Average Error: 14.7 → 0.3
Time: 19.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r468861 = r;
        double r468862 = b;
        double r468863 = sin(r468862);
        double r468864 = a;
        double r468865 = r468864 + r468862;
        double r468866 = cos(r468865);
        double r468867 = r468863 / r468866;
        double r468868 = r468861 * r468867;
        return r468868;
}
↓
double f(double r, double a, double b) {
        double r468869 = r;
        double r468870 = b;
        double r468871 = sin(r468870);
        double r468872 = r468869 * r468871;
        double r468873 = a;
        double r468874 = cos(r468873);
        double r468875 = cos(r468870);
        double r468876 = r468874 * r468875;
        double r468877 = sin(r468873);
        double r468878 = r468877 * r468871;
        double r468879 = r468876 - r468878;
        double r468880 = r468872 / r468879;
        return r468880;
}

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 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))