Average Error: 32.4 → 32.4
Time: 1.9s
Precision: binary64
\[\frac{1 + \sqrt{{x}^{2} - 1}}{\sqrt{{x}^{2} - 1}}\]
↓
\[\frac{1 + \sqrt{{x}^{2} - 1}}{\sqrt{{x}^{2} - 1}}\]
\frac{1 + \sqrt{{x}^{2} - 1}}{\sqrt{{x}^{2} - 1}}
↓
\frac{1 + \sqrt{{x}^{2} - 1}}{\sqrt{{x}^{2} - 1}}
double code(double x) {
	return ((double) (((double) (1.0 + ((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0)))))) / ((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 + ((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0)))))) / ((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.4

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

  2. Final simplification32.4

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

Reproduce

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