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

↓

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

double f(double r, double a, double b) {
        double r1073553 = r;
        double r1073554 = b;
        double r1073555 = sin(r1073554);
        double r1073556 = a;
        double r1073557 = r1073556 + r1073554;
        double r1073558 = cos(r1073557);
        double r1073559 = r1073555 / r1073558;
        double r1073560 = r1073553 * r1073559;
        return r1073560;
}

↓

double f(double r, double a, double b) {
        double r1073561 = r;
        double r1073562 = a;
        double r1073563 = cos(r1073562);
        double r1073564 = b;
        double r1073565 = cos(r1073564);
        double r1073566 = sin(r1073564);
        double r1073567 = r1073565 / r1073566;
        double r1073568 = r1073563 * r1073567;
        double r1073569 = sin(r1073562);
        double r1073570 = r1073568 - r1073569;
        double r1073571 = r1073561 / r1073570;
        return r1073571;
}

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 15.1
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
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 associate-*r/0.3
\[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
Taylor expanded around -inf 0.3
\[\leadsto \color{blue}{\frac{\sin b \cdot r}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
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 2019101 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))

Error

Derivation

Reproduce