Average Error: 14.9 → 0.4
Time: 26.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r660973 = r;
        double r660974 = b;
        double r660975 = sin(r660974);
        double r660976 = a;
        double r660977 = r660976 + r660974;
        double r660978 = cos(r660977);
        double r660979 = r660975 / r660978;
        double r660980 = r660973 * r660979;
        return r660980;
}
↓
double f(double r, double a, double b) {
        double r660981 = 1.0;
        double r660982 = b;
        double r660983 = cos(r660982);
        double r660984 = a;
        double r660985 = cos(r660984);
        double r660986 = r660983 * r660985;
        double r660987 = sin(r660982);
        double r660988 = sin(r660984);
        double r660989 = r660987 * r660988;
        double r660990 = r660986 - r660989;
        double r660991 = r660981 / r660990;
        double r660992 = r;
        double r660993 = r660992 * r660987;
        double r660994 = r660991 * r660993;
        return r660994;
}

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 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  6. Applied associate-*r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019130 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))