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

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

  2. Simplified15.3

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

  6. Applied div-inv0.4

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

  7. Applied associate-*r*0.4

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

  8. Simplified0.4

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

  10. Applied associate-*l*0.4

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

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