Average Error: 14.8 → 0.2
Time: 1.6s
Precision: binary64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -666584851557.733765:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \mathbf{elif}\;y \le 5.69001529938029932 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -666584851557.733765:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\

\mathbf{elif}\;y \le 5.69001529938029932 \cdot 10^{-64}:\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{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 ((y <= -666584851557.7338)) {
		VAR = ((double) (((double) (x * 2.0)) / ((double) (((double) (x / y)) - 1.0))));
	} else {
		double VAR_1;
		if ((y <= 5.690015299380299e-64)) {
			VAR_1 = ((double) (((double) (x / ((double) (x - y)))) * ((double) (y * 2.0))));
		} else {
			VAR_1 = ((double) (((double) (x * 2.0)) / ((double) (((double) (x - y)) / y))));
		}
		VAR = VAR_1;
	}
	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

Original14.8
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -666584851557.733765

    1. Initial program 16.6

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

    3. Applied associate-/l*0.1

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

    5. Applied div-sub0.1

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

    6. Simplified0.1

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

    if -666584851557.733765 < y < 5.69001529938029932e-64

    1. Initial program 14.8

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

    3. Applied associate-/l*15.6

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

    5. Applied div-inv15.8

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

    6. Applied times-frac0.2

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

    7. Simplified0.0

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

    if 5.69001529938029932e-64 < y

    1. Initial program 13.6

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

    3. Applied associate-/l*0.6

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -666584851557.733765:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} - 1}\\ \mathbf{elif}\;y \le 5.69001529938029932 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 8.364504563556443e+16) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))