Average Error: 15.1 → 0.4
Time: 27.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r903979 = r;
        double r903980 = b;
        double r903981 = sin(r903980);
        double r903982 = a;
        double r903983 = r903982 + r903980;
        double r903984 = cos(r903983);
        double r903985 = r903981 / r903984;
        double r903986 = r903979 * r903985;
        return r903986;
}
↓
double f(double r, double a, double b) {
        double r903987 = r;
        double r903988 = b;
        double r903989 = cos(r903988);
        double r903990 = a;
        double r903991 = cos(r903990);
        double r903992 = r903989 * r903991;
        double r903993 = sin(r903988);
        double r903994 = r903992 / r903993;
        double r903995 = sin(r903990);
        double r903996 = r903994 - r903995;
        double r903997 = r903987 / r903996;
        return r903997;
}

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 div-sub0.4

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019144 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))