Average Error: 17.8 → 13.3
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 ((((double) (((double) (((double) (-2.0 * J)) * ((double) cos(((double) (K / 2.0)))))) * ((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (((double) cos(((double) (K / 2.0)))) * ((double) (J * 2.0)))))), 2.0)))))))) <= -inf.0)) {
		VAR = ((double) (((double) (((double) (-2.0 * J)) * ((double) cos(((double) (K / 2.0)))))) * ((double) (U * ((double) (((double) sqrt(0.25)) / ((double) (J * ((double) cos(((double) (K * 0.5))))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (((double) (-2.0 * J)) * ((double) cos(((double) (K / 2.0)))))) * ((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (((double) cos(((double) (K / 2.0)))) * ((double) (J * 2.0)))))), 2.0)))))))) <= 2.9562275782773536e+301)) {
			VAR_1 = ((double) (((double) (((double) (-2.0 * J)) * ((double) cos(((double) (K / 2.0)))))) * ((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (((double) cos(((double) (K / 2.0)))) * ((double) (J * 2.0)))))), 2.0))))))));
		} else {
			VAR_1 = ((double) (-2.0 * ((double) (J * ((double) (((double) cos(((double) (K / 2.0)))) * ((double) (U * ((double) (((double) sqrt(0.25)) / ((double) (J * ((double) cos(((double) (K * 0.5))))))))))))))));
		}
		VAR = VAR_1;
	}
	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 3 regimes
  2. if  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))  < -inf.0
    1. Initial program 64.0
      \[\]
    2. Taylor expanded around inf 46.3
      \[\leadsto \]
    3. Simplified46.4
      \[\leadsto \]
    if -inf.0 <  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))  < 2.9562275782773536e301
    1. Initial program 0.1
      \[\]
    if 2.9562275782773536e301 <  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 
    1. Initial program 60.6
      \[\]
    2. Simplified60.5
      \[\leadsto \]
    3. Taylor expanded around inf 46.5
      \[\leadsto \]
    4. Simplified46.5
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification13.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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)))))