Average Error: 14.6 → 0.4
Time: 3.4s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.11960665332501271 \cdot 10^{35} \lor \neg \left(y \le 4.5875694303008083 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array}\]
\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):\\
\;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\

\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x \cdot 2}{x - 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 * y) / (x - y)));
	} else {
		temp = (y * ((x * 2.0) / (x - 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 associate-*l*14.3

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

    5. Applied times-frac0.7

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

    6. Simplified0.7

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

    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 *-un-lft-identity15.0

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

    4. Applied *-commutative15.0

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

    5. Applied times-frac0.1

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

    6. Simplified0.1

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

  4. Final simplification0.4

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

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)))