Average Error: 14.8 → 0.4
Time: 27.8s
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 r25466 = r;
        double r25467 = b;
        double r25468 = sin(r25467);
        double r25469 = a;
        double r25470 = r25469 + r25467;
        double r25471 = cos(r25470);
        double r25472 = r25468 / r25471;
        double r25473 = r25466 * r25472;
        return r25473;
}
↓
double f(double r, double a, double b) {
        double r25474 = r;
        double r25475 = a;
        double r25476 = cos(r25475);
        double r25477 = b;
        double r25478 = cos(r25477);
        double r25479 = r25476 * r25478;
        double r25480 = sin(r25477);
        double r25481 = r25479 / r25480;
        double r25482 = sin(r25475);
        double r25483 = r25481 - r25482;
        double r25484 = r25474 / r25483;
        return r25484;
}

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 pow10.4

    \[\leadsto r \cdot \color{blue}{{\left(\frac{1}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\right)}^{1}}\]

  9. Applied pow10.4

    \[\leadsto \color{blue}{{r}^{1}} \cdot {\left(\frac{1}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\right)}^{1}\]

  10. Applied pow-prod-down0.4

    \[\leadsto \color{blue}{{\left(r \cdot \frac{1}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\right)}^{1}}\]

  11. Simplified0.4

    \[\leadsto {\color{blue}{\left(\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\right)}}^{1}\]

  12. 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)))))