Average Error: 31.4 → 31.4
Time: 6.0s
Precision: binary64
\[\frac{1}{{x}^{2}} - \frac{1 + \cos x}{\left(2 \cdot x\right) \cdot \sin x}\]
↓
\[\frac{1}{{x}^{2}} - \frac{1 + \cos x}{\left(2 \cdot x\right) \cdot \sin x}\]
\frac{1}{{x}^{2}} - \frac{1 + \cos x}{\left(2 \cdot x\right) \cdot \sin x}
↓
\frac{1}{{x}^{2}} - \frac{1 + \cos x}{\left(2 \cdot x\right) \cdot \sin x}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) pow(x, 2.0)))) - ((double) (((double) (1.0 + ((double) cos(x)))) / ((double) (((double) (2.0 * x)) * ((double) sin(x))))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) pow(x, 2.0)))) - ((double) (((double) (1.0 + ((double) cos(x)))) / ((double) (((double) (2.0 * x)) * ((double) sin(x))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.4

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

  2. Final simplification31.4

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (/ 1 (pow x 2)) (/ (+ 1 (cos x)) (* (* 2 x) (sin x))))"
  :precision binary64
  (- (/ 1.0 (pow x 2.0)) (/ (+ 1.0 (cos x)) (* (* 2.0 x) (sin x)))))