Average Error: 17.8 → 8.0
Time: 13.2s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
↓
\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := \left(-2 \cdot \mathsf{hypot}\left(1, \frac{U}{\left(J \cdot -2\right) \cdot t_0}\right)\right) \cdot \left(J \cdot t_0\right)\\ \mathbf{if}\;J \leq 5.545996234148348 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J \leq 1.1675397400157695 \cdot 10^{-256}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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 (* (* -2.0 (hypot 1.0 (/ U (* (* J -2.0) t_0)))) (* J t_0))))
   (if (<= J 5.545996234148348e-304)
     t_1
     (if (<= J 1.1675397400157695e-256) U t_1))))
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 = (-2.0 * hypot(1.0, (U / ((J * -2.0) * t_0)))) * (J * t_0);
	double tmp;
	if (J <= 5.545996234148348e-304) {
		tmp = t_1;
	} else if (J <= 1.1675397400157695e-256) {
		tmp = U;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 = (-2.0 * Math.hypot(1.0, (U / ((J * -2.0) * t_0)))) * (J * t_0);
	double tmp;
	if (J <= 5.545996234148348e-304) {
		tmp = t_1;
	} else if (J <= 1.1675397400157695e-256) {
		tmp = U;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 = (-2.0 * math.hypot(1.0, (U / ((J * -2.0) * t_0)))) * (J * t_0)
	tmp = 0
	if J <= 5.545996234148348e-304:
		tmp = t_1
	elif J <= 1.1675397400157695e-256:
		tmp = U
	else:
		tmp = t_1
	return tmp

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 = Float64(Float64(-2.0 * hypot(1.0, Float64(U / Float64(Float64(J * -2.0) * t_0)))) * Float64(J * t_0))
	tmp = 0.0
	if (J <= 5.545996234148348e-304)
		tmp = t_1;
	elseif (J <= 1.1675397400157695e-256)
		tmp = U;
	else
		tmp = t_1;
	end
	return tmp
end

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 = (-2.0 * hypot(1.0, (U / ((J * -2.0) * t_0)))) * (J * t_0);
	tmp = 0.0;
	if (J <= 5.545996234148348e-304)
		tmp = t_1;
	elseif (J <= 1.1675397400157695e-256)
		tmp = U;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

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[(N[(-2.0 * N[Sqrt[1.0 ^ 2 + N[(U / N[(N[(J * -2.0), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * N[(J * t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[J, 5.545996234148348e-304], t$95$1, If[LessEqual[J, 1.1675397400157695e-256], U, t$95$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}}
↓
\begin{array}{l}
t_0 := \cos \left(\frac{K}{2}\right)\\
t_1 := \left(-2 \cdot \mathsf{hypot}\left(1, \frac{U}{\left(J \cdot -2\right) \cdot t_0}\right)\right) \cdot \left(J \cdot t_0\right)\\
\mathbf{if}\;J \leq 5.545996234148348 \cdot 10^{-304}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;J \leq 1.1675397400157695 \cdot 10^{-256}:\\
\;\;\;\;U\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

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 J < 5.54599623414834767e-304 or 1.16753974001576945e-256 < J

    1. Initial program 16.6

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

    2. Simplified6.9

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

    3. Applied egg-rr8.1

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}\right)}^{3}} \]

    4. Applied egg-rr6.9

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

    if 5.54599623414834767e-304 < J < 1.16753974001576945e-256

    1. Initial program 47.7

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

    2. Simplified30.9

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

    3. Taylor expanded in U around -inf 32.8

      \[\leadsto \color{blue}{U} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification8.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \leq 5.545996234148348 \cdot 10^{-304}:\\ \;\;\;\;\left(-2 \cdot \mathsf{hypot}\left(1, \frac{U}{\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)\right) \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)\\ \mathbf{elif}\;J \leq 1.1675397400157695 \cdot 10^{-256}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \mathsf{hypot}\left(1, \frac{U}{\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)\right) \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022133 
(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)))))