Average Error: 31.3 → 31.3
Time: 4.6s
Precision: binary64
\[\frac{1 - \cos x}{x \cdot \sin x}\]
↓
\[\frac{1 - \cos x}{x \cdot \sin x}\]
\frac{1 - \cos x}{x \cdot \sin x}
↓
\frac{1 - \cos x}{x \cdot \sin x}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) (x * ((double) sin(x))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) (x * ((double) sin(x))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 31.3

    \[\frac{1 - \cos x}{x \cdot \sin x}\]

  2. Final simplification31.3

    \[\leadsto \frac{1 - \cos x}{x \cdot \sin x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (- 1 (cos x)) (* x (sin x)))"
  :precision binary64
  (/ (- 1.0 (cos x)) (* x (sin x))))