Average Error: 15.5 → 0.3
Time: 26.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r23720 = r;
        double r23721 = b;
        double r23722 = sin(r23721);
        double r23723 = r23720 * r23722;
        double r23724 = a;
        double r23725 = r23724 + r23721;
        double r23726 = cos(r23725);
        double r23727 = r23723 / r23726;
        return r23727;
}
↓
double f(double r, double a, double b) {
        double r23728 = r;
        double r23729 = b;
        double r23730 = sin(r23729);
        double r23731 = a;
        double r23732 = cos(r23731);
        double r23733 = cos(r23729);
        double r23734 = r23732 * r23733;
        double r23735 = sin(r23731);
        double r23736 = r23730 * r23735;
        double r23737 = r23734 - r23736;
        double r23738 = r23730 / r23737;
        double r23739 = r23728 * r23738;
        return r23739;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  7. Applied associate-*l*0.4

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

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