Average Error: 15.4 → 0.3
Time: 12.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b \cdot r}{\cos a \cdot \cos b + \left(-\sin a \cdot \sin b\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b \cdot r}{\cos a \cdot \cos b + \left(-\sin a \cdot \sin b\right)}
double f(double r, double a, double b) {
        double r23860 = r;
        double r23861 = b;
        double r23862 = sin(r23861);
        double r23863 = a;
        double r23864 = r23863 + r23861;
        double r23865 = cos(r23864);
        double r23866 = r23862 / r23865;
        double r23867 = r23860 * r23866;
        return r23867;
}
↓
double f(double r, double a, double b) {
        double r23868 = b;
        double r23869 = sin(r23868);
        double r23870 = r;
        double r23871 = r23869 * r23870;
        double r23872 = a;
        double r23873 = cos(r23872);
        double r23874 = cos(r23868);
        double r23875 = r23873 * r23874;
        double r23876 = sin(r23872);
        double r23877 = r23876 * r23869;
        double r23878 = -r23877;
        double r23879 = r23875 + r23878;
        double r23880 = r23871 / r23879;
        return r23880;
}

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 15.4

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

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019308 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))