Average Error: 0.6 → 0.6
Time: 1.4s
Precision: binary64
\[\frac{1}{1 + \sqrt{1 - 2^{x}}}\]
↓
\[\frac{1}{1 + \sqrt{1 - 2^{x}}}\]
\frac{1}{1 + \sqrt{1 - 2^{x}}}
↓
\frac{1}{1 + \sqrt{1 - 2^{x}}}
double code(double x) {
	return ((double) (1.0 / ((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) exp2(x))))))))));
}
↓
double code(double x) {
	return ((double) (1.0 / ((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) exp2(x))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

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