Average Error: 15.0 → 0.4
Time: 6.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin b}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{1}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r17388 = r;
        double r17389 = b;
        double r17390 = sin(r17389);
        double r17391 = r17388 * r17390;
        double r17392 = a;
        double r17393 = r17392 + r17389;
        double r17394 = cos(r17393);
        double r17395 = r17391 / r17394;
        return r17395;
}
↓
double f(double r, double a, double b) {
        double r17396 = r;
        double r17397 = 1.0;
        double r17398 = b;
        double r17399 = cos(r17398);
        double r17400 = a;
        double r17401 = cos(r17400);
        double r17402 = r17399 * r17401;
        double r17403 = sin(r17400);
        double r17404 = sin(r17398);
        double r17405 = r17403 * r17404;
        double r17406 = r17402 - r17405;
        double r17407 = r17406 / r17404;
        double r17408 = r17397 / r17407;
        double r17409 = r17396 * r17408;
        return r17409;
}

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 15.0

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  10. Applied clear-num0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020049 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))