Maksimov and Kolovsky, Equation (4)

Average Accuracy: 85.8% → 73.4%

Time: 20.6s

Precision: binary64

Cost: 14352

• Unsound rule application detected in e-graph. Results may not be sound.

• 49.5% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := U + t_0 \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ t_2 := U + \left(-0.125 \cdot \left(K \cdot K\right) + 1\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\\ \mathbf{if}\;\ell \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 5.6:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq 246:\\ \;\;\;\;t_0 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) + U\\ \mathbf{elif}\;\ell \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))

↓

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0)))
        (t_1 (+ U (* t_0 (* (pow l 3.0) (* J 0.3333333333333333)))))
        (t_2
         (+ U (* (+ (* -0.125 (* K K)) 1.0) (* (- (exp l) (exp (- l))) J)))))
   (if (<= l 3.5e+100)
     t_1
     (if (<= l 5.6)
       t_2
       (if (<= l 246.0)
         (+ (* t_0 (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))) U)
         (if (<= l 4.6e+67) t_2 t_1))))))

C

double code(double J, double l, double K, double U) {
	return ((J * (exp(l) - exp(-l))) * cos((K / 2.0))) + U;
}

↓

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = U + (t_0 * (pow(l, 3.0) * (J * 0.3333333333333333)));
	double t_2 = U + (((-0.125 * (K * K)) + 1.0) * ((exp(l) - exp(-l)) * J));
	double tmp;
	if (l <= 3.5e+100) {
		tmp = t_1;
	} else if (l <= 5.6) {
		tmp = t_2;
	} else if (l <= 246.0) {
		tmp = (t_0 * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0)))) + U;
	} else if (l <= 4.6e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = ((j * (exp(l) - exp(-l))) * cos((k / 2.0d0))) + u
end function

↓

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = cos((k / 2.0d0))
    t_1 = u + (t_0 * ((l ** 3.0d0) * (j * 0.3333333333333333d0)))
    t_2 = u + ((((-0.125d0) * (k * k)) + 1.0d0) * ((exp(l) - exp(-l)) * j))
    if (l <= 3.5d+100) then
        tmp = t_1
    else if (l <= 5.6d0) then
        tmp = t_2
    else if (l <= 246.0d0) then
        tmp = (t_0 * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0)))) + u
    else if (l <= 4.6d+67) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

↓

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = U + (t_0 * (Math.pow(l, 3.0) * (J * 0.3333333333333333)));
	double t_2 = U + (((-0.125 * (K * K)) + 1.0) * ((Math.exp(l) - Math.exp(-l)) * J));
	double tmp;
	if (l <= 3.5e+100) {
		tmp = t_1;
	} else if (l <= 5.6) {
		tmp = t_2;
	} else if (l <= 246.0) {
		tmp = (t_0 * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0)))) + U;
	} else if (l <= 4.6e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	return ((J * (math.exp(l) - math.exp(-l))) * math.cos((K / 2.0))) + U

↓

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = U + (t_0 * (math.pow(l, 3.0) * (J * 0.3333333333333333)))
	t_2 = U + (((-0.125 * (K * K)) + 1.0) * ((math.exp(l) - math.exp(-l)) * J))
	tmp = 0
	if l <= 3.5e+100:
		tmp = t_1
	elif l <= 5.6:
		tmp = t_2
	elif l <= 246.0:
		tmp = (t_0 * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0)))) + U
	elif l <= 4.6e+67:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(J, l, K, U)
	return Float64(Float64(Float64(J * Float64(exp(l) - exp(Float64(-l)))) * cos(Float64(K / 2.0))) + U)
end

↓

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(U + Float64(t_0 * Float64((l ^ 3.0) * Float64(J * 0.3333333333333333))))
	t_2 = Float64(U + Float64(Float64(Float64(-0.125 * Float64(K * K)) + 1.0) * Float64(Float64(exp(l) - exp(Float64(-l))) * J)))
	tmp = 0.0
	if (l <= 3.5e+100)
		tmp = t_1;
	elseif (l <= 5.6)
		tmp = t_2;
	elseif (l <= 246.0)
		tmp = Float64(Float64(t_0 * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))) + U);
	elseif (l <= 4.6e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = ((J * (exp(l) - exp(-l))) * cos((K / 2.0))) + U;
end

↓

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = U + (t_0 * ((l ^ 3.0) * (J * 0.3333333333333333)));
	t_2 = U + (((-0.125 * (K * K)) + 1.0) * ((exp(l) - exp(-l)) * J));
	tmp = 0.0;
	if (l <= 3.5e+100)
		tmp = t_1;
	elseif (l <= 5.6)
		tmp = t_2;
	elseif (l <= 246.0)
		tmp = (t_0 * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0)))) + U;
	elseif (l <= 4.6e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := N[(N[(N[(J * N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]

↓

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(U + N[(t$95$0 * N[(N[Power[l, 3.0], $MachinePrecision] * N[(J * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(U + N[(N[(N[(-0.125 * N[(K * K), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, 3.5e+100], t$95$1, If[LessEqual[l, 5.6], t$95$2, If[LessEqual[l, 246.0], N[(N[(t$95$0 * N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], If[LessEqual[l, 4.6e+67], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < 3.49999999999999976e100 or 4.5999999999999997e67 < l

   1. Initial program 85.9%

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

   2. Taylor expanded in l around 0 86.2%

      \[\leadsto \left(J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3} + 2 \cdot \ell\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   3. Taylor expanded in l around inf 71.4%

      \[\leadsto \color{blue}{\left(0.3333333333333333 \cdot \left({\ell}^{3} \cdot J\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   4. Simplified 71.4%

      \[\leadsto \color{blue}{\left({\ell}^{3} \cdot \left(0.3333333333333333 \cdot J\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
      Step-by-step derivation

      [Start] 71.4	\[ \left(0.3333333333333333 \cdot \left({\ell}^{3} \cdot J\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
      associate-*r* [=>] 71.4	\[ \color{blue}{\left(\left(0.3333333333333333 \cdot {\ell}^{3}\right) \cdot J\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
      *-commutative [=>] 71.4	\[ \left(\color{blue}{\left({\ell}^{3} \cdot 0.3333333333333333\right)} \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
      associate-*r* [<=] 71.4	\[ \color{blue}{\left({\ell}^{3} \cdot \left(0.3333333333333333 \cdot J\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   if 3.49999999999999976e100 < l < 5.5999999999999996 or 246 < l < 4.5999999999999997e67

   1. Initial program 85.9%

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

   2. Taylor expanded in K around 0 21.9%

      \[\leadsto \color{blue}{\left(\left(e^{\ell} - e^{-\ell}\right) \cdot J + -0.125 \cdot \left({K}^{2} \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\right)\right)} + U \]

   3. Simplified 64.9%

      \[\leadsto \color{blue}{\left(-0.125 \cdot \left(K \cdot K\right) + 1\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)} + U \]
      Step-by-step derivation

      [Start] 21.9	\[ \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J + -0.125 \cdot \left({K}^{2} \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\right)\right) + U \]
      associate-*r* [=>] 21.9	\[ \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J + \color{blue}{\left(-0.125 \cdot {K}^{2}\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)}\right) + U \]
      distribute-rgt1-in [=>] 64.9	\[ \color{blue}{\left(-0.125 \cdot {K}^{2} + 1\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)} + U \]
      unpow2 [=>] 64.9	\[ \left(-0.125 \cdot \color{blue}{\left(K \cdot K\right)} + 1\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right) + U \]

   if 5.5999999999999996 < l < 246

   1. Initial program 85.9%

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

   2. Taylor expanded in l around 0 86.2%

      \[\leadsto \left(J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3} + 2 \cdot \ell\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ \mathbf{elif}\;\ell \leq 5.6:\\ \;\;\;\;U + \left(-0.125 \cdot \left(K \cdot K\right) + 1\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\\ \mathbf{elif}\;\ell \leq 246:\\ \;\;\;\;\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) + U\\ \mathbf{elif}\;\ell \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;U + \left(-0.125 \cdot \left(K \cdot K\right) + 1\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	52.1%
Cost	46216

\[\begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ t_1 := t_0 \leq 4 \cdot 10^{-6}\\ t_2 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;t_1:\\ \;\;\;\;t_0 \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\\ \mathbf{elif}\;t_1:\\ \;\;\;\;t_2 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + t_2 \cdot \left(t_0 \cdot J\right)\\ \end{array} \]

Alternative 2
Accuracy	52.0%
Cost	46089

\[\begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_0 \leq 4 \cdot 10^{-6} \lor \neg \left(t_0 \leq 1000000\right):\\ \;\;\;\;t_0 \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) + U\\ \end{array} \]

Alternative 3
Accuracy	73.4%
Cost	14220

\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := U + t_0 \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ t_2 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 0.65:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq 7000:\\ \;\;\;\;t_0 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) + U\\ \mathbf{elif}\;\ell \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	73.4%
Cost	14096

\[\begin{array}{l} t_0 := U + \cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ t_1 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 0.62:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 7000:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\right)\\ \mathbf{elif}\;\ell \leq 1.8 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	72.9%
Cost	13577

\[\begin{array}{l} \mathbf{if}\;\ell \leq 3.7 \lor \neg \left(\ell \leq 7000\right):\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	64.3%
Cost	7633

\[\begin{array}{l} t_0 := U + 2 \cdot \left(\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\right)\\ \mathbf{if}\;\ell \leq 5.6 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 245000:\\ \;\;\;\;U + J \cdot \left(24 + \left(K \cdot K\right) \cdot \left(-768 + \left(K \cdot K\right) \cdot 4096\right)\right)\\ \mathbf{elif}\;\ell \leq 240 \lor \neg \left(\ell \leq 1.7 \cdot 10^{+135}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(-8738.133333333333 \cdot {K}^{6}\right)\\ \end{array} \]

Alternative 7
Accuracy	71.4%
Cost	7564

\[\begin{array}{l} t_0 := U + J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\\ \mathbf{if}\;\ell \leq 1860:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 600:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\right)\\ \mathbf{elif}\;\ell \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;U + J \cdot \left(-8738.133333333333 \cdot {K}^{6}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Accuracy	25.2%
Cost	7441

\[\begin{array}{l} t_0 := U + J \cdot \left(24 + \left(K \cdot K\right) \cdot \left(-768 + \left(K \cdot K\right) \cdot 4096\right)\right)\\ \mathbf{if}\;\ell \leq 245000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 340:\\ \;\;\;\;U\\ \mathbf{elif}\;\ell \leq 1.98 \cdot 10^{+31} \lor \neg \left(\ell \leq 5.5 \cdot 10^{+217}\right):\\ \;\;\;\;U + -0.0013020833333333333 \cdot \left(J \cdot {K}^{4}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Accuracy	25.4%
Cost	7441

\[\begin{array}{l} t_0 := U + J \cdot \left(24 + \left(K \cdot K\right) \cdot \left(-768 + \left(K \cdot K\right) \cdot 4096\right)\right)\\ \mathbf{if}\;\ell \leq 245000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 415:\\ \;\;\;\;U\\ \mathbf{elif}\;\ell \leq 3.25 \cdot 10^{+31} \lor \neg \left(\ell \leq 1.55 \cdot 10^{+218}\right):\\ \;\;\;\;U + J \cdot \left(-8738.133333333333 \cdot {K}^{6}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Accuracy	24.5%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;\ell \leq 245000:\\ \;\;\;\;U + J \cdot \left(24 + \left(K \cdot K\right) \cdot \left(-768 + \left(K \cdot K\right) \cdot 4096\right)\right)\\ \mathbf{elif}\;\ell \leq 310:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(24 + K \cdot \left(K \cdot -768\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	10.7%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\ell \leq 620:\\ \;\;\;\;J \cdot \left(-8 + \left(K \cdot K\right) \cdot 256\right)\\ \mathbf{elif}\;\ell \leq 200:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(24 + K \cdot \left(K \cdot -768\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	9.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\ell \leq 460 \lor \neg \left(\ell \leq 3.85 \cdot 10^{+31}\right):\\ \;\;\;\;J \cdot \left(-8 + \left(K \cdot K\right) \cdot 256\right)\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 13
Accuracy	10.5%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\ell \leq 750:\\ \;\;\;\;J \cdot \left(-8 + \left(K \cdot K\right) \cdot 256\right)\\ \mathbf{elif}\;\ell \leq 510:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U + \left(K \cdot K\right) \cdot \left(J \cdot -768\right)\\ \end{array} \]

Alternative 14
Accuracy	2.8%
Cost	64

\[1 \]

Alternative 15
Accuracy	36.7%
Cost	64

\[U \]

Reproduce

herbie shell --seed 2023159 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))