Maksimov and Kolovsky, Equation (3)

Average Accuracy: 71.6% → 85.6%

Time: 27.7s

Precision: binary64

Cost: 20880

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot t_0\right)}\right)\\ t_2 := \left(\left(J \cdot -2\right) \cdot t_0\right) \cdot t_1\\ \mathbf{if}\;J \leq -2.3 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;J \leq -4.2 \cdot 10^{-262}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq -1.05 \cdot 10^{-269}:\\ \;\;\;\;-2 \cdot \left(t_0 \cdot \left(J \cdot t_1\right)\right)\\ \mathbf{elif}\;J \leq 5.8 \cdot 10^{-183}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

(FPCore (J K U)
 :precision binary64
 (*
  (* (* -2.0 J) (cos (/ K 2.0)))
  (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

↓

(FPCore (J K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0)))
        (t_1 (hypot 1.0 (/ U (* 2.0 (* J t_0)))))
        (t_2 (* (* (* J -2.0) t_0) t_1)))
   (if (<= J -2.3e-210)
     t_2
     (if (<= J -4.2e-262)
       (- U)
       (if (<= J -1.05e-269)
         (* -2.0 (* t_0 (* J t_1)))
         (if (<= J 5.8e-183) U t_2))))))

C

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 t_0 = cos((K / 2.0));
	double t_1 = hypot(1.0, (U / (2.0 * (J * t_0))));
	double t_2 = ((J * -2.0) * t_0) * t_1;
	double tmp;
	if (J <= -2.3e-210) {
		tmp = t_2;
	} else if (J <= -4.2e-262) {
		tmp = -U;
	} else if (J <= -1.05e-269) {
		tmp = -2.0 * (t_0 * (J * t_1));
	} else if (J <= 5.8e-183) {
		tmp = U;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double J, double K, double U) {
	return ((-2.0 * J) * Math.cos((K / 2.0))) * Math.sqrt((1.0 + Math.pow((U / ((2.0 * J) * Math.cos((K / 2.0)))), 2.0)));
}

↓

public static double code(double J, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.hypot(1.0, (U / (2.0 * (J * t_0))));
	double t_2 = ((J * -2.0) * t_0) * t_1;
	double tmp;
	if (J <= -2.3e-210) {
		tmp = t_2;
	} else if (J <= -4.2e-262) {
		tmp = -U;
	} else if (J <= -1.05e-269) {
		tmp = -2.0 * (t_0 * (J * t_1));
	} else if (J <= 5.8e-183) {
		tmp = U;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(J, K, U):
	return ((-2.0 * J) * math.cos((K / 2.0))) * math.sqrt((1.0 + math.pow((U / ((2.0 * J) * math.cos((K / 2.0)))), 2.0)))

↓

def code(J, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.hypot(1.0, (U / (2.0 * (J * t_0))))
	t_2 = ((J * -2.0) * t_0) * t_1
	tmp = 0
	if J <= -2.3e-210:
		tmp = t_2
	elif J <= -4.2e-262:
		tmp = -U
	elif J <= -1.05e-269:
		tmp = -2.0 * (t_0 * (J * t_1))
	elif J <= 5.8e-183:
		tmp = U
	else:
		tmp = t_2
	return tmp

Julia

function code(J, K, U)
	return Float64(Float64(Float64(-2.0 * J) * cos(Float64(K / 2.0))) * sqrt(Float64(1.0 + (Float64(U / Float64(Float64(2.0 * J) * cos(Float64(K / 2.0)))) ^ 2.0))))
end

↓

function code(J, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = hypot(1.0, Float64(U / Float64(2.0 * Float64(J * t_0))))
	t_2 = Float64(Float64(Float64(J * -2.0) * t_0) * t_1)
	tmp = 0.0
	if (J <= -2.3e-210)
		tmp = t_2;
	elseif (J <= -4.2e-262)
		tmp = Float64(-U);
	elseif (J <= -1.05e-269)
		tmp = Float64(-2.0 * Float64(t_0 * Float64(J * t_1)));
	elseif (J <= 5.8e-183)
		tmp = U;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp = code(J, K, U)
	tmp = ((-2.0 * J) * cos((K / 2.0))) * sqrt((1.0 + ((U / ((2.0 * J) * cos((K / 2.0)))) ^ 2.0)));
end

↓

function tmp_2 = code(J, K, U)
	t_0 = cos((K / 2.0));
	t_1 = hypot(1.0, (U / (2.0 * (J * t_0))));
	t_2 = ((J * -2.0) * t_0) * t_1;
	tmp = 0.0;
	if (J <= -2.3e-210)
		tmp = t_2;
	elseif (J <= -4.2e-262)
		tmp = -U;
	elseif (J <= -1.05e-269)
		tmp = -2.0 * (t_0 * (J * t_1));
	elseif (J <= 5.8e-183)
		tmp = U;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, K_, U_] := N[(N[(N[(-2.0 * J), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 + N[Power[N[(U / N[(N[(2.0 * J), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[J_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[1.0 ^ 2 + N[(U / N[(2.0 * N[(J * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(J * -2.0), $MachinePrecision] * t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision]}, If[LessEqual[J, -2.3e-210], t$95$2, If[LessEqual[J, -4.2e-262], (-U), If[LessEqual[J, -1.05e-269], N[(-2.0 * N[(t$95$0 * N[(J * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[J, 5.8e-183], U, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if J < -2.3e-210 or 5.8000000000000001e-183 < J

   1. Initial program 79.8%

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

   2. Simplified 93.9%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)} \]
      Proof

      [Start] 79.8	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      unpow2 [=>] 79.8	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + \color{blue}{\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}}} \]
      hypot-1-def [=>] 93.9	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\mathsf{hypot}\left(1, \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)} \]
      associate-*l* [=>] 93.9	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\color{blue}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}}\right) \]

   if -2.3e-210 < J < -4.1999999999999999e-262

   1. Initial program 35.3%

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

   2. Simplified 59.6%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)} \]
      Proof

      [Start] 35.3	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      unpow2 [=>] 35.3	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + \color{blue}{\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}}} \]
      hypot-1-def [=>] 59.6	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\mathsf{hypot}\left(1, \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)} \]
      associate-*l* [=>] 59.6	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\color{blue}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}}\right) \]

   3. Taylor expanded in J around 0 46.1%

      \[\leadsto \color{blue}{-1 \cdot U} \]

   4. Simplified 46.1%

      \[\leadsto \color{blue}{-U} \]
      Proof

      [Start] 46.1	\[ -1 \cdot U \]
      mul-1-neg [=>] 46.1	\[ \color{blue}{-U} \]

   if -4.1999999999999999e-262 < J < -1.05000000000000002e-269

   1. Initial program 31.7%

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

   2. Simplified 58.3%

      \[\leadsto \color{blue}{-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\right)} \]
      Proof

      [Start] 31.7	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      associate-*l* [=>] 31.7	\[ \color{blue}{\left(-2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)\right)} \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      associate-*l* [=>] 31.7	\[ \color{blue}{-2 \cdot \left(\left(J \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)} \]
      *-commutative [=>] 31.7	\[ -2 \cdot \left(\color{blue}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right) \]
      associate-*l* [=>] 31.7	\[ -2 \cdot \color{blue}{\left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)\right)} \]
      unpow2 [=>] 31.7	\[ -2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \sqrt{1 + \color{blue}{\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}}}\right)\right) \]
      hypot-1-def [=>] 58.3	\[ -2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \color{blue}{\mathsf{hypot}\left(1, \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}\right)\right) \]
      associate-*l* [=>] 58.3	\[ -2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \mathsf{hypot}\left(1, \frac{U}{\color{blue}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}}\right)\right)\right) \]

   if -1.05000000000000002e-269 < J < 5.8000000000000001e-183

   1. Initial program 34.4%

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

   2. Simplified 59.8%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)} \]
      Proof

      [Start] 34.4	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      unpow2 [=>] 34.4	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + \color{blue}{\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}}} \]
      hypot-1-def [=>] 59.8	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\mathsf{hypot}\left(1, \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)} \]
      associate-*l* [=>] 59.8	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\color{blue}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}}\right) \]

   3. Taylor expanded in U around -inf 48.4%

      \[\leadsto \color{blue}{U} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;J \leq -2.3 \cdot 10^{-210}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\\ \mathbf{elif}\;J \leq -4.2 \cdot 10^{-262}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq -1.05 \cdot 10^{-269}:\\ \;\;\;\;-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\right)\\ \mathbf{elif}\;J \leq 5.8 \cdot 10^{-183}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	85.5%
Cost	20881

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := -2 \cdot \left(t_0 \cdot \left(J \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot t_0\right)}\right)\right)\right)\\ \mathbf{if}\;J \leq -4.3 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq -4.5 \cdot 10^{-262}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq -2 \cdot 10^{-272} \lor \neg \left(J \leq 3.2 \cdot 10^{-182}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 2
Accuracy	72.8%
Cost	14092

\[\begin{array}{l} t_0 := \left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{J \cdot 2}\right)\\ \mathbf{if}\;J \leq -2.7 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq -4.3 \cdot 10^{-262}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 4.2 \cdot 10^{-181}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	62.7%
Cost	7832

\[\begin{array}{l} t_0 := \left(J \cdot -2\right) \cdot \mathsf{hypot}\left(1, \frac{U}{J \cdot 2}\right)\\ t_1 := \left(J \cdot -2\right) \cdot \cos \left(K \cdot 0.5\right)\\ \mathbf{if}\;J \leq -4.6 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq -4.3 \cdot 10^{-262}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 7 \cdot 10^{-183}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 1.25 \cdot 10^{+49}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	58.1%
Cost	7244

\[\begin{array}{l} t_0 := \left(J \cdot -2\right) \cdot \cos \left(K \cdot 0.5\right)\\ \mathbf{if}\;J \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq -4.4 \cdot 10^{-262}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 1.85 \cdot 10^{-175}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	38.1%
Cost	920

\[\begin{array}{l} \mathbf{if}\;U \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;-U\\ \mathbf{elif}\;U \leq -9.2 \cdot 10^{-131}:\\ \;\;\;\;U\\ \mathbf{elif}\;U \leq 1.02 \cdot 10^{-88}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;U \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;-U\\ \mathbf{elif}\;U \leq 5.5 \cdot 10^{+187}:\\ \;\;\;\;U\\ \mathbf{elif}\;U \leq 8.6 \cdot 10^{+216}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 6
Accuracy	27.0%
Cost	788

\[\begin{array}{l} \mathbf{if}\;U \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;-U\\ \mathbf{elif}\;U \leq -4 \cdot 10^{-201}:\\ \;\;\;\;U\\ \mathbf{elif}\;U \leq 4.3 \cdot 10^{+101}:\\ \;\;\;\;-U\\ \mathbf{elif}\;U \leq 2.4 \cdot 10^{+185}:\\ \;\;\;\;U\\ \mathbf{elif}\;U \leq 4.2 \cdot 10^{+217}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 7
Accuracy	27.4%
Cost	64

\[U \]

Reproduce

herbie shell --seed 2023133 
(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)))))