Average Error: 15.3 → 0.4
Time: 6.7s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}
double code(double r, double a, double b) {
	return ((double) (r * ((double) (((double) sin(b)) / ((double) cos(((double) (a + b))))))));
}
↓
double code(double r, double a, double b) {
	return ((double) (r / ((double) (((double) (((double) cos(b)) / ((double) (((double) sin(b)) / ((double) cos(a)))))) - ((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 15.3

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

  3. Applied cos-sum0.3

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

  4. Taylor expanded around inf 0.3

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

  5. Simplified0.4

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

  7. Applied clear-num0.4

    \[\leadsto \frac{r}{\color{blue}{\frac{1}{\frac{\sin b}{\cos a}}} \cdot \cos b - \sin a}\]
  8. Using strategy rm

  9. Applied associate-*l/0.4

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020185 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))