Average Error: 7.8 → 0.4
Time: 10.7s
Precision: 64
$\frac{2 \cdot x}{\frac{x - y}{y}}$
$\begin{array}{l} \mathbf{if}\;x \le -5.091827858905314 \cdot 10^{+93}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \le 1.71649334501874 \cdot 10^{-21}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}$
\frac{2 \cdot x}{\frac{x - y}{y}}
\begin{array}{l}
\mathbf{if}\;x \le -5.091827858905314 \cdot 10^{+93}:\\
\;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\

\mathbf{elif}\;x \le 1.71649334501874 \cdot 10^{-21}:\\
\;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\

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

\end{array}
double f(double x, double y) {
double r9054540 = 2.0;
double r9054541 = x;
double r9054542 = r9054540 * r9054541;
double r9054543 = y;
double r9054544 = r9054541 - r9054543;
double r9054545 = r9054544 / r9054543;
double r9054546 = r9054542 / r9054545;
return r9054546;
}


double f(double x, double y) {
double r9054547 = x;
double r9054548 = -5.091827858905314e+93;
bool r9054549 = r9054547 <= r9054548;
double r9054550 = 2.0;
double r9054551 = r9054550 * r9054547;
double r9054552 = y;
double r9054553 = r9054547 - r9054552;
double r9054554 = r9054551 / r9054553;
double r9054555 = r9054554 * r9054552;
double r9054556 = 1.71649334501874e-21;
bool r9054557 = r9054547 <= r9054556;
double r9054558 = r9054552 / r9054553;
double r9054559 = r9054551 * r9054558;
double r9054560 = r9054557 ? r9054559 : r9054555;
double r9054561 = r9054549 ? r9054555 : r9054560;
return r9054561;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if x < -5.091827858905314e+93 or 1.71649334501874e-21 < x

1. Initial program 16.6

$\frac{2 \cdot x}{\frac{x - y}{y}}$
2. Using strategy rm
3. Applied associate-/r/0.1

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

## if -5.091827858905314e+93 < x < 1.71649334501874e-21

1. Initial program 0.6

$\frac{2 \cdot x}{\frac{x - y}{y}}$
2. Using strategy rm
3. Applied div-inv0.7

$\leadsto \color{blue}{\left(2 \cdot x\right) \cdot \frac{1}{\frac{x - y}{y}}}$
4. Simplified0.6

$\leadsto \left(2 \cdot x\right) \cdot \color{blue}{\frac{y}{x - y}}$
3. Recombined 2 regimes into one program.
4. Final simplification0.4

$\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.091827858905314 \cdot 10^{+93}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \le 1.71649334501874 \cdot 10^{-21}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}$

# Reproduce

herbie shell --seed 1
(FPCore (x y)
:name "2*x/((x-y)/y)"
(/ (* 2 x) (/ (- x y) y)))