Average Error: 14.9 → 0.4
Time: 28.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b
double f(double r, double a, double b) {
        double r749289 = r;
        double r749290 = b;
        double r749291 = sin(r749290);
        double r749292 = a;
        double r749293 = r749292 + r749290;
        double r749294 = cos(r749293);
        double r749295 = r749291 / r749294;
        double r749296 = r749289 * r749295;
        return r749296;
}
↓
double f(double r, double a, double b) {
        double r749297 = r;
        double r749298 = a;
        double r749299 = cos(r749298);
        double r749300 = b;
        double r749301 = cos(r749300);
        double r749302 = r749299 * r749301;
        double r749303 = sin(r749300);
        double r749304 = sin(r749298);
        double r749305 = r749303 * r749304;
        double r749306 = r749302 - r749305;
        double r749307 = r749297 / r749306;
        double r749308 = r749307 * r749303;
        return r749308;
}

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 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  6. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\sin b \cdot r}{\color{blue}{1 \cdot \left(\cos a \cdot \cos b - \sin b \cdot \sin a\right)}}\]

  7. Applied times-frac0.4

    \[\leadsto \color{blue}{\frac{\sin b}{1} \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}}\]

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019152 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))