Average Error: 15.6 → 0.4
Time: 6.7s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}
(FPCore (r a b) :precision binary64 (* r (/ (sin b) (cos (+ a b)))))
↓
(FPCore (r a b)
 :precision binary64
 (* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))))
double code(double r, double a, double b) {
	return r * (sin(b) / cos(a + b));
}
↓
double code(double r, double a, double b) {
	return sin(b) * (r / ((cos(a) * cos(b)) - (sin(b) * 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 15.6

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

  3. Applied cos-sum_binary640.3

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

  5. Applied associate-*r/_binary640.3

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

  6. Simplified0.3

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

  8. Applied *-un-lft-identity_binary640.3

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

  9. Applied times-frac_binary640.4

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

  10. Simplified0.4

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020233 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))