Cannot sample enough valid points. (more)

\[1 \leq y \land y \leq 9999\]
\[\begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) = 0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right)} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right)}\\ \end{array}\]
\begin{array}{l}
\mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) = 0:\\
\;\;\;\;1\\

\mathbf{else}:\\
\;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right)} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right)}\\

\end{array}
double code(double y) {
	double VAR;
	if ((((double) (((double) (((double) fabs(((double) (y - ((double) sqrt(((double) (((double) (y * y)) + 1.0)))))))) - (1.0 / ((double) (y + ((double) sqrt(((double) (((double) (y * y)) + 1.0))))))))) * ((double) (((double) fabs(((double) (y - ((double) sqrt(((double) (((double) (y * y)) + 1.0)))))))) - (1.0 / ((double) (y + ((double) sqrt(((double) (((double) (y * y)) + 1.0))))))))))) == 0.0)) {
		VAR = 1.0;
	} else {
		VAR = (((double) (((double) exp(((double) (((double) (((double) fabs(((double) (y - ((double) sqrt(((double) (((double) (y * y)) + 1.0)))))))) - (1.0 / ((double) (y + ((double) sqrt(((double) (((double) (y * y)) + 1.0))))))))) * ((double) (((double) fabs(((double) (y - ((double) sqrt(((double) (((double) (y * y)) + 1.0)))))))) - (1.0 / ((double) (y + ((double) sqrt(((double) (((double) (y * y)) + 1.0))))))))))))) - 1.0)) / ((double) (((double) (((double) fabs(((double) (y - ((double) sqrt(((double) (((double) (y * y)) + 1.0)))))))) - (1.0 / ((double) (y + ((double) sqrt(((double) (((double) (y * y)) + 1.0))))))))) * ((double) (((double) fabs(((double) (y - ((double) sqrt(((double) (((double) (y * y)) + 1.0)))))))) - (1.0 / ((double) (y + ((double) sqrt(((double) (((double) (y * y)) + 1.0))))))))))));
	}
	return VAR;
}

Reproduce

herbie shell --seed 2020196 
(FPCore (y)
  :name "Kahan's Monster"
  :precision binary64
  :pre (<= 1.0 y 9999.0)
  (if (== (* (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))) (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0)))))) 0.0) 1.0 (/ (- (exp (* (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))) (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))))) 1.0) (* (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))) (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0)))))))))