Average Error: 0.8 → 0.8
Time: 1.9s
Precision: binary64
\[\frac{1 - \sqrt{1 - 2^{x}}}{2}\]
↓
\[\frac{1 - \sqrt{1 - 2^{x}}}{2}\]
\frac{1 - \sqrt{1 - 2^{x}}}{2}
↓
\frac{1 - \sqrt{1 - 2^{x}}}{2}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) exp2(x)))))))) / 2.0));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) exp2(x)))))))) / 2.0));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.8

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

  2. Final simplification0.8

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

Reproduce

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