Average Error: 17.9 → 8.4
Time: 8.9s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
↓
\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := J \cdot t_0\\ \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot t_0\right) \cdot \sqrt{1 + {\left(\frac{U}{t_0 \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq -\infty:\\ \;\;\;\;-2 \cdot \left(U \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(t_1 \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot t_1}\right)\right)\\ \end{array} \]
(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 (* J t_0)))
   (if (<=
        (* (* (* -2.0 J) t_0) (sqrt (+ 1.0 (pow (/ U (* t_0 (* J 2.0))) 2.0))))
        (- INFINITY))
     (* -2.0 (* U 0.5))
     (* -2.0 (* t_1 (hypot 1.0 (/ U (* 2.0 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 = J * t_0;
	double tmp;
	if ((((-2.0 * J) * t_0) * sqrt((1.0 + pow((U / (t_0 * (J * 2.0))), 2.0)))) <= -((double) INFINITY)) {
		tmp = -2.0 * (U * 0.5);
	} else {
		tmp = -2.0 * (t_1 * hypot(1.0, (U / (2.0 * 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 = J * t_0;
	double tmp;
	if ((((-2.0 * J) * t_0) * Math.sqrt((1.0 + Math.pow((U / (t_0 * (J * 2.0))), 2.0)))) <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 * (U * 0.5);
	} else {
		tmp = -2.0 * (t_1 * Math.hypot(1.0, (U / (2.0 * 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 = J * t_0
	tmp = 0
	if (((-2.0 * J) * t_0) * math.sqrt((1.0 + math.pow((U / (t_0 * (J * 2.0))), 2.0)))) <= -math.inf:
		tmp = -2.0 * (U * 0.5)
	else:
		tmp = -2.0 * (t_1 * math.hypot(1.0, (U / (2.0 * 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(J * t_0)
	tmp = 0.0
	if (Float64(Float64(Float64(-2.0 * J) * t_0) * sqrt(Float64(1.0 + (Float64(U / Float64(t_0 * Float64(J * 2.0))) ^ 2.0)))) <= Float64(-Inf))
		tmp = Float64(-2.0 * Float64(U * 0.5));
	else
		tmp = Float64(-2.0 * Float64(t_1 * hypot(1.0, Float64(U / Float64(2.0 * 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 = J * t_0;
	tmp = 0.0;
	if ((((-2.0 * J) * t_0) * sqrt((1.0 + ((U / (t_0 * (J * 2.0))) ^ 2.0)))) <= -Inf)
		tmp = -2.0 * (U * 0.5);
	else
		tmp = -2.0 * (t_1 * hypot(1.0, (U / (2.0 * 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[(J * t$95$0), $MachinePrecision]}, If[LessEqual[N[(N[(N[(-2.0 * J), $MachinePrecision] * t$95$0), $MachinePrecision] * N[Sqrt[N[(1.0 + N[Power[N[(U / N[(t$95$0 * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(-2.0 * N[(U * 0.5), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(t$95$1 * N[Sqrt[1.0 ^ 2 + N[(U / N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

\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 := J \cdot t_0\\
\mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot t_0\right) \cdot \sqrt{1 + {\left(\frac{U}{t_0 \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq -\infty:\\
\;\;\;\;-2 \cdot \left(U \cdot 0.5\right)\\

\mathbf{else}:\\
\;\;\;\;-2 \cdot \left(t_1 \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot t_1}\right)\right)\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) < -inf.0

    1. Initial program 64.0

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

    2. Simplified29.0

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

    3. Applied egg-rr29.8

      \[\leadsto -2 \cdot \left(\mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right) \cdot \color{blue}{{\left(\sqrt[3]{J \cdot \cos \left(K \cdot 0.5\right)}\right)}^{3}}\right) \]

    4. Applied egg-rr29.4

      \[\leadsto -2 \cdot \left(\mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right) \cdot \color{blue}{\left({\left(\sqrt[3]{\cos \left(K \cdot 0.5\right)}\right)}^{2} \cdot \left(\sqrt[3]{\cos \left(K \cdot 0.5\right)} \cdot J\right)\right)}\right) \]

    5. Taylor expanded in U around inf 31.5

      \[\leadsto -2 \cdot \color{blue}{\left(0.5 \cdot U\right)} \]

    if -inf.0 < (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

    1. Initial program 10.3

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

    2. Simplified4.5

      \[\leadsto \color{blue}{-2 \cdot \left(\mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right) \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)\right)} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification8.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq -\infty:\\ \;\;\;\;-2 \cdot \left(U \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(J \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022212 
(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)))))