Average Error: 14.8 → 0.4
Time: 26.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r25440 = r;
        double r25441 = b;
        double r25442 = sin(r25441);
        double r25443 = a;
        double r25444 = r25443 + r25441;
        double r25445 = cos(r25444);
        double r25446 = r25442 / r25445;
        double r25447 = r25440 * r25446;
        return r25447;
}
↓
double f(double r, double a, double b) {
        double r25448 = r;
        double r25449 = a;
        double r25450 = cos(r25449);
        double r25451 = b;
        double r25452 = cos(r25451);
        double r25453 = r25450 * r25452;
        double r25454 = sin(r25451);
        double r25455 = r25453 / r25454;
        double r25456 = sin(r25449);
        double r25457 = r25455 - r25456;
        double r25458 = r25448 / r25457;
        return r25458;
}

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

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 clear-num0.4

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

  6. Simplified0.4

    \[\leadsto r \cdot \frac{1}{\color{blue}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}}\]
  7. Using strategy rm

  8. Applied un-div-inv0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019303 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))