Average Error: 31.7 → 31.7
Time: 1.1s
Precision: binary64
\[\sqrt{\frac{1}{{x}^{2}} - 1}\]
↓
\[\sqrt{\frac{1}{{x}^{2}} - 1}\]
\sqrt{\frac{1}{{x}^{2}} - 1}
↓
\sqrt{\frac{1}{{x}^{2}} - 1}
double code(double x) {
	return ((double) sqrt(((double) (((double) (1.0 / ((double) pow(x, 2.0)))) - 1.0))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (1.0 / ((double) pow(x, 2.0)))) - 1.0))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 31.7

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

  2. Final simplification31.7

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

Reproduce

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