Average Error: 15.1 → 0.5
Time: 7.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}{\sin b}}
double f(double r, double a, double b) {
        double r17992 = r;
        double r17993 = b;
        double r17994 = sin(r17993);
        double r17995 = a;
        double r17996 = r17995 + r17993;
        double r17997 = cos(r17996);
        double r17998 = r17994 / r17997;
        double r17999 = r17992 * r17998;
        return r17999;
}
↓
double f(double r, double a, double b) {
        double r18000 = r;
        double r18001 = a;
        double r18002 = cos(r18001);
        double r18003 = b;
        double r18004 = cos(r18003);
        double r18005 = r18002 * r18004;
        double r18006 = sin(r18001);
        double r18007 = sin(r18003);
        double r18008 = r18006 * r18007;
        double r18009 = exp(r18008);
        double r18010 = log(r18009);
        double r18011 = r18005 - r18010;
        double r18012 = r18011 / r18007;
        double r18013 = r18000 / r18012;
        return r18013;
}

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 15.1

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

  5. Applied associate-*r/0.3

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

  7. Applied associate-/l*0.4

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

  9. Applied add-log-exp0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2020100 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))