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

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

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(- (/ (sin (/ x 2)) (sin (/ y 2))) 1)"
  :precision binary64
  (- (/ (sin (/ x 2.0)) (sin (/ y 2.0))) 1.0))