Average Error: 15.2 → 0.4
Time: 6.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b
double f(double r, double a, double b) {
        double r18105 = r;
        double r18106 = b;
        double r18107 = sin(r18106);
        double r18108 = a;
        double r18109 = r18108 + r18106;
        double r18110 = cos(r18109);
        double r18111 = r18107 / r18110;
        double r18112 = r18105 * r18111;
        return r18112;
}
↓
double f(double r, double a, double b) {
        double r18113 = r;
        double r18114 = a;
        double r18115 = cos(r18114);
        double r18116 = b;
        double r18117 = cos(r18116);
        double r18118 = r18115 * r18117;
        double r18119 = sin(r18114);
        double r18120 = sin(r18116);
        double r18121 = r18119 * r18120;
        double r18122 = r18118 - r18121;
        double r18123 = r18113 / r18122;
        double r18124 = r18123 * r18120;
        return r18124;
}

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 15.2

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

  7. Applied associate-/l*0.4

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

  9. Applied associate-/r/0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020065 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))