Average Error: 10.8 → 10.8
Time: 1.1s
Precision: binary64
\[\sqrt{1 + x} - \sqrt{{x}^{2}}\]
↓
\[\sqrt{1 + x} - \sqrt{{x}^{2}}\]
\sqrt{1 + x} - \sqrt{{x}^{2}}
↓
\sqrt{1 + x} - \sqrt{{x}^{2}}
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + x)))) - ((double) sqrt(((double) pow(x, 2.0))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + x)))) - ((double) sqrt(((double) pow(x, 2.0))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 10.8

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

  2. Final simplification10.8

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

Reproduce

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