Average Error: 22.6 → 0.3
Time: 11.5min
Precision: binary64
\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -26325748948677744 \lor \neg \left(y \le 111713444.686850891\right):\\ \;\;\;\;\frac{1}{y} \cdot \left(1 - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x - 1}{y + 1} \cdot y\\ \end{array}\]
1 - \frac{\left(1 - x\right) \cdot y}{y + 1}
↓
\begin{array}{l}
\mathbf{if}\;y \le -26325748948677744 \lor \neg \left(y \le 111713444.686850891\right):\\
\;\;\;\;\frac{1}{y} \cdot \left(1 - x\right) + x\\

\mathbf{else}:\\
\;\;\;\;1 + \frac{x - 1}{y + 1} \cdot y\\

\end{array}
double code(double x, double y) {
	return ((double) (1.0 - (((double) (((double) (1.0 - x)) * y)) / ((double) (y + 1.0)))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -26325748948677744.0) || !(y <= 111713444.68685089))) {
		VAR = ((double) (((double) ((1.0 / y) * ((double) (1.0 - x)))) + x));
	} else {
		VAR = ((double) (1.0 + ((double) ((((double) (x - 1.0)) / ((double) (y + 1.0))) * y))));
	}
	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

Original22.6
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -26325748948677744 or 111713444.686850891 < y

    1. Initial program 46.9

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]

    2. Taylor expanded around inf 0.1

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

    3. Simplified0.1

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

    if -26325748948677744 < y < 111713444.686850891

    1. Initial program 0.4

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
    2. Using strategy rm

    3. Applied sub-neg0.4

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

    4. Simplified0.4

      \[\leadsto 1 + \color{blue}{\frac{x - 1}{y + 1} \cdot y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -26325748948677744 \lor \neg \left(y \le 111713444.686850891\right):\\ \;\;\;\;\frac{1}{y} \cdot \left(1 - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x - 1}{y + 1} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))