Average Error: 14.7 → 0.3
Time: 50.6s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r2148980 = r;
        double r2148981 = b;
        double r2148982 = sin(r2148981);
        double r2148983 = r2148980 * r2148982;
        double r2148984 = a;
        double r2148985 = r2148984 + r2148981;
        double r2148986 = cos(r2148985);
        double r2148987 = r2148983 / r2148986;
        return r2148987;
}
↓
double f(double r, double a, double b) {
        double r2148988 = r;
        double r2148989 = b;
        double r2148990 = sin(r2148989);
        double r2148991 = a;
        double r2148992 = cos(r2148991);
        double r2148993 = cos(r2148989);
        double r2148994 = r2148992 * r2148993;
        double r2148995 = sin(r2148991);
        double r2148996 = r2148995 * r2148990;
        double r2148997 = r2148994 - r2148996;
        double r2148998 = r2148990 / r2148997;
        double r2148999 = r2148988 * r2148998;
        return r2148999;
}

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

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

  3. Applied cos-sum0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))