Average Error: 14.6 → 1.0
Time: 2.9s
Precision: binary64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -1.54048815934693065 \cdot 10^{-18} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -2.17408644625624733 \cdot 10^{-304} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 5.0368410606991103 \cdot 10^{-306}\right) \land \frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.13149732853840599 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -1.54048815934693065 \cdot 10^{-18} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -2.17408644625624733 \cdot 10^{-304} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 5.0368410606991103 \cdot 10^{-306}\right) \land \frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.13149732853840599 \cdot 10^{-112}\right):\\
\;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(x \cdot 2\right) \cdot 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 (((((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= -1.5404881593469307e-18) || !((((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= -2.1740864462562473e-304) || (!(((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= 5.03684106069911e-306) && (((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= 2.131497328538406e-112))))) {
		VAR = ((double) (x * ((double) (2.0 * ((double) (y / ((double) (x - y))))))));
	} else {
		VAR = ((double) (((double) (((double) (x * 2.0)) * 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

Original14.6
Target0.3
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (* x 2.0) y) (- x y)) < -1.54048815934693065e-18 or -2.17408644625624733e-304 < (/ (* (* x 2.0) y) (- x y)) < 5.0368410606991103e-306 or 2.13149732853840599e-112 < (/ (* (* x 2.0) y) (- x y))

    1. Initial program 30.0

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

    2. Simplified1.3

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

    if -1.54048815934693065e-18 < (/ (* (* x 2.0) y) (- x y)) < -2.17408644625624733e-304 or 5.0368410606991103e-306 < (/ (* (* x 2.0) y) (- x y)) < 2.13149732853840599e-112

    1. Initial program 0.7

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -1.54048815934693065 \cdot 10^{-18} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -2.17408644625624733 \cdot 10^{-304} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 5.0368410606991103 \cdot 10^{-306}\right) \land \frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 2.13149732853840599 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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)))