Average Error: 15.5 → 0.4
Time: 9.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b
double f(double r, double a, double b) {
        double r26868 = r;
        double r26869 = b;
        double r26870 = sin(r26869);
        double r26871 = a;
        double r26872 = r26871 + r26869;
        double r26873 = cos(r26872);
        double r26874 = r26870 / r26873;
        double r26875 = r26868 * r26874;
        return r26875;
}
↓
double f(double r, double a, double b) {
        double r26876 = r;
        double r26877 = a;
        double r26878 = cos(r26877);
        double r26879 = b;
        double r26880 = cos(r26879);
        double r26881 = r26878 * r26880;
        double r26882 = sin(r26877);
        double r26883 = sin(r26879);
        double r26884 = r26882 * r26883;
        double r26885 = r26881 - r26884;
        double r26886 = r26876 / r26885;
        double r26887 = r26886 * r26883;
        return r26887;
}

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 15.5

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 clear-num0.4

    \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]
  6. Using strategy rm

  7. Applied associate-/r/0.4

    \[\leadsto r \cdot \color{blue}{\left(\frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\right)}\]

  8. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right) \cdot \sin b}\]

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))