Average Error: 15.3 → 0.4
Time: 26.6s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a}{\frac{1}{\frac{\cos b}{\sin b}}} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a}{\frac{1}{\frac{\cos b}{\sin b}}} - \sin a}
double f(double r, double a, double b) {
        double r24471 = r;
        double r24472 = b;
        double r24473 = sin(r24472);
        double r24474 = r24471 * r24473;
        double r24475 = a;
        double r24476 = r24475 + r24472;
        double r24477 = cos(r24476);
        double r24478 = r24474 / r24477;
        return r24478;
}
↓
double f(double r, double a, double b) {
        double r24479 = r;
        double r24480 = a;
        double r24481 = cos(r24480);
        double r24482 = 1.0;
        double r24483 = b;
        double r24484 = cos(r24483);
        double r24485 = sin(r24483);
        double r24486 = r24484 / r24485;
        double r24487 = r24482 / r24486;
        double r24488 = r24481 / r24487;
        double r24489 = sin(r24480);
        double r24490 = r24488 - r24489;
        double r24491 = r24479 / r24490;
        return r24491;
}

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 associate-/l*0.4

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

  6. Simplified0.4

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

  8. Applied associate-/l*0.4

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

  10. Applied clear-num0.4

    \[\leadsto \frac{r}{\frac{\cos a}{\color{blue}{\frac{1}{\frac{\cos b}{\sin b}}}} - \sin a}\]

  11. Final simplification0.4

    \[\leadsto \frac{r}{\frac{\cos a}{\frac{1}{\frac{\cos b}{\sin b}}} - \sin a}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))