Average Error: 14.8 → 0.4
Time: 12.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{1}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}
double f(double r, double a, double b) {
        double r17905 = r;
        double r17906 = b;
        double r17907 = sin(r17906);
        double r17908 = a;
        double r17909 = r17908 + r17906;
        double r17910 = cos(r17909);
        double r17911 = r17907 / r17910;
        double r17912 = r17905 * r17911;
        return r17912;
}
↓
double f(double r, double a, double b) {
        double r17913 = r;
        double r17914 = 1.0;
        double r17915 = b;
        double r17916 = cos(r17915);
        double r17917 = sin(r17915);
        double r17918 = a;
        double r17919 = cos(r17918);
        double r17920 = r17917 / r17919;
        double r17921 = r17916 / r17920;
        double r17922 = sin(r17918);
        double r17923 = r17921 - r17922;
        double r17924 = r17914 / r17923;
        double r17925 = r17913 * r17924;
        return r17925;
}

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

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

  8. Applied associate-/l*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020046 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))