Average Error: 15.2 → 0.4
Time: 40.9s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r
double f(double r, double a, double b) {
        double r2237768 = r;
        double r2237769 = b;
        double r2237770 = sin(r2237769);
        double r2237771 = r2237768 * r2237770;
        double r2237772 = a;
        double r2237773 = r2237772 + r2237769;
        double r2237774 = cos(r2237773);
        double r2237775 = r2237771 / r2237774;
        return r2237775;
}
↓
double f(double r, double a, double b) {
        double r2237776 = b;
        double r2237777 = sin(r2237776);
        double r2237778 = a;
        double r2237779 = cos(r2237778);
        double r2237780 = cos(r2237776);
        double r2237781 = r2237779 * r2237780;
        double r2237782 = sin(r2237778);
        double r2237783 = r2237782 * r2237777;
        double r2237784 = exp(r2237783);
        double r2237785 = log(r2237784);
        double r2237786 = r2237781 - r2237785;
        double r2237787 = r2237777 / r2237786;
        double r2237788 = r;
        double r2237789 = r2237787 * r2237788;
        return r2237789;
}

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 15.2

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

  9. Applied add-log-exp0.4

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

  10. Final simplification0.4

    \[\leadsto \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r\]

Reproduce

herbie shell --seed 2019104 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))