Average Error: 15.1 → 0.2
Time: 1.7s
Precision: binary64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -270744910897807.88 \lor \neg \left(y \leq 7.327974932373526 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -270744910897807.88 \lor \neg \left(y \leq 7.327974932373526 \cdot 10^{-57}\right):\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

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

\end{array}
(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))
↓
(FPCore (x y)
 :precision binary64
 (if (or (<= y -270744910897807.88) (not (<= y 7.327974932373526e-57)))
   (/ (* x 2.0) (/ (- x y) y))
   (* (/ x (- x y)) (* y 2.0))))
double code(double x, double y) {
	return (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)));
}
↓
double code(double x, double y) {
	double tmp;
	if (((y <= -270744910897807.88) || !(y <= 7.327974932373526e-57))) {
		tmp = (((double) (x * 2.0)) / (((double) (x - y)) / y));
	} else {
		tmp = ((double) ((x / ((double) (x - y))) * ((double) (y * 2.0))));
	}
	return tmp;
}

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
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x < 8.364504563556443 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -270744910897807.88 or 7.3279749323735261e-57 < y

    1. Initial program 15.1

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

    3. Applied associate-/l*_binary640.4

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

    if -270744910897807.88 < y < 7.3279749323735261e-57

    1. Initial program 15.1

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

    3. Applied associate-/l*_binary6416.4

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

    5. Applied div-inv_binary6416.5

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

    6. Applied times-frac_binary640.2

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

    7. Simplified0.0

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -270744910897807.88 \lor \neg \left(y \leq 7.327974932373526 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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)))