Average Error: 14.6 → 0.4
Time: 2.4s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.11960665332501271 \cdot 10^{35} \lor \neg \left(y \le 4.5875694303008083 \cdot 10^{-84}\right):\\ \;\;\;\;\left(x \cdot 2\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{x - y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -7.11960665332501271 \cdot 10^{35} \lor \neg \left(y \le 4.5875694303008083 \cdot 10^{-84}\right):\\
\;\;\;\;\left(x \cdot 2\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{x - y}\right)\right)\\

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

\end{array}
double code(double x, double y) {
	return (((x * 2.0) * y) / (x - y));
}
↓
double code(double x, double y) {
	double temp;
	if (((y <= -7.119606653325013e+35) || !(y <= 4.587569430300808e-84))) {
		temp = ((x * 2.0) * log1p(expm1((y / (x - y)))));
	} else {
		temp = (((x * 2.0) / (x - y)) * y);
	}
	return temp;
}

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

Derivation

  1. Split input into 2 regimes

  2. if y < -7.119606653325013e+35 or 4.587569430300808e-84 < y

    1. Initial program 14.3

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

    3. Applied *-un-lft-identity14.3

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    7. Applied log1p-expm1-u0.6

      \[\leadsto \left(x \cdot 2\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{x - y}\right)\right)}\]

    if -7.119606653325013e+35 < y < 4.587569430300808e-84

    1. Initial program 15.0

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

    3. Applied associate-/l*16.0

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

    5. Applied associate-/r/0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.11960665332501271 \cdot 10^{35} \lor \neg \left(y \le 4.5875694303008083 \cdot 10^{-84}\right):\\ \;\;\;\;\left(x \cdot 2\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{x - y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 +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)))