Average Error: 0.3 → 0.3
Time: 1.9s
Precision: binary64
\[x - \left(\sin x - \frac{\frac{x}{2}}{\cos x - \frac{1}{2}}\right)\]
↓
\[x - \left(\sin x - \frac{\frac{x}{2}}{\cos x - \frac{1}{2}}\right)\]
x - \left(\sin x - \frac{\frac{x}{2}}{\cos x - \frac{1}{2}}\right)
↓
x - \left(\sin x - \frac{\frac{x}{2}}{\cos x - \frac{1}{2}}\right)
double code(double x) {
	return ((double) (x - ((double) (((double) sin(x)) - ((double) (((double) (x / 2.0)) / ((double) (((double) cos(x)) - ((double) (1.0 / 2.0))))))))));
}
↓
double code(double x) {
	return ((double) (x - ((double) (((double) sin(x)) - ((double) (((double) (x / 2.0)) / ((double) (((double) cos(x)) - ((double) (1.0 / 2.0))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  2. Final simplification0.3

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

Reproduce

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