Average Error: 15.1 → 0.4
Time: 20.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b
double f(double r, double a, double b) {
        double r1002698 = r;
        double r1002699 = b;
        double r1002700 = sin(r1002699);
        double r1002701 = a;
        double r1002702 = r1002701 + r1002699;
        double r1002703 = cos(r1002702);
        double r1002704 = r1002700 / r1002703;
        double r1002705 = r1002698 * r1002704;
        return r1002705;
}
↓
double f(double r, double a, double b) {
        double r1002706 = r;
        double r1002707 = a;
        double r1002708 = cos(r1002707);
        double r1002709 = b;
        double r1002710 = cos(r1002709);
        double r1002711 = r1002708 * r1002710;
        double r1002712 = sin(r1002709);
        double r1002713 = sin(r1002707);
        double r1002714 = r1002712 * r1002713;
        double r1002715 = r1002711 - r1002714;
        double r1002716 = r1002706 / r1002715;
        double r1002717 = r1002716 * r1002712;
        return r1002717;
}

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 15.1

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Using strategy rm

  7. Applied *-commutative0.3

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

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

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

  10. Applied times-frac0.4

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019172 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))