Average Error: 18.4 → 13.7
Time: 8.9s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} = -inf.0 \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \le 1.7811757699890062 \cdot 10^{305}\right):\\ \;\;\;\;-2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(U \cdot \frac{\sqrt{0.25}}{J \cdot \cos \left(K \cdot 0.5\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\\ \end{array}\]
\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} = -inf.0 \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \le 1.7811757699890062 \cdot 10^{305}\right):\\
\;\;\;\;-2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(U \cdot \frac{\sqrt{0.25}}{J \cdot \cos \left(K \cdot 0.5\right)}\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\\

\end{array}
double code(double J, double K, double U) {
	return ((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) (2.0 * J)) * ((double) cos((K / 2.0)))))), 2.0))))))));
}
↓
double code(double J, double K, double U) {
	double VAR;
	if (((((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) cos((K / 2.0))) * ((double) (J * 2.0))))), 2.0)))))))) <= -inf.0) || !(((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) cos((K / 2.0))) * ((double) (J * 2.0))))), 2.0)))))))) <= 1.7811757699890062e+305))) {
		VAR = ((double) (-2.0 * ((double) (J * ((double) (((double) cos((K / 2.0))) * ((double) (U * (((double) sqrt(0.25)) / ((double) (J * ((double) cos(((double) (K * 0.5)))))))))))))));
	} else {
		VAR = ((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) cos((K / 2.0))) * ((double) (J * 2.0))))), 2.0))))))));
	}
	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 (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < -inf.0 or 1.7811757699890062e305 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

    1. Initial program 63.3

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]

    2. Simplified63.3

      \[\leadsto \color{blue}{-2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}\right)\right)}\]

    3. Taylor expanded around inf 47.2

      \[\leadsto -2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \color{blue}{\frac{U \cdot \sqrt{0.25}}{J \cdot \cos \left(0.5 \cdot K\right)}}\right)\right)\]

    4. Simplified47.2

      \[\leadsto -2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \color{blue}{\left(U \cdot \frac{\sqrt{0.25}}{J \cdot \cos \left(K \cdot 0.5\right)}\right)}\right)\right)\]

    if -inf.0 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < 1.7811757699890062e305

    1. Initial program 0.1

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification13.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} = -inf.0 \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \le 1.7811757699890062 \cdot 10^{305}\right):\\ \;\;\;\;-2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(U \cdot \frac{\sqrt{0.25}}{J \cdot \cos \left(K \cdot 0.5\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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)))))