Average Error: 15.0 → 0.3
Time: 11.6s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r17814 = r;
        double r17815 = b;
        double r17816 = sin(r17815);
        double r17817 = r17814 * r17816;
        double r17818 = a;
        double r17819 = r17818 + r17815;
        double r17820 = cos(r17819);
        double r17821 = r17817 / r17820;
        return r17821;
}
↓
double f(double r, double a, double b) {
        double r17822 = r;
        double r17823 = b;
        double r17824 = sin(r17823);
        double r17825 = cos(r17823);
        double r17826 = a;
        double r17827 = cos(r17826);
        double r17828 = r17825 * r17827;
        double r17829 = sin(r17826);
        double r17830 = r17824 * r17829;
        double r17831 = r17828 - r17830;
        double r17832 = r17824 / r17831;
        double r17833 = r17822 * r17832;
        return r17833;
}

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 15.0

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 add-log-exp0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))