Average Error: 53.6 → 0.3
Time: 4.4s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) log(((double) (x + ((double) sqrt(((double) (((double) (x * x)) + 1.0))))))));
}

↓
double code(double x) {
	double VAR;
	if ((x <= -0.9962455178555384)) {
		VAR = ((double) log(((double) (((double) (0.125 / ((double) pow(x, 3.0)))) - ((double) (((double) (0.5 / x)) + ((double) (0.0625 / ((double) pow(x, 5.0))))))))));
	} else {
		double VAR_1;
		if ((x <= 0.8850881000200332)) {
			VAR_1 = ((double) (((double) log(((double) sqrt(1.0)))) + ((double) (((double) (x / ((double) sqrt(1.0)))) + ((double) (((double) pow(((double) (x / ((double) sqrt(1.0)))), 3.0)) * -0.16666666666666666))))));
		} else {
			VAR_1 = ((double) log(((double) (x + ((double) (x + ((double) (((double) (0.5 / x)) - ((double) (0.125 / ((double) pow(x, 3.0))))))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original53.6
Target45.4
Herbie0.3
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  x  < -0.996245517855538387
    1. Initial program 62.8
      \[\]
    2. Taylor expanded around -inf 0.2
      \[\leadsto \]
    3. Simplified0.2
      \[\leadsto \]
    if -0.996245517855538387 <  x  < 0.88508810002003324
    1. Initial program 58.6
      \[\]
    2. Taylor expanded around 0 0.3
      \[\leadsto \]
    3. Simplified0.3
      \[\leadsto \]
    if 0.88508810002003324 <  x 
    1. Initial program 33.2
      \[\]
    2. Taylor expanded around inf 0.2
      \[\leadsto \]
    3. Simplified0.2
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "Hyperbolic arcsine"
  :precision binary64

  :herbie-target
  (if (< x 0.0) (log (/ -1.0 (- x (sqrt (+ (* x x) 1.0))))) (log (+ x (sqrt (+ (* x x) 1.0)))))

  (log (+ x (sqrt (+ (* x x) 1.0)))))