Average Error: 22.4 → 0.7
Time: 2.4s
Precision: binary64
\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.7844287365435281 \cdot 10^{34} \lor \neg \left(y \le 126209508.385812238\right):\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 - \left(\left(1 - x\right) \cdot y\right) \cdot \frac{1}{y + 1}\\ \end{array}\]
1 - \frac{\left(1 - x\right) \cdot y}{y + 1}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.7844287365435281 \cdot 10^{34} \lor \neg \left(y \le 126209508.385812238\right):\\
\;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\

\mathbf{else}:\\
\;\;\;\;1 - \left(\left(1 - x\right) \cdot y\right) \cdot \frac{1}{y + 1}\\

\end{array}
double code(double x, double y) {
	return ((double) (1.0 - ((double) (((double) (((double) (1.0 - x)) * y)) / ((double) (y + 1.0))))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -1.784428736543528e+34) || !(y <= 126209508.38581224))) {
		VAR = ((double) (((double) (1.0 * ((double) (((double) (1.0 / y)) - ((double) (x / y)))))) + x));
	} else {
		VAR = ((double) (1.0 - ((double) (((double) (((double) (1.0 - x)) * y)) * ((double) (1.0 / ((double) (y + 1.0))))))));
	}
	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

Original22.4
Target0.3
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.7844287365435281e34 or 126209508.385812238 < y

    1. Initial program 46.6

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

    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

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

    if -1.7844287365435281e34 < y < 126209508.385812238

    1. Initial program 1.2

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

    3. Applied div-inv1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.7844287365435281 \cdot 10^{34} \lor \neg \left(y \le 126209508.385812238\right):\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 - \left(\left(1 - x\right) \cdot y\right) \cdot \frac{1}{y + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(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))))