Average Error: 15.4 → 0.2
Time: 1.6s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.2808867942706159 \cdot 10^{46} \lor \neg \left(y \le 1.47192102037964442 \cdot 10^{-77}\right):\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -7.2808867942706159 \cdot 10^{46} \lor \neg \left(y \le 1.47192102037964442 \cdot 10^{-77}\right):\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\

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

\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 <= -7.280886794270616e+46) || !(y <= 1.4719210203796444e-77))) {
		VAR = ((x * 2.0) * (y / (x - y)));
	} else {
		VAR = ((x / (x - y)) * (y * 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

Original15.4
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 2 regimes

  2. if y < -7.280886794270616e+46 or 1.4719210203796444e-77 < y

    1. Initial program 15.9

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

    3. Applied *-un-lft-identity15.9

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    if -7.280886794270616e+46 < y < 1.4719210203796444e-77

    1. Initial program 15.0

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

    3. Applied associate-/l*15.2

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

    5. Applied div-inv15.4

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

    6. Applied times-frac0.3

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

    7. Simplified0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.2808867942706159 \cdot 10^{46} \lor \neg \left(y \le 1.47192102037964442 \cdot 10^{-77}\right):\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 +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)))