Average Error: 59.6 → 59.6
Time: 3.0s
Precision: binary64
\[x - \sqrt{2^{x} - 1}\]
↓
\[x - \sqrt{2^{x} - 1}\]
x - \sqrt{2^{x} - 1}
↓
x - \sqrt{2^{x} - 1}
double code(double x) {
	return ((double) (x - ((double) sqrt(((double) (((double) exp2(x)) - 1.0))))));
}
↓
double code(double x) {
	return ((double) (x - ((double) sqrt(((double) (((double) exp2(x)) - 1.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.6

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

  2. Final simplification59.6

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- x (sqrt (- (exp2 x) 1)))"
  :precision binary64
  (- x (sqrt (- (exp2 x) 1.0))))