Average Error: 15.1 → 0.4
Time: 23.4s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r
double f(double r, double a, double b) {
        double r614019 = r;
        double r614020 = b;
        double r614021 = sin(r614020);
        double r614022 = r614019 * r614021;
        double r614023 = a;
        double r614024 = r614023 + r614020;
        double r614025 = cos(r614024);
        double r614026 = r614022 / r614025;
        return r614026;
}
↓
double f(double r, double a, double b) {
        double r614027 = b;
        double r614028 = sin(r614027);
        double r614029 = a;
        double r614030 = cos(r614029);
        double r614031 = cos(r614027);
        double r614032 = r614030 * r614031;
        double r614033 = sin(r614029);
        double r614034 = r614033 * r614028;
        double r614035 = r614034 * r614034;
        double r614036 = r614035 * r614034;
        double r614037 = cbrt(r614036);
        double r614038 = r614032 - r614037;
        double r614039 = r614028 / r614038;
        double r614040 = r;
        double r614041 = r614039 * r614040;
        return r614041;
}

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. Using strategy rm

  9. Applied add-cbrt-cube0.4

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

  10. Applied add-cbrt-cube0.4

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

  11. Applied cbrt-unprod0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019139 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))