Average Error: 31.8 → 31.8
Time: 2.5s
Precision: binary64
\[\frac{1 - \cos x}{{x}^{2}}\]
↓
\[\frac{1 - \cos x}{{x}^{2}}\]
\frac{1 - \cos x}{{x}^{2}}
↓
\frac{1 - \cos x}{{x}^{2}}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) pow(x, 2.0))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) pow(x, 2.0))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 31.8

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

  2. Final simplification31.8

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

Reproduce

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