Average Error: 15.0 → 0.4
Time: 36.4s
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 r1155643 = r;
        double r1155644 = b;
        double r1155645 = sin(r1155644);
        double r1155646 = a;
        double r1155647 = r1155646 + r1155644;
        double r1155648 = cos(r1155647);
        double r1155649 = r1155645 / r1155648;
        double r1155650 = r1155643 * r1155649;
        return r1155650;
}
↓
double f(double r, double a, double b) {
        double r1155651 = r;
        double r1155652 = a;
        double r1155653 = cos(r1155652);
        double r1155654 = b;
        double r1155655 = cos(r1155654);
        double r1155656 = sin(r1155654);
        double r1155657 = r1155655 / r1155656;
        double r1155658 = r1155653 * r1155657;
        double r1155659 = sin(r1155652);
        double r1155660 = r1155658 - r1155659;
        double r1155661 = r1155651 / r1155660;
        return r1155661;
}

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 pow10.3

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

  6. Applied pow10.3

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

  7. Applied pow-prod-down0.3

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

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