Average Error: 15.3 → 0.3
Time: 6.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17107 = r;
        double r17108 = b;
        double r17109 = sin(r17108);
        double r17110 = a;
        double r17111 = r17110 + r17108;
        double r17112 = cos(r17111);
        double r17113 = r17109 / r17112;
        double r17114 = r17107 * r17113;
        return r17114;
}
↓
double f(double r, double a, double b) {
        double r17115 = r;
        double r17116 = b;
        double r17117 = sin(r17116);
        double r17118 = r17115 * r17117;
        double r17119 = a;
        double r17120 = cos(r17119);
        double r17121 = cos(r17116);
        double r17122 = r17120 * r17121;
        double r17123 = sin(r17119);
        double r17124 = r17123 * r17117;
        double r17125 = r17122 - r17124;
        double r17126 = r17118 / r17125;
        return r17126;
}

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 associate-*r/0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))