Average Error: 14.8 → 0.4
Time: 16.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b
double f(double r, double a, double b) {
        double r26773 = r;
        double r26774 = b;
        double r26775 = sin(r26774);
        double r26776 = r26773 * r26775;
        double r26777 = a;
        double r26778 = r26777 + r26774;
        double r26779 = cos(r26778);
        double r26780 = r26776 / r26779;
        return r26780;
}
↓
double f(double r, double a, double b) {
        double r26781 = r;
        double r26782 = a;
        double r26783 = cos(r26782);
        double r26784 = b;
        double r26785 = cos(r26784);
        double r26786 = r26783 * r26785;
        double r26787 = sin(r26782);
        double r26788 = sin(r26784);
        double r26789 = r26787 * r26788;
        double r26790 = r26786 - r26789;
        double r26791 = r26781 / r26790;
        double r26792 = r26791 * r26788;
        return r26792;
}

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 14.8

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 associate-/l*0.4

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

  7. Applied associate-/r/0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019298 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))