Average Error: 55.0 → 55.0
Time: 3.7s
Precision: binary64
\[\frac{\left(1 - \frac{{x}^{2}}{2}\right) - \cos x}{{x}^{4}}\]
↓
\[\frac{\left(1 - \frac{{x}^{2}}{2}\right) - \cos x}{{x}^{4}}\]
\frac{\left(1 - \frac{{x}^{2}}{2}\right) - \cos x}{{x}^{4}}
↓
\frac{\left(1 - \frac{{x}^{2}}{2}\right) - \cos x}{{x}^{4}}
double code(double x) {
	return ((double) (((double) (((double) (1.0 - ((double) (((double) pow(x, 2.0)) / 2.0)))) - ((double) cos(x)))) / ((double) pow(x, 4.0))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (1.0 - ((double) (((double) pow(x, 2.0)) / 2.0)))) - ((double) cos(x)))) / ((double) pow(x, 4.0))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 55.0

    \[\frac{\left(1 - \frac{{x}^{2}}{2}\right) - \cos x}{{x}^{4}}\]

  2. Final simplification55.0

    \[\leadsto \frac{\left(1 - \frac{{x}^{2}}{2}\right) - \cos x}{{x}^{4}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (- (- 1 (/ (pow x 2) 2)) (cos x)) (pow x 4))"
  :precision binary64
  (/ (- (- 1.0 (/ (pow x 2.0) 2.0)) (cos x)) (pow x 4.0)))