Average Error: 15.1 → 0.4
Time: 6.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r15838 = r;
        double r15839 = b;
        double r15840 = sin(r15839);
        double r15841 = a;
        double r15842 = r15841 + r15839;
        double r15843 = cos(r15842);
        double r15844 = r15840 / r15843;
        double r15845 = r15838 * r15844;
        return r15845;
}
↓
double f(double r, double a, double b) {
        double r15846 = r;
        double r15847 = b;
        double r15848 = sin(r15847);
        double r15849 = r15846 * r15848;
        double r15850 = 1.0;
        double r15851 = a;
        double r15852 = cos(r15851);
        double r15853 = cos(r15847);
        double r15854 = r15852 * r15853;
        double r15855 = sin(r15851);
        double r15856 = r15855 * r15848;
        double r15857 = r15854 - r15856;
        double r15858 = r15850 / r15857;
        double r15859 = r15849 * r15858;
        return r15859;
}

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 15.1

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

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

Reproduce

herbie shell --seed 2020001 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))