Average Error: 14.8 → 0.4
Time: 22.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a} \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a} \cdot r
double f(double r, double a, double b) {
        double r939024 = r;
        double r939025 = b;
        double r939026 = sin(r939025);
        double r939027 = a;
        double r939028 = r939027 + r939025;
        double r939029 = cos(r939028);
        double r939030 = r939026 / r939029;
        double r939031 = r939024 * r939030;
        return r939031;
}
↓
double f(double r, double a, double b) {
        double r939032 = 1.0;
        double r939033 = b;
        double r939034 = cos(r939033);
        double r939035 = sin(r939033);
        double r939036 = a;
        double r939037 = cos(r939036);
        double r939038 = r939035 / r939037;
        double r939039 = r939034 / r939038;
        double r939040 = sin(r939036);
        double r939041 = r939039 - r939040;
        double r939042 = r939032 / r939041;
        double r939043 = r;
        double r939044 = r939042 * r939043;
        return r939044;
}

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 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))