Average Error: 14.8 → 0.4
Time: 6.6s
Precision: binary64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\left(\cos b \cdot \cos a\right) \cdot \frac{1}{\sin b} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\left(\cos b \cdot \cos a\right) \cdot \frac{1}{\sin b} - \sin a}
double code(double r, double a, double b) {
	return ((double) (((double) (r * ((double) sin(b)))) / ((double) cos(((double) (a + b))))));
}
↓
double code(double r, double a, double b) {
	return ((double) (r / ((double) (((double) (((double) (((double) cos(b)) * ((double) cos(a)))) * ((double) (1.0 / ((double) sin(b)))))) - ((double) sin(a))))));
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]

  2. Simplified14.8

    \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}}\]
  3. Using strategy rm

  4. Applied cos-sum0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}}\]

  5. Taylor expanded around inf 0.3

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}}\]

  6. Simplified0.4

    \[\leadsto \color{blue}{\frac{r}{\cos b \cdot \frac{\cos a}{\sin b} - \sin a}}\]
  7. Using strategy rm

  8. Applied div-inv0.4

    \[\leadsto \frac{r}{\cos b \cdot \color{blue}{\left(\cos a \cdot \frac{1}{\sin b}\right)} - \sin a}\]

  9. Applied associate-*r*0.4

    \[\leadsto \frac{r}{\color{blue}{\left(\cos b \cdot \cos a\right) \cdot \frac{1}{\sin b}} - \sin a}\]

  10. Final simplification0.4

    \[\leadsto \frac{r}{\left(\cos b \cdot \cos a\right) \cdot \frac{1}{\sin b} - \sin a}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))