Average Error: 15.0 → 0.4
Time: 33.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}\]
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 r1073455 = r;
        double r1073456 = b;
        double r1073457 = sin(r1073456);
        double r1073458 = a;
        double r1073459 = r1073458 + r1073456;
        double r1073460 = cos(r1073459);
        double r1073461 = r1073457 / r1073460;
        double r1073462 = r1073455 * r1073461;
        return r1073462;
}
↓
double f(double r, double a, double b) {
        double r1073463 = r;
        double r1073464 = a;
        double r1073465 = cos(r1073464);
        double r1073466 = b;
        double r1073467 = cos(r1073466);
        double r1073468 = sin(r1073466);
        double r1073469 = r1073467 / r1073468;
        double r1073470 = r1073465 * r1073469;
        double r1073471 = sin(r1073464);
        double r1073472 = r1073470 - r1073471;
        double r1073473 = r1073463 / r1073472;
        return r1073473;
}

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 15.0

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

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019119 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))