Average Error: 14.9 → 0.3
Time: 23.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r928784 = r;
        double r928785 = b;
        double r928786 = sin(r928785);
        double r928787 = r928784 * r928786;
        double r928788 = a;
        double r928789 = r928788 + r928785;
        double r928790 = cos(r928789);
        double r928791 = r928787 / r928790;
        return r928791;
}
↓
double f(double r, double a, double b) {
        double r928792 = r;
        double r928793 = b;
        double r928794 = sin(r928793);
        double r928795 = a;
        double r928796 = cos(r928795);
        double r928797 = cos(r928793);
        double r928798 = r928796 * r928797;
        double r928799 = sin(r928795);
        double r928800 = r928799 * r928794;
        double r928801 = r928798 - r928800;
        double r928802 = r928794 / r928801;
        double r928803 = r928792 * r928802;
        return r928803;
}

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

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

  3. Applied cos-sum0.3

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

  5. Applied associate-/l*0.4

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

  7. Applied div-inv0.4

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))