Average Error: 59.5 → 59.5
Time: 2.5s
Precision: binary64
\[\sqrt{2 - \sqrt{4 - {x}^{2}}}\]
↓
\[\sqrt{2 - \sqrt{4 - {x}^{2}}}\]
\sqrt{2 - \sqrt{4 - {x}^{2}}}
↓
\sqrt{2 - \sqrt{4 - {x}^{2}}}
double code(double x) {
	return ((double) sqrt(((double) (2.0 - ((double) sqrt(((double) (4.0 - ((double) pow(x, 2.0))))))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (2.0 - ((double) sqrt(((double) (4.0 - ((double) pow(x, 2.0))))))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 59.5

    \[\sqrt{2 - \sqrt{4 - {x}^{2}}}\]

  2. Final simplification59.5

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(sqrt (- 2 (sqrt (- 4 (pow x 2)))))"
  :precision binary64
  (sqrt (- 2.0 (sqrt (- 4.0 (pow x 2.0))))))