Average Error: 15.1 → 0.3
Time: 6.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17577 = r;
        double r17578 = b;
        double r17579 = sin(r17578);
        double r17580 = r17577 * r17579;
        double r17581 = a;
        double r17582 = r17581 + r17578;
        double r17583 = cos(r17582);
        double r17584 = r17580 / r17583;
        return r17584;
}
↓
double f(double r, double a, double b) {
        double r17585 = r;
        double r17586 = b;
        double r17587 = sin(r17586);
        double r17588 = cos(r17586);
        double r17589 = a;
        double r17590 = cos(r17589);
        double r17591 = r17588 * r17590;
        double r17592 = sin(r17589);
        double r17593 = r17592 * r17587;
        double r17594 = r17591 - r17593;
        double r17595 = r17587 / r17594;
        double r17596 = r17585 * r17595;
        return r17596;
}

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 15.1

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020020 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))