Average Error: 16.0 → 16.0
Time: 1.4s
Precision: binary64
\[\sqrt{{x}^{2} + 1} - \sqrt{x}\]
↓
\[\sqrt{{x}^{2} + 1} - \sqrt{x}\]
\sqrt{{x}^{2} + 1} - \sqrt{x}
↓
\sqrt{{x}^{2} + 1} - \sqrt{x}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0)))) - ((double) sqrt(x))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0)))) - ((double) sqrt(x))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.0

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

  2. Final simplification16.0

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

Reproduce

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