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

↓

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

double f(double r, double a, double b) {
        double r1235237 = r;
        double r1235238 = b;
        double r1235239 = sin(r1235238);
        double r1235240 = a;
        double r1235241 = r1235240 + r1235238;
        double r1235242 = cos(r1235241);
        double r1235243 = r1235239 / r1235242;
        double r1235244 = r1235237 * r1235243;
        return r1235244;
}

↓

double f(double r, double a, double b) {
        double r1235245 = r;
        double r1235246 = a;
        double r1235247 = cos(r1235246);
        double r1235248 = b;
        double r1235249 = cos(r1235248);
        double r1235250 = sin(r1235248);
        double r1235251 = r1235249 / r1235250;
        double r1235252 = r1235247 * r1235251;
        double r1235253 = sin(r1235246);
        double r1235254 = r1235252 - r1235253;
        double r1235255 = r1235245 / r1235254;
        return r1235255;
}

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

↓

\frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}

Derivation

Initial program 15.0
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Using strategy rm
Applied cos-sum0.3
\[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
Using strategy rm
Applied div-inv0.4
\[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]
Applied associate-*r*0.4
\[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
Taylor expanded around inf 0.3
\[\leadsto \color{blue}{\frac{\sin b \cdot r}{\cos a \cdot \cos b - \sin b \cdot \sin a}}\]
Simplified0.4
\[\leadsto \color{blue}{\frac{r}{\frac{\cos b}{\sin b} \cdot \cos a - \sin a}}\]
Final simplification0.4
\[\leadsto \frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}\]

Reproduce

herbie shell --seed 2019102 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))

Error

Derivation

Reproduce