Average Error: 14.5 → 0.4
Time: 20.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\sin b \cdot \frac{r}{\cos a \cdot \cos b - \log \left(e^{\sin b \cdot \sin a}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\sin b \cdot \frac{r}{\cos a \cdot \cos b - \log \left(e^{\sin b \cdot \sin a}\right)}
double f(double r, double a, double b) {
        double r27835 = r;
        double r27836 = b;
        double r27837 = sin(r27836);
        double r27838 = a;
        double r27839 = r27838 + r27836;
        double r27840 = cos(r27839);
        double r27841 = r27837 / r27840;
        double r27842 = r27835 * r27841;
        return r27842;
}
↓
double f(double r, double a, double b) {
        double r27843 = b;
        double r27844 = sin(r27843);
        double r27845 = r;
        double r27846 = a;
        double r27847 = cos(r27846);
        double r27848 = cos(r27843);
        double r27849 = r27847 * r27848;
        double r27850 = sin(r27846);
        double r27851 = r27844 * r27850;
        double r27852 = exp(r27851);
        double r27853 = log(r27852);
        double r27854 = r27849 - r27853;
        double r27855 = r27845 / r27854;
        double r27856 = r27844 * r27855;
        return r27856;
}

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 14.5

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

  2. Simplified14.5

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

  4. Applied cos-sum0.3

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

  5. Simplified0.3

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

  6. Simplified0.3

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

  8. Applied add-cbrt-cube0.4

    \[\leadsto \sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}}\]

  9. Applied add-cbrt-cube0.4

    \[\leadsto \sin b \cdot \frac{r}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\sin a \cdot \sin a\right) \cdot \sin a}} \cdot \sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}\]

  10. Applied cbrt-unprod0.4

    \[\leadsto \sin b \cdot \frac{r}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin a\right) \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin b\right) \cdot \sin b\right)}}}\]

  11. Simplified0.4

    \[\leadsto \sin b \cdot \frac{r}{\cos a \cdot \cos b - \sqrt[3]{\color{blue}{{\left(\sin b \cdot \sin a\right)}^{3}}}}\]
  12. Using strategy rm

  13. Applied add-log-exp0.4

    \[\leadsto \sin b \cdot \frac{r}{\cos a \cdot \cos b - \color{blue}{\log \left(e^{\sqrt[3]{{\left(\sin b \cdot \sin a\right)}^{3}}}\right)}}\]

  14. Simplified0.4

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

  15. Final simplification0.4

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

Reproduce

herbie shell --seed 2019194 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))