Average Error: 29.5 → 29.5
Time: 1.8s
Precision: binary64
\[\cos \left(\tan^{-1} \left(\frac{r}{d}\right)\right)\]
↓
\[\cos \left(\tan^{-1} \left(\frac{r}{d}\right)\right)\]
\cos \left(\tan^{-1} \left(\frac{r}{d}\right)\right)
↓
\cos \left(\tan^{-1} \left(\frac{r}{d}\right)\right)
double code(double r, double d) {
	return ((double) cos(((double) atan(((double) (r / d))))));
}
↓
double code(double r, double d) {
	return ((double) cos(((double) atan(((double) (r / d))))));
}

Error

Bits error versus r

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.5

    \[\cos \left(\tan^{-1} \left(\frac{r}{d}\right)\right)\]

  2. Final simplification29.5

    \[\leadsto \cos \left(\tan^{-1} \left(\frac{r}{d}\right)\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (r d)
  :name "(cos (atan (/ r d)))"
  :precision binary64
  (cos (atan (/ r d))))