Average Error: 15.4 → 0.4
Time: 6.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r17965 = r;
        double r17966 = b;
        double r17967 = sin(r17966);
        double r17968 = a;
        double r17969 = r17968 + r17966;
        double r17970 = cos(r17969);
        double r17971 = r17967 / r17970;
        double r17972 = r17965 * r17971;
        return r17972;
}
↓
double f(double r, double a, double b) {
        double r17973 = r;
        double r17974 = a;
        double r17975 = cos(r17974);
        double r17976 = b;
        double r17977 = cos(r17976);
        double r17978 = r17975 * r17977;
        double r17979 = sin(r17974);
        double r17980 = sin(r17976);
        double r17981 = r17979 * r17980;
        double r17982 = r17978 - r17981;
        double r17983 = r17982 / r17980;
        double r17984 = r17973 / r17983;
        return r17984;
}

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 15.4

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020002 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))