Average Error: 15.3 → 0.3
Time: 25.0s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r794736 = r;
        double r794737 = b;
        double r794738 = sin(r794737);
        double r794739 = r794736 * r794738;
        double r794740 = a;
        double r794741 = r794740 + r794737;
        double r794742 = cos(r794741);
        double r794743 = r794739 / r794742;
        return r794743;
}
↓
double f(double r, double a, double b) {
        double r794744 = r;
        double r794745 = b;
        double r794746 = sin(r794745);
        double r794747 = a;
        double r794748 = cos(r794747);
        double r794749 = cos(r794745);
        double r794750 = r794748 * r794749;
        double r794751 = sin(r794747);
        double r794752 = r794751 * r794746;
        double r794753 = r794750 - r794752;
        double r794754 = r794746 / r794753;
        double r794755 = r794744 * r794754;
        return r794755;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019133 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))