Average Error: 14.7 → 0.3
Time: 13.7s
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 r29054 = r;
        double r29055 = b;
        double r29056 = sin(r29055);
        double r29057 = a;
        double r29058 = r29057 + r29055;
        double r29059 = cos(r29058);
        double r29060 = r29056 / r29059;
        double r29061 = r29054 * r29060;
        return r29061;
}
↓
double f(double r, double a, double b) {
        double r29062 = r;
        double r29063 = b;
        double r29064 = sin(r29063);
        double r29065 = r29062 * r29064;
        double r29066 = a;
        double r29067 = cos(r29066);
        double r29068 = cos(r29063);
        double r29069 = r29067 * r29068;
        double r29070 = sin(r29066);
        double r29071 = r29070 * r29064;
        double r29072 = r29069 - r29071;
        double r29073 = r29065 / r29072;
        return r29073;
}

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 14.7

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

  7. Applied associate-/r/0.4

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

  8. Applied associate-*r*0.4

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

  9. Simplified0.3

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

  11. Applied flip--0.4

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))