Maksimov and Kolovsky, Equation (3)

Average Error: 18.2 → 8.5

Time: 22.9s

Precision: binary64

Cost: 20617

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;J \leq -4.7 \cdot 10^{-231} \lor \neg \left(J \leq 1.5 \cdot 10^{-286}\right):\\ \;\;\;\;\left(t_0 \cdot \left(J \cdot -2\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot t_0\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array} \]

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))))
   (if (or (<= J -4.7e-231) (not (<= J 1.5e-286)))
     (* (* t_0 (* J -2.0)) (hypot 1.0 (/ U (* 2.0 (* J t_0)))))
     (- U))))

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 tmp;
	if ((J <= -4.7e-231) || !(J <= 1.5e-286)) {
		tmp = (t_0 * (J * -2.0)) * hypot(1.0, (U / (2.0 * (J * t_0))));
	} else {
		tmp = -U;
	}
	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 tmp;
	if ((J <= -4.7e-231) || !(J <= 1.5e-286)) {
		tmp = (t_0 * (J * -2.0)) * Math.hypot(1.0, (U / (2.0 * (J * t_0))));
	} else {
		tmp = -U;
	}
	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))
	tmp = 0
	if (J <= -4.7e-231) or not (J <= 1.5e-286):
		tmp = (t_0 * (J * -2.0)) * math.hypot(1.0, (U / (2.0 * (J * t_0))))
	else:
		tmp = -U
	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))
	tmp = 0.0
	if ((J <= -4.7e-231) || !(J <= 1.5e-286))
		tmp = Float64(Float64(t_0 * Float64(J * -2.0)) * hypot(1.0, Float64(U / Float64(2.0 * Float64(J * t_0)))));
	else
		tmp = Float64(-U);
	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));
	tmp = 0.0;
	if ((J <= -4.7e-231) || ~((J <= 1.5e-286)))
		tmp = (t_0 * (J * -2.0)) * hypot(1.0, (U / (2.0 * (J * t_0))));
	else
		tmp = -U;
	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]}, If[Or[LessEqual[J, -4.7e-231], N[Not[LessEqual[J, 1.5e-286]], $MachinePrecision]], N[(N[(t$95$0 * N[(J * -2.0), $MachinePrecision]), $MachinePrecision] * N[Sqrt[1.0 ^ 2 + N[(U / N[(2.0 * N[(J * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], (-U)]]

Derivation

1. Split input into 2 regimes

2. if J < -4.7000000000000002e-231 or 1.5e-286 < J

   1. Initial program 15.8

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

   2. Simplified 6.3

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

      [Start] 15.8	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      unpow2 [=>] 15.8	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + \color{blue}{\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}}} \]
      hypot-1-def [=>] 6.3	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\mathsf{hypot}\left(1, \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)} \]
      associate-*l* [=>] 6.3	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\color{blue}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}}\right) \]

   if -4.7000000000000002e-231 < J < 1.5e-286

   1. Initial program 45.1

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

   2. Simplified 28.1

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

      [Start] 45.1	\[ \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
      associate-*l* [=>] 45.1	\[ \color{blue}{\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)} \]
      unpow2 [=>] 45.1	\[ \left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + \color{blue}{\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}}}\right) \]
      hypot-1-def [=>] 28.1	\[ \left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \color{blue}{\mathsf{hypot}\left(1, \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}\right) \]
      *-commutative [=>] 28.1	\[ \left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\color{blue}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}}\right)\right) \]
      *-commutative [=>] 28.1	\[ \left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \color{blue}{\left(J \cdot 2\right)}}\right)\right) \]

   3. Taylor expanded in J around 0 33.1

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

   4. Simplified 33.1

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

      [Start] 33.1	\[ -1 \cdot U \]
      mul-1-neg [=>] 33.1	\[ \color{blue}{-U} \]

3. Recombined 2 regimes into one program.

4. Final simplification 8.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;J \leq -4.7 \cdot 10^{-231} \lor \neg \left(J \leq 1.5 \cdot 10^{-286}\right):\\ \;\;\;\;\left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot -2\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array} \]

Alternatives

Alternative 1
Error	8.5
Cost	20617

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;J \leq -1.05 \cdot 10^{-232} \lor \neg \left(J \leq 1.75 \cdot 10^{-286}\right):\\ \;\;\;\;-2 \cdot \left(t_0 \cdot \left(J \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot t_0\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array} \]

Alternative 2
Error	8.5
Cost	20616

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;J \leq -7.5 \cdot 10^{-235}:\\ \;\;\;\;-2 \cdot \left(t_0 \cdot \left(J \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot t_0\right)}\right)\right)\right)\\ \mathbf{elif}\;J \leq 1.5 \cdot 10^{-286}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 \cdot \mathsf{hypot}\left(1, \frac{U}{t_0 \cdot \left(J \cdot 2\right)}\right)\right) \cdot \left(J \cdot -2\right)\\ \end{array} \]

Alternative 3
Error	17.4
Cost	14620

\[\begin{array}{l} t_0 := \left(\cos \left(\frac{K}{2}\right) \cdot \mathsf{hypot}\left(1, \frac{U \cdot 0.5}{J}\right)\right) \cdot \left(J \cdot -2\right)\\ \mathbf{if}\;J \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq 1.75 \cdot 10^{-289}:\\ \;\;\;\;-2 \cdot \left(J \cdot \frac{J}{U}\right) - U\\ \mathbf{elif}\;J \leq 5.6 \cdot 10^{-241}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 1.28 \cdot 10^{-233}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 4 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq 7.3 \cdot 10^{-205}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;\left(J \cdot -2\right) \cdot \mathsf{hypot}\left(1, 0.5 \cdot \frac{U}{J}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	17.3
Cost	14620

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := \left(t_0 \cdot \mathsf{hypot}\left(1, \frac{U \cdot 0.5}{J}\right)\right) \cdot \left(J \cdot -2\right)\\ \mathbf{if}\;J \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq 1.9 \cdot 10^{-291}:\\ \;\;\;\;-2 \cdot \left(J \cdot \frac{J}{U}\right) - U\\ \mathbf{elif}\;J \leq 5.5 \cdot 10^{-239}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 5.6 \cdot 10^{-233}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 4 \cdot 10^{-219}:\\ \;\;\;\;\left(t_0 \cdot \left(J \cdot -2\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{J \cdot 2}\right)\\ \mathbf{elif}\;J \leq 1.05 \cdot 10^{-205}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 2.55 \cdot 10^{-117}:\\ \;\;\;\;\left(J \cdot -2\right) \cdot \mathsf{hypot}\left(1, 0.5 \cdot \frac{U}{J}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	17.3
Cost	14620

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := \left(t_0 \cdot \mathsf{hypot}\left(1, \frac{U \cdot 0.5}{J}\right)\right) \cdot \left(J \cdot -2\right)\\ \mathbf{if}\;J \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq 4.6 \cdot 10^{-290}:\\ \;\;\;\;\frac{-2}{\frac{\frac{U}{J}}{J \cdot {\cos \left(K \cdot 0.5\right)}^{2}}} - U\\ \mathbf{elif}\;J \leq 6.8 \cdot 10^{-245}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 1.15 \cdot 10^{-232}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 4 \cdot 10^{-220}:\\ \;\;\;\;\left(t_0 \cdot \left(J \cdot -2\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{J \cdot 2}\right)\\ \mathbf{elif}\;J \leq 1.9 \cdot 10^{-206}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 3.85 \cdot 10^{-118}:\\ \;\;\;\;\left(J \cdot -2\right) \cdot \mathsf{hypot}\left(1, 0.5 \cdot \frac{U}{J}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	23.5
Cost	7832

\[\begin{array}{l} t_0 := \left(J \cdot -2\right) \cdot \mathsf{hypot}\left(1, 0.5 \cdot \frac{U}{J}\right)\\ t_1 := \cos \left(K \cdot 0.5\right) \cdot \left(J \cdot -2\right)\\ \mathbf{if}\;J \leq -2.7 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq 8.5 \cdot 10^{-287}:\\ \;\;\;\;-2 \cdot \left(J \cdot \frac{J}{U}\right) - U\\ \mathbf{elif}\;J \leq 1.15 \cdot 10^{-244}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 1.1 \cdot 10^{-234}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \leq 5 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	25.6
Cost	7376

\[\begin{array}{l} t_0 := -2 \cdot \left(J \cdot \frac{J}{U}\right) - U\\ t_1 := \cos \left(K \cdot 0.5\right) \cdot \left(J \cdot -2\right)\\ \mathbf{if}\;J \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq 1.85 \cdot 10^{-291}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq 3.5 \cdot 10^{-209}:\\ \;\;\;\;U\\ \mathbf{elif}\;J \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	40.3
Cost	1448

\[\begin{array}{l} \mathbf{if}\;K \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq -0.0011:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq -7.5 \cdot 10^{-213}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 7.2 \cdot 10^{-221}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq 1.5 \cdot 10^{-164}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq 6 \cdot 10^{+165}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 2.3 \cdot 10^{+211}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 9
Error	40.3
Cost	1448

\[\begin{array}{l} \mathbf{if}\;K \leq -7.4 \cdot 10^{+127}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq -0.00036:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq -5.1 \cdot 10^{-213}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq -1.7 \cdot 10^{-249}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 1.2 \cdot 10^{-212}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq 1.15 \cdot 10^{-164}:\\ \;\;\;\;-2 \cdot \left(J \cdot \frac{J}{U}\right) - U\\ \mathbf{elif}\;K \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq 3.1 \cdot 10^{+60}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq 6 \cdot 10^{+165}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 2.9 \cdot 10^{+210}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 10
Error	40.8
Cost	1448

\[\begin{array}{l} \mathbf{if}\;K \leq -4.4 \cdot 10^{+128}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq -6.2 \cdot 10^{-34}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq -5.3 \cdot 10^{-213}:\\ \;\;\;\;\left(J \cdot -2\right) \cdot \left(1 + \left(\frac{U}{J} \cdot \frac{U}{J}\right) \cdot 0.125\right)\\ \mathbf{elif}\;K \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 5.2 \cdot 10^{-211}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq 6.8 \cdot 10^{-163}:\\ \;\;\;\;-2 \cdot \left(J \cdot \frac{J}{U}\right) - U\\ \mathbf{elif}\;K \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;J \cdot -2\\ \mathbf{elif}\;K \leq 7.7 \cdot 10^{+59}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq 5.8 \cdot 10^{+165}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 3 \cdot 10^{+211}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 11
Error	47.3
Cost	920

\[\begin{array}{l} \mathbf{if}\;K \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq -6.8 \cdot 10^{-202}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq -9 \cdot 10^{-249}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 3.9 \cdot 10^{+60}:\\ \;\;\;\;-U\\ \mathbf{elif}\;K \leq 5.4 \cdot 10^{+165}:\\ \;\;\;\;U\\ \mathbf{elif}\;K \leq 2.4 \cdot 10^{+214}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 12
Error	47.0
Cost	64

\[U \]

Reproduce

herbie shell --seed 2023059 
(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)))))