Average Error: 14.9 → 0.4
Time: 37.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)} \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)} \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}
double f(double r, double a, double b) {
        double r1360397 = r;
        double r1360398 = b;
        double r1360399 = sin(r1360398);
        double r1360400 = r1360397 * r1360399;
        double r1360401 = a;
        double r1360402 = r1360401 + r1360398;
        double r1360403 = cos(r1360402);
        double r1360404 = r1360400 / r1360403;
        return r1360404;
}
↓
double f(double r, double a, double b) {
        double r1360405 = r;
        double r1360406 = b;
        double r1360407 = sin(r1360406);
        double r1360408 = r1360405 * r1360407;
        double r1360409 = a;
        double r1360410 = cos(r1360409);
        double r1360411 = cos(r1360406);
        double r1360412 = r1360410 * r1360411;
        double r1360413 = sin(r1360409);
        double r1360414 = r1360407 * r1360413;
        double r1360415 = r1360414 * r1360414;
        double r1360416 = r1360414 * r1360415;
        double r1360417 = cbrt(r1360416);
        double r1360418 = r1360417 * r1360415;
        double r1360419 = cbrt(r1360418);
        double r1360420 = r1360412 - r1360419;
        double r1360421 = r1360408 / r1360420;
        return r1360421;
}

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 14.9

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}}}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}}}}\]

  8. Final simplification0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)} \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}\]

Reproduce

herbie shell --seed 2019107 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))