Average Error: 15.1 → 0.4
Time: 32.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right)\right)} \cdot \left(\sin a \cdot \sin b\right)}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right)\right)} \cdot \left(\sin a \cdot \sin b\right)}}
double f(double r, double a, double b) {
        double r703994 = r;
        double r703995 = b;
        double r703996 = sin(r703995);
        double r703997 = a;
        double r703998 = r703997 + r703995;
        double r703999 = cos(r703998);
        double r704000 = r703996 / r703999;
        double r704001 = r703994 * r704000;
        return r704001;
}
↓
double f(double r, double a, double b) {
        double r704002 = r;
        double r704003 = b;
        double r704004 = sin(r704003);
        double r704005 = a;
        double r704006 = cos(r704005);
        double r704007 = cos(r704003);
        double r704008 = r704006 * r704007;
        double r704009 = sin(r704005);
        double r704010 = r704009 * r704004;
        double r704011 = r704010 * r704010;
        double r704012 = r704011 * r704011;
        double r704013 = r704011 * r704012;
        double r704014 = cbrt(r704013);
        double r704015 = r704014 * r704010;
        double r704016 = cbrt(r704015);
        double r704017 = r704008 - r704016;
        double r704018 = r704004 / r704017;
        double r704019 = r704002 * r704018;
        return r704019;
}

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

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

  3. Applied cos-sum0.3

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

  5. Applied add-cbrt-cube0.4

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

  6. Applied add-cbrt-cube0.4

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

  7. Applied cbrt-unprod0.4

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

  8. Simplified0.4

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

  10. Applied add-cbrt-cube0.4

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

  11. Final simplification0.4

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

Reproduce

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