Average Error: 0.7 → 0.7
Time: 2.4s
Precision: binary64
\[\sqrt{\frac{1 - \sqrt{1 - 2^{x}}}{2}}\]
↓
\[\sqrt{\frac{1 - \sqrt{1 - 2^{x}}}{2}}\]
\sqrt{\frac{1 - \sqrt{1 - 2^{x}}}{2}}
↓
\sqrt{\frac{1 - \sqrt{1 - 2^{x}}}{2}}
double code(double x) {
	return ((double) sqrt(((double) (((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) exp2(x)))))))) / 2.0))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) exp2(x)))))))) / 2.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.7

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

  2. Final simplification0.7

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(sqrt (/ (- 1 (sqrt (- 1 (exp2 x)))) 2))"
  :precision binary64
  (sqrt (/ (- 1.0 (sqrt (- 1.0 (exp2 x)))) 2.0)))