Average Error: 15.5 → 0.4
Time: 28.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r24652 = r;
        double r24653 = b;
        double r24654 = sin(r24653);
        double r24655 = a;
        double r24656 = r24655 + r24653;
        double r24657 = cos(r24656);
        double r24658 = r24654 / r24657;
        double r24659 = r24652 * r24658;
        return r24659;
}
↓
double f(double r, double a, double b) {
        double r24660 = r;
        double r24661 = a;
        double r24662 = cos(r24661);
        double r24663 = b;
        double r24664 = cos(r24663);
        double r24665 = r24662 * r24664;
        double r24666 = sin(r24663);
        double r24667 = r24665 / r24666;
        double r24668 = sin(r24661);
        double r24669 = r24667 - r24668;
        double r24670 = r24660 / r24669;
        return r24670;
}

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 15.5

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))