Average Error: 15.5 → 0.4
Time: 26.8s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\frac{\left(\cos a \cdot \cos b\right) \cdot \left(\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)\right)}{\left(\cos a \cdot \cos b\right) \cdot \left(\sin b \cdot \sin a + \cos a \cdot \cos b\right) + \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)} - \frac{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}{\left(\cos a \cdot \cos b\right) \cdot \left(\sin b \cdot \sin a + \cos a \cdot \cos b\right) + \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\frac{\left(\cos a \cdot \cos b\right) \cdot \left(\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)\right)}{\left(\cos a \cdot \cos b\right) \cdot \left(\sin b \cdot \sin a + \cos a \cdot \cos b\right) + \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)} - \frac{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}{\left(\cos a \cdot \cos b\right) \cdot \left(\sin b \cdot \sin a + \cos a \cdot \cos b\right) + \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)}}
double f(double r, double a, double b) {
        double r1288965 = r;
        double r1288966 = b;
        double r1288967 = sin(r1288966);
        double r1288968 = r1288965 * r1288967;
        double r1288969 = a;
        double r1288970 = r1288969 + r1288966;
        double r1288971 = cos(r1288970);
        double r1288972 = r1288968 / r1288971;
        return r1288972;
}
↓
double f(double r, double a, double b) {
        double r1288973 = r;
        double r1288974 = b;
        double r1288975 = sin(r1288974);
        double r1288976 = r1288973 * r1288975;
        double r1288977 = a;
        double r1288978 = cos(r1288977);
        double r1288979 = cos(r1288974);
        double r1288980 = r1288978 * r1288979;
        double r1288981 = r1288980 * r1288980;
        double r1288982 = r1288980 * r1288981;
        double r1288983 = sin(r1288977);
        double r1288984 = r1288975 * r1288983;
        double r1288985 = r1288984 + r1288980;
        double r1288986 = r1288980 * r1288985;
        double r1288987 = r1288984 * r1288984;
        double r1288988 = r1288986 + r1288987;
        double r1288989 = r1288982 / r1288988;
        double r1288990 = r1288984 * r1288987;
        double r1288991 = r1288990 / r1288988;
        double r1288992 = r1288989 - r1288991;
        double r1288993 = r1288976 / r1288992;
        return r1288993;
}

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 15.5

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

  3. Applied cos-sum0.3

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

  5. Applied flip3--0.4

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^{3} - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) + \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\sin a \cdot \sin b\right)\right)}}}\]

  6. Simplified0.4

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

  7. Simplified0.4

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

  9. Applied div-sub0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))