Average Error: 44.1 → 44.1
Time: 5.3s
Precision: binary64
\[\frac{1 + \cos \left(k \cdot {\left(\sqrt{{x}^{2} + {y}^{2}}\right)}^{2}\right)}{2}\]
↓
\[\frac{1 + \cos \left(k \cdot {\left(\sqrt{{x}^{2} + {y}^{2}}\right)}^{2}\right)}{2}\]
\frac{1 + \cos \left(k \cdot {\left(\sqrt{{x}^{2} + {y}^{2}}\right)}^{2}\right)}{2}
↓
\frac{1 + \cos \left(k \cdot {\left(\sqrt{{x}^{2} + {y}^{2}}\right)}^{2}\right)}{2}
double code(double k, double x, double y) {
	return ((double) (((double) (1.0 + ((double) cos(((double) (k * ((double) pow(((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(y, 2.0)))))), 2.0)))))))) / 2.0));
}
↓
double code(double k, double x, double y) {
	return ((double) (((double) (1.0 + ((double) cos(((double) (k * ((double) pow(((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(y, 2.0)))))), 2.0)))))))) / 2.0));
}

Error

Bits error versus k

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 44.1

    \[\frac{1 + \cos \left(k \cdot {\left(\sqrt{{x}^{2} + {y}^{2}}\right)}^{2}\right)}{2}\]

  2. Final simplification44.1

    \[\leadsto \frac{1 + \cos \left(k \cdot {\left(\sqrt{{x}^{2} + {y}^{2}}\right)}^{2}\right)}{2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (k x y)
  :name "(/ (+ 1 (cos (* k (pow (sqrt (+ (pow x 2) (pow y 2))) 2)))) 2)"
  :precision binary64
  (/ (+ 1.0 (cos (* k (pow (sqrt (+ (pow x 2.0) (pow y 2.0))) 2.0)))) 2.0))