Average Error: 18.3 → 20.2
Time: 11.1s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double J, double K, double U) {
	return ((double) (((double) (((double) (-2.0 * J)) * ((double) cos(((double) (K / 2.0)))))) * ((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (((double) (2.0 * J)) * ((double) cos(((double) (K / 2.0)))))))), 2.0))))))));
}

↓
double code(double J, double K, double U) {
	double VAR;
	if (((J <= -1.8154118417069826e-206) || !(J <= 1.4979404704575452e-118))) {
		VAR = ((double) (-2.0 * ((double) (J * ((double) (((double) cos(((double) (K / 2.0)))) * ((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (J * ((double) (2.0 * ((double) cos(((double) (K / 2.0)))))))))), 2.0))))))))))));
	} else {
		VAR = ((double) (-2.0 * ((double) (J * ((double) (((double) cos(((double) (K / 2.0)))) * ((double) (((double) (U / J)) * ((double) (((double) sqrt(0.25)) / ((double) cos(((double) (K * 0.5))))))))))))));
	}
	return VAR;
}

Error
Bits error versus J
Bits error versus K
Bits error versus U
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  J  < -1.81541184170698256e-206 or 1.49794047045754518e-118 <  J 
    1. Initial program 11.6
      \[\]
    2. Simplified11.6
      \[\leadsto \]
    if -1.81541184170698256e-206 <  J  < 1.49794047045754518e-118
    1. Initial program 39.4
      \[\]
    2. Simplified39.5
      \[\leadsto \]
    3. Taylor expanded around inf 47.2
      \[\leadsto \]
    4. Simplified47.3
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification20.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  :precision binary64
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))