Average Error: 15.2 → 0.4
Time: 6.9s
Precision: binary64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos b \cdot \frac{\cos a}{\sin b} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos b \cdot \frac{\cos a}{\sin b} - \sin a}
(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))
↓
(FPCore (r a b)
 :precision binary64
 (/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a))))
double code(double r, double a, double b) {
	return (((double) (r * ((double) sin(b)))) / ((double) cos(((double) (a + b)))));
}
↓
double code(double r, double a, double b) {
	return (r / ((double) (((double) (((double) cos(b)) * (((double) cos(a)) / ((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 Error: 15.2 bits

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

  3. Applied cos-sumError: 0.3 bits

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

  5. Applied associate-/l*Error: 0.4 bits

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

  6. SimplifiedError: 0.4 bits

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

  8. Applied div-invError: 0.4 bits

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

  9. Applied associate-*l*Error: 0.4 bits

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

  10. SimplifiedError: 0.4 bits

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

  11. Final simplificationError: 0.4 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))