Average Error: 32.2 → 32.2
Time: 4.1s
Precision: binary64
\[\log \left(x + \sqrt{{x}^{2} - 1}\right)\]
↓
\[\log \left(x + \sqrt{{x}^{2} - 1}\right)\]
\log \left(x + \sqrt{{x}^{2} - 1}\right)
↓
\log \left(x + \sqrt{{x}^{2} - 1}\right)
double code(double x) {
	return ((double) log(((double) (x + ((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0))))))));
}
↓
double code(double x) {
	return ((double) log(((double) (x + ((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.2

    \[\log \left(x + \sqrt{{x}^{2} - 1}\right)\]

  2. Final simplification32.2

    \[\leadsto \log \left(x + \sqrt{{x}^{2} - 1}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(log (+ x (sqrt (- (pow x 2) 1))))"
  :precision binary64
  (log (+ x (sqrt (- (pow x 2.0) 1.0)))))