Average Error: 15.2 → 0.3
Time: 23.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \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 r1107681 = r;
        double r1107682 = b;
        double r1107683 = sin(r1107682);
        double r1107684 = r1107681 * r1107683;
        double r1107685 = a;
        double r1107686 = r1107685 + r1107682;
        double r1107687 = cos(r1107686);
        double r1107688 = r1107684 / r1107687;
        return r1107688;
}
↓
double f(double r, double a, double b) {
        double r1107689 = r;
        double r1107690 = b;
        double r1107691 = sin(r1107690);
        double r1107692 = r1107689 * r1107691;
        double r1107693 = a;
        double r1107694 = cos(r1107693);
        double r1107695 = cos(r1107690);
        double r1107696 = r1107694 * r1107695;
        double r1107697 = sin(r1107693);
        double r1107698 = r1107697 * r1107691;
        double r1107699 = r1107696 - r1107698;
        double r1107700 = r1107692 / r1107699;
        return r1107700;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around -inf 0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))