Average Error: 39.5 → 39.5
Time: 1.3s
Precision: binary64
\[x - \sqrt{\left|2^{x} - 1\right|}\]
↓
\[x - \sqrt{\left|2^{x} - 1\right|}\]
x - \sqrt{\left|2^{x} - 1\right|}
↓
x - \sqrt{\left|2^{x} - 1\right|}
double code(double x) {
	return ((double) (x - ((double) sqrt(((double) fabs(((double) (((double) exp2(x)) - 1.0))))))));
}
↓
double code(double x) {
	return ((double) (x - ((double) sqrt(((double) fabs(((double) (((double) exp2(x)) - 1.0))))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.5

    \[x - \sqrt{\left|2^{x} - 1\right|}\]

  2. Final simplification39.5

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

Reproduce

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