Average Error: 59.6 → 59.6
Time: 3.2s
Precision: binary64
\[\sqrt{2 - 2 \cdot \sqrt{1 - \frac{{x}^{2}}{4}}}\]
↓
\[\sqrt{2 - 2 \cdot \sqrt{1 - \frac{{x}^{2}}{4}}}\]
\sqrt{2 - 2 \cdot \sqrt{1 - \frac{{x}^{2}}{4}}}
↓
\sqrt{2 - 2 \cdot \sqrt{1 - \frac{{x}^{2}}{4}}}
double code(double x) {
	return ((double) sqrt(((double) (2.0 - ((double) (2.0 * ((double) sqrt(((double) (1.0 - ((double) (((double) pow(x, 2.0)) / 4.0))))))))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (2.0 - ((double) (2.0 * ((double) sqrt(((double) (1.0 - ((double) (((double) pow(x, 2.0)) / 4.0))))))))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 59.6

    \[\sqrt{2 - 2 \cdot \sqrt{1 - \frac{{x}^{2}}{4}}}\]

  2. Final simplification59.6

    \[\leadsto \sqrt{2 - 2 \cdot \sqrt{1 - \frac{{x}^{2}}{4}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (- 2 (* 2 (sqrt (- 1 (/ (pow x 2) 4))))))"
  :precision binary64
  (sqrt (- 2.0 (* 2.0 (sqrt (- 1.0 (/ (pow x 2.0) 4.0)))))))