Average Error: 45.7 → 45.7
Time: 1.6s
Precision: binary64
\[\frac{\sqrt{{x}^{2} + 1} - 1}{x}\]
↓
\[\frac{\sqrt{{x}^{2} + 1} - 1}{x}\]
\frac{\sqrt{{x}^{2} + 1} - 1}{x}
↓
\frac{\sqrt{{x}^{2} + 1} - 1}{x}
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0)))) - 1.0)) / x));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0)))) - 1.0)) / x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.7

    \[\frac{\sqrt{{x}^{2} + 1} - 1}{x}\]

  2. Final simplification45.7

    \[\leadsto \frac{\sqrt{{x}^{2} + 1} - 1}{x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (- (sqrt (+ (pow x 2) 1)) 1) x)"
  :precision binary64
  (/ (- (sqrt (+ (pow x 2.0) 1.0)) 1.0) x))