Average Error: 3.6 → 3.6
Time: 3.2s
Precision: binary64
\[\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(q \cdot q\right) \cdot q}}\right)}{3}\right)\]
↓
\[\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(q \cdot q\right) \cdot q}}\right)}{3}\right)\]
\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(q \cdot q\right) \cdot q}}\right)}{3}\right)
↓
\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(q \cdot q\right) \cdot q}}\right)}{3}\right)
double code(double r, double q) {
	return ((double) cos(((double) (((double) acos(((double) (r / ((double) sqrt(((double) (((double) (q * q)) * q)))))))) / 3.0))));
}
↓
double code(double r, double q) {
	return ((double) cos(((double) (((double) acos(((double) (r / ((double) sqrt(((double) (((double) (q * q)) * q)))))))) / 3.0))));
}

Error

Bits error versus r

Bits error versus q

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.6

    \[\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(q \cdot q\right) \cdot q}}\right)}{3}\right)\]

  2. Final simplification3.6

    \[\leadsto \cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(q \cdot q\right) \cdot q}}\right)}{3}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (r q)
  :name "(cos (/ (acos (/ r (sqrt (* (* q q) q)))) 3))"
  :precision binary64
  (cos (/ (acos (/ r (sqrt (* (* q q) q)))) 3.0)))