Average Error: 0.2 → 0.2
Time: 2.9s
Precision: binary64
\[\frac{1}{\sin \left(\frac{x}{2}\right)} - \frac{1}{\sin \left(\frac{y}{2}\right)}\]
↓
\[\frac{1}{\sin \left(\frac{x}{2}\right)} - \frac{1}{\sin \left(\frac{y}{2}\right)}\]
\frac{1}{\sin \left(\frac{x}{2}\right)} - \frac{1}{\sin \left(\frac{y}{2}\right)}
↓
\frac{1}{\sin \left(\frac{x}{2}\right)} - \frac{1}{\sin \left(\frac{y}{2}\right)}
double code(double x, double y) {
	return ((double) (((double) (1.0 / ((double) sin(((double) (x / 2.0)))))) - ((double) (1.0 / ((double) sin(((double) (y / 2.0))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 / ((double) sin(((double) (x / 2.0)))))) - ((double) (1.0 / ((double) sin(((double) (y / 2.0))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

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