Average Error: 14.9 → 0.4
Time: 27.8s
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 r968458 = r;
        double r968459 = b;
        double r968460 = sin(r968459);
        double r968461 = a;
        double r968462 = r968461 + r968459;
        double r968463 = cos(r968462);
        double r968464 = r968460 / r968463;
        double r968465 = r968458 * r968464;
        return r968465;
}
↓
double f(double r, double a, double b) {
        double r968466 = r;
        double r968467 = a;
        double r968468 = cos(r968467);
        double r968469 = b;
        double r968470 = cos(r968469);
        double r968471 = sin(r968469);
        double r968472 = r968470 / r968471;
        double r968473 = r968468 * r968472;
        double r968474 = sin(r968467);
        double r968475 = r968473 - r968474;
        double r968476 = r968466 / r968475;
        return r968476;
}

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. Using strategy rm

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

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

  6. Applied associate-*l*0.3

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

  7. Simplified0.4

    \[\leadsto 1 \cdot \color{blue}{\frac{r}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}}\]
  8. Using strategy rm

  9. Applied associate-/r/0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019169 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))