Average Error: 15.2 → 0.4
Time: 21.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a - \sin b \cdot \sin a}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a - \sin b \cdot \sin a}{\sin b}}
double f(double r, double a, double b) {
        double r1091802 = r;
        double r1091803 = b;
        double r1091804 = sin(r1091803);
        double r1091805 = a;
        double r1091806 = r1091805 + r1091803;
        double r1091807 = cos(r1091806);
        double r1091808 = r1091804 / r1091807;
        double r1091809 = r1091802 * r1091808;
        return r1091809;
}
↓
double f(double r, double a, double b) {
        double r1091810 = r;
        double r1091811 = b;
        double r1091812 = cos(r1091811);
        double r1091813 = a;
        double r1091814 = cos(r1091813);
        double r1091815 = r1091812 * r1091814;
        double r1091816 = sin(r1091811);
        double r1091817 = sin(r1091813);
        double r1091818 = r1091816 * r1091817;
        double r1091819 = r1091815 - r1091818;
        double r1091820 = r1091819 / r1091816;
        double r1091821 = r1091810 / r1091820;
        return r1091821;
}

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 15.2

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

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

  7. Applied associate-/l*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019192 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))