Average Error: 15.1 → 0.4
Time: 20.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{r}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{r}}
double f(double r, double a, double b) {
        double r444763 = r;
        double r444764 = b;
        double r444765 = sin(r444764);
        double r444766 = r444763 * r444765;
        double r444767 = a;
        double r444768 = r444767 + r444764;
        double r444769 = cos(r444768);
        double r444770 = r444766 / r444769;
        return r444770;
}
↓
double f(double r, double a, double b) {
        double r444771 = b;
        double r444772 = sin(r444771);
        double r444773 = a;
        double r444774 = cos(r444773);
        double r444775 = cos(r444771);
        double r444776 = r444774 * r444775;
        double r444777 = sin(r444773);
        double r444778 = r444777 * r444772;
        double r444779 = r444776 - r444778;
        double r444780 = r;
        double r444781 = r444779 / r444780;
        double r444782 = r444772 / r444781;
        return r444782;
}

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

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

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

  10. Applied associate-/l*0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019153 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))