Average Error: 15.3 → 0.4
Time: 6.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin b}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{1}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r17224 = r;
        double r17225 = b;
        double r17226 = sin(r17225);
        double r17227 = r17224 * r17226;
        double r17228 = a;
        double r17229 = r17228 + r17225;
        double r17230 = cos(r17229);
        double r17231 = r17227 / r17230;
        return r17231;
}
↓
double f(double r, double a, double b) {
        double r17232 = r;
        double r17233 = 1.0;
        double r17234 = b;
        double r17235 = cos(r17234);
        double r17236 = a;
        double r17237 = cos(r17236);
        double r17238 = r17235 * r17237;
        double r17239 = sin(r17236);
        double r17240 = sin(r17234);
        double r17241 = r17239 * r17240;
        double r17242 = r17238 - r17241;
        double r17243 = r17242 / r17240;
        double r17244 = r17233 / r17243;
        double r17245 = r17232 * r17244;
        return r17245;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  10. Applied clear-num0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))