Average Error: 15.1 → 0.3
Time: 1.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.163047387422238 \cdot 10^{43} \lor \neg \left(y \le 1.08841297465868926 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{\frac{x - y}{2 \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.163047387422238 \cdot 10^{43} \lor \neg \left(y \le 1.08841297465868926 \cdot 10^{-50}\right):\\
\;\;\;\;\frac{x}{\frac{x - y}{2 \cdot y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\

\end{array}
double code(double x, double y) {
	return (((x * 2.0) * y) / (x - y));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -4.163047387422238e+43) || !(y <= 1.0884129746586893e-50))) {
		VAR = (x / ((x - y) / (2.0 * y)));
	} else {
		VAR = (y / ((x - y) / (x * 2.0)));
	}
	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
Target0.3
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 y < -4.163047387422238e+43 or 1.0884129746586893e-50 < y

    1. Initial program 15.8

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

    3. Applied associate-*l*15.9

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

    4. Applied associate-/l*0.3

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

    if -4.163047387422238e+43 < y < 1.0884129746586893e-50

    1. Initial program 14.3

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

    3. Applied *-commutative14.3

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

    4. Applied associate-/l*0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.163047387422238 \cdot 10^{43} \lor \neg \left(y \le 1.08841297465868926 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{\frac{x - y}{2 \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020071 +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)))