Average Error: 14.8 → 0.3
Time: 10.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17612 = r;
        double r17613 = b;
        double r17614 = sin(r17613);
        double r17615 = a;
        double r17616 = r17615 + r17613;
        double r17617 = cos(r17616);
        double r17618 = r17614 / r17617;
        double r17619 = r17612 * r17618;
        return r17619;
}
↓
double f(double r, double a, double b) {
        double r17620 = r;
        double r17621 = b;
        double r17622 = sin(r17621);
        double r17623 = r17620 * r17622;
        double r17624 = cos(r17621);
        double r17625 = a;
        double r17626 = cos(r17625);
        double r17627 = r17624 * r17626;
        double r17628 = sin(r17625);
        double r17629 = r17628 * r17622;
        double r17630 = r17627 - r17629;
        double r17631 = r17623 / r17630;
        return r17631;
}

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. 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. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))