Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[\sqrt{1 - \frac{\sqrt{1 - {x}^{2}}}{2}}\]
↓
\[\sqrt{1 - \frac{\sqrt{1 - {x}^{2}}}{2}}\]
\sqrt{1 - \frac{\sqrt{1 - {x}^{2}}}{2}}
↓
\sqrt{1 - \frac{\sqrt{1 - {x}^{2}}}{2}}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (((double) sqrt(((double) (1.0 - ((double) pow(x, 2.0)))))) / 2.0))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (((double) sqrt(((double) (1.0 - ((double) pow(x, 2.0)))))) / 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 0.0

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

  2. Final simplification0.0

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

Reproduce

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