Average Error: 14.9 → 0.3
Time: 6.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r16778 = r;
        double r16779 = b;
        double r16780 = sin(r16779);
        double r16781 = r16778 * r16780;
        double r16782 = a;
        double r16783 = r16782 + r16779;
        double r16784 = cos(r16783);
        double r16785 = r16781 / r16784;
        return r16785;
}
↓
double f(double r, double a, double b) {
        double r16786 = r;
        double r16787 = b;
        double r16788 = sin(r16787);
        double r16789 = cos(r16787);
        double r16790 = a;
        double r16791 = cos(r16790);
        double r16792 = r16789 * r16791;
        double r16793 = sin(r16790);
        double r16794 = r16793 * r16788;
        double r16795 = r16792 - r16794;
        double r16796 = r16788 / r16795;
        double r16797 = r16786 * r16796;
        return r16797;
}

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 *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))