Average Error: 44.5 → 44.5
Time: 8.7s
Precision: binary64
\[\cos \left(\frac{n + \sqrt{{n}^{2} - {d}^{2}}}{\sqrt{2 \cdot \left(n + \sqrt{{n}^{2} - {d}^{2}}\right)}}\right)\]
↓
\[\cos \left(\frac{n + \sqrt{{n}^{2} - {d}^{2}}}{\sqrt{2 \cdot \left(n + \sqrt{{n}^{2} - {d}^{2}}\right)}}\right)\]
\cos \left(\frac{n + \sqrt{{n}^{2} - {d}^{2}}}{\sqrt{2 \cdot \left(n + \sqrt{{n}^{2} - {d}^{2}}\right)}}\right)
↓
\cos \left(\frac{n + \sqrt{{n}^{2} - {d}^{2}}}{\sqrt{2 \cdot \left(n + \sqrt{{n}^{2} - {d}^{2}}\right)}}\right)
double code(double n, double d) {
	return ((double) cos(((double) (((double) (n + ((double) sqrt(((double) (((double) pow(n, 2.0)) - ((double) pow(d, 2.0)))))))) / ((double) sqrt(((double) (2.0 * ((double) (n + ((double) sqrt(((double) (((double) pow(n, 2.0)) - ((double) pow(d, 2.0))))))))))))))));
}
↓
double code(double n, double d) {
	return ((double) cos(((double) (((double) (n + ((double) sqrt(((double) (((double) pow(n, 2.0)) - ((double) pow(d, 2.0)))))))) / ((double) sqrt(((double) (2.0 * ((double) (n + ((double) sqrt(((double) (((double) pow(n, 2.0)) - ((double) pow(d, 2.0))))))))))))))));
}

Error

Bits error versus n

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 44.5

    \[\cos \left(\frac{n + \sqrt{{n}^{2} - {d}^{2}}}{\sqrt{2 \cdot \left(n + \sqrt{{n}^{2} - {d}^{2}}\right)}}\right)\]

  2. Final simplification44.5

    \[\leadsto \cos \left(\frac{n + \sqrt{{n}^{2} - {d}^{2}}}{\sqrt{2 \cdot \left(n + \sqrt{{n}^{2} - {d}^{2}}\right)}}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (n d)
  :name "(cos (/ (+ n (sqrt (- (pow n 2) (pow d 2)))) (sqrt (* 2 (+ n (sqrt (- (pow n 2) (pow d 2))))))))"
  :precision binary64
  (cos (/ (+ n (sqrt (- (pow n 2.0) (pow d 2.0)))) (sqrt (* 2.0 (+ n (sqrt (- (pow n 2.0) (pow d 2.0)))))))))