Average Error: 15.4 → 0.1
Time: 1.5s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.2808867942706159 \cdot 10^{46}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;y \le 4.5816633026862325 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -7.2808867942706159 \cdot 10^{46}:\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\

\mathbf{elif}\;y \le 4.5816633026862325 \cdot 10^{-25}:\\
\;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\

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

\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)) {
		VAR = ((x * 2.0) * (y / (x - y)));
	} else {
		double VAR_1;
		if ((y <= 4.5816633026862325e-25)) {
			VAR_1 = (y / ((x - y) / (x * 2.0)));
		} else {
			VAR_1 = ((x * 2.0) / ((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

Original15.4
Target0.3
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -7.280886794270616e+46

    1. Initial program 19.0

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
    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-inv0.1

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

    6. Simplified0.1

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

    if -7.280886794270616e+46 < y < 4.5816633026862325e-25

    1. Initial program 14.0

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

    3. Applied *-commutative14.0

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

    4. Applied associate-/l*0.2

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

    if 4.5816633026862325e-25 < y

    1. Initial program 15.4

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

    3. Applied associate-/l*0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.2808867942706159 \cdot 10^{46}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;y \le 4.5816633026862325 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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)))