.4

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

    if -3.3025625264723485e-30 < x < 1.1664771137907874e-74

    1. Initial program 16.5

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

    3. Applied *-un-lft-identity16.5

      \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]

    4. Applied times-frac0.0

      \[\leadsto \color{blue}{\frac{x \cdot 2}{1} \cdot \frac{y}{x - y}}\]

    5. Simplified0.0

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.30256252647234854 \cdot 10^{-30} \lor \neg \left(x \le 1.16647711379078738 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 
(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)))