Average Error: 15.3 → 0.4
Time: 7.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r18787 = r;
        double r18788 = b;
        double r18789 = sin(r18788);
        double r18790 = a;
        double r18791 = r18790 + r18788;
        double r18792 = cos(r18791);
        double r18793 = r18789 / r18792;
        double r18794 = r18787 * r18793;
        return r18794;
}
↓
double f(double r, double a, double b) {
        double r18795 = r;
        double r18796 = 1.0;
        double r18797 = a;
        double r18798 = cos(r18797);
        double r18799 = b;
        double r18800 = cos(r18799);
        double r18801 = r18798 * r18800;
        double r18802 = sin(r18797);
        double r18803 = sin(r18799);
        double r18804 = r18802 * r18803;
        double r18805 = r18801 - r18804;
        double r18806 = r18805 / r18803;
        double r18807 = r18796 / r18806;
        double r18808 = r18795 * r18807;
        return r18808;
}

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 15.3

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020034 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))