Average Error: 14.8 → 0.4
Time: 16.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r23619 = r;
        double r23620 = b;
        double r23621 = sin(r23620);
        double r23622 = a;
        double r23623 = r23622 + r23620;
        double r23624 = cos(r23623);
        double r23625 = r23621 / r23624;
        double r23626 = r23619 * r23625;
        return r23626;
}
↓
double f(double r, double a, double b) {
        double r23627 = r;
        double r23628 = b;
        double r23629 = cos(r23628);
        double r23630 = a;
        double r23631 = cos(r23630);
        double r23632 = r23629 * r23631;
        double r23633 = sin(r23628);
        double r23634 = r23632 / r23633;
        double r23635 = sin(r23630);
        double r23636 = r23634 - r23635;
        double r23637 = r23627 / r23636;
        return r23637;
}

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 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Simplified0.3

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

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

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

  7. Applied associate-*l*0.3

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019305 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))