Average Error: 17.9 → 13.1
Time: 16.4s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double J, double K, double U) {
	return ((-2.0 * J) * cos(K / 2.0)) * sqrt(1.0 + pow((U / ((2.0 * J) * cos(K / 2.0))), 2.0));
}

↓
double code(double J, double K, double U) {
	double tmp;
	if (((((-2.0 * J) * cos(K / 2.0)) * sqrt(1.0 + pow((U / (cos(K / 2.0) * (J * 2.0))), 2.0))) <= -inf.0) || !((((-2.0 * J) * cos(K / 2.0)) * sqrt(1.0 + pow((U / (cos(K / 2.0) * (J * 2.0))), 2.0))) <= 4.1603818497604356e+303)) {
		tmp = ((-2.0 * J) * cos(K / 2.0)) * ((U * sqrt(0.25)) / (J * cos(K * 0.5)));
	} else {
		tmp = ((-2.0 * J) * cos(K / 2.0)) * sqrt(1.0 + pow((U / (cos(K / 2.0) * (J * 2.0))), 2.0));
	}
	return tmp;
}

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  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))  < -inf.0 or 4.160381849760436e303 <  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 
    1. Initial program 63.0
      \[\]
    2. Taylor expanded around inf 46.1
      \[\leadsto \]
    3. Simplified46.1
      \[\leadsto \]
    if -inf.0 <  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))  < 4.160381849760436e303
    1. Initial program 0.1
      \[\]
  3. Recombined 2 regimes into one program.
  4. Final simplification13.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020338 
(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)))))