Average Error: 15.5 → 0.4
Time: 6.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r16671 = r;
        double r16672 = b;
        double r16673 = sin(r16672);
        double r16674 = a;
        double r16675 = r16674 + r16672;
        double r16676 = cos(r16675);
        double r16677 = r16673 / r16676;
        double r16678 = r16671 * r16677;
        return r16678;
}
↓
double f(double r, double a, double b) {
        double r16679 = r;
        double r16680 = b;
        double r16681 = sin(r16680);
        double r16682 = r16679 * r16681;
        double r16683 = a;
        double r16684 = cos(r16683);
        double r16685 = cos(r16680);
        double r16686 = r16684 * r16685;
        double r16687 = sin(r16683);
        double r16688 = r16687 * r16681;
        double r16689 = exp(r16688);
        double r16690 = log(r16689);
        double r16691 = r16686 - r16690;
        double r16692 = r16682 / r16691;
        return r16692;
}

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

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

  3. Applied cos-sum0.3

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

  5. Applied associate-*r/0.3

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

  7. Applied add-log-exp0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019354 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))