Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[\sqrt{1 - \frac{1}{{x}^{2}}}\]
↓
\[\sqrt{1 - \frac{1}{{x}^{2}}}\]
\sqrt{1 - \frac{1}{{x}^{2}}}
↓
\sqrt{1 - \frac{1}{{x}^{2}}}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (1.0 / ((double) pow(x, 2.0))))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (1.0 / ((double) pow(x, 2.0))))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

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