Average Error: 39.1 → 39.1
Time: 1.2s
Precision: binary64
\[\frac{1 - \frac{1}{2^{x}}}{4}\]
↓
\[\frac{1 - \frac{1}{2^{x}}}{4}\]
\frac{1 - \frac{1}{2^{x}}}{4}
↓
\frac{1 - \frac{1}{2^{x}}}{4}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) (1.0 / ((double) exp2(x)))))) / 4.0));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) (1.0 / ((double) exp2(x)))))) / 4.0));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.1

    \[\frac{1 - \frac{1}{2^{x}}}{4}\]

  2. Final simplification39.1

    \[\leadsto \frac{1 - \frac{1}{2^{x}}}{4}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (- 1 (/ 1 (exp2 x))) 4)"
  :precision binary64
  (/ (- 1.0 (/ 1.0 (exp2 x))) 4.0))