Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 85.8% → 99.7%

Time: 9.9s

Alternatives: 10

Speedup: 1.4×

• 49.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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

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;
}

Python

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

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

MATLAB

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

Initial Program: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

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;
}

Python

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

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

MATLAB

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

Alternative 1: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\left(t_0 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(\ell \cdot \left(2 \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- (exp l) (exp (- l)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e-8)))
     (+ (* (* t_0 J) (cos (/ K 2.0))) U)
     (+ U (* J (* l (* 2.0 (cos (* K 0.5)))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = exp(l) - exp(-l);
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 2e-8)) {
		tmp = ((t_0 * J) * cos((K / 2.0))) + U;
	} else {
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	}
	return tmp;
}

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.exp(l) - Math.exp(-l);
	double tmp;
	if ((t_0 <= -Double.POSITIVE_INFINITY) || !(t_0 <= 2e-8)) {
		tmp = ((t_0 * J) * Math.cos((K / 2.0))) + U;
	} else {
		tmp = U + (J * (l * (2.0 * Math.cos((K * 0.5)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.exp(l) - math.exp(-l)
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 2e-8):
		tmp = ((t_0 * J) * math.cos((K / 2.0))) + U
	else:
		tmp = U + (J * (l * (2.0 * math.cos((K * 0.5)))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(exp(l) - exp(Float64(-l)))
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !(t_0 <= 2e-8))
		tmp = Float64(Float64(Float64(t_0 * J) * cos(Float64(K / 2.0))) + U);
	else
		tmp = Float64(U + Float64(J * Float64(l * Float64(2.0 * cos(Float64(K * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = exp(l) - exp(-l);
	tmp = 0.0;
	if ((t_0 <= -Inf) || ~((t_0 <= 2e-8)))
		tmp = ((t_0 * J) * cos((K / 2.0))) + U;
	else
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 2e-8]], $MachinePrecision]], N[(N[(N[(t$95$0 * J), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(J * N[(l * N[(2.0 * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 95.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + \cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ t_1 := \left(e^{\ell} - e^{-\ell}\right) \cdot J + U\\ \mathbf{if}\;\ell \leq -1.1 \cdot 10^{+121}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -0.165:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 0.0038:\\ \;\;\;\;U + J \cdot \left(\ell \cdot \left(2 \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{elif}\;\ell \leq 3.25 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0
         (+ U (* (cos (/ K 2.0)) (* (pow l 3.0) (* J 0.3333333333333333)))))
        (t_1 (+ (* (- (exp l) (exp (- l))) J) U)))
   (if (<= l -1.1e+121)
     t_0
     (if (<= l -0.165)
       t_1
       (if (<= l 0.0038)
         (+ U (* J (* l (* 2.0 (cos (* K 0.5))))))
         (if (<= l 3.25e+102) t_1 t_0))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + (cos((K / 2.0)) * (pow(l, 3.0) * (J * 0.3333333333333333)));
	double t_1 = ((exp(l) - exp(-l)) * J) + U;
	double tmp;
	if (l <= -1.1e+121) {
		tmp = t_0;
	} else if (l <= -0.165) {
		tmp = t_1;
	} else if (l <= 0.0038) {
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	} else if (l <= 3.25e+102) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = u + (cos((k / 2.0d0)) * ((l ** 3.0d0) * (j * 0.3333333333333333d0)))
    t_1 = ((exp(l) - exp(-l)) * j) + u
    if (l <= (-1.1d+121)) then
        tmp = t_0
    else if (l <= (-0.165d0)) then
        tmp = t_1
    else if (l <= 0.0038d0) then
        tmp = u + (j * (l * (2.0d0 * cos((k * 0.5d0)))))
    else if (l <= 3.25d+102) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = U + (Math.cos((K / 2.0)) * (Math.pow(l, 3.0) * (J * 0.3333333333333333)));
	double t_1 = ((Math.exp(l) - Math.exp(-l)) * J) + U;
	double tmp;
	if (l <= -1.1e+121) {
		tmp = t_0;
	} else if (l <= -0.165) {
		tmp = t_1;
	} else if (l <= 0.0038) {
		tmp = U + (J * (l * (2.0 * Math.cos((K * 0.5)))));
	} else if (l <= 3.25e+102) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + (math.cos((K / 2.0)) * (math.pow(l, 3.0) * (J * 0.3333333333333333)))
	t_1 = ((math.exp(l) - math.exp(-l)) * J) + U
	tmp = 0
	if l <= -1.1e+121:
		tmp = t_0
	elif l <= -0.165:
		tmp = t_1
	elif l <= 0.0038:
		tmp = U + (J * (l * (2.0 * math.cos((K * 0.5)))))
	elif l <= 3.25e+102:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64((l ^ 3.0) * Float64(J * 0.3333333333333333))))
	t_1 = Float64(Float64(Float64(exp(l) - exp(Float64(-l))) * J) + U)
	tmp = 0.0
	if (l <= -1.1e+121)
		tmp = t_0;
	elseif (l <= -0.165)
		tmp = t_1;
	elseif (l <= 0.0038)
		tmp = Float64(U + Float64(J * Float64(l * Float64(2.0 * cos(Float64(K * 0.5))))));
	elseif (l <= 3.25e+102)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + (cos((K / 2.0)) * ((l ^ 3.0) * (J * 0.3333333333333333)));
	t_1 = ((exp(l) - exp(-l)) * J) + U;
	tmp = 0.0;
	if (l <= -1.1e+121)
		tmp = t_0;
	elseif (l <= -0.165)
		tmp = t_1;
	elseif (l <= 0.0038)
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	elseif (l <= 3.25e+102)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[l, 3.0], $MachinePrecision] * N[(J * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision] + U), $MachinePrecision]}, If[LessEqual[l, -1.1e+121], t$95$0, If[LessEqual[l, -0.165], t$95$1, If[LessEqual[l, 0.0038], N[(U + N[(J * N[(l * N[(2.0 * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 3.25e+102], t$95$1, t$95$0]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 78.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq 0.1:\\ \;\;\;\;U + J \cdot \left(\ell \cdot \left(2 \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(\ell \cdot 2 + {\ell}^{3} \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) 0.1)
   (+ U (* J (* l (* 2.0 (cos (* K 0.5))))))
   (+ U (* J (+ (* l 2.0) (* (pow l 3.0) 0.3333333333333333))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= 0.1) {
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	} else {
		tmp = U + (J * ((l * 2.0) + (pow(l, 3.0) * 0.3333333333333333)));
	}
	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
    real(8) :: tmp
    if (cos((k / 2.0d0)) <= 0.1d0) then
        tmp = u + (j * (l * (2.0d0 * cos((k * 0.5d0)))))
    else
        tmp = u + (j * ((l * 2.0d0) + ((l ** 3.0d0) * 0.3333333333333333d0)))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= 0.1) {
		tmp = U + (J * (l * (2.0 * Math.cos((K * 0.5)))));
	} else {
		tmp = U + (J * ((l * 2.0) + (Math.pow(l, 3.0) * 0.3333333333333333)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= 0.1:
		tmp = U + (J * (l * (2.0 * math.cos((K * 0.5)))))
	else:
		tmp = U + (J * ((l * 2.0) + (math.pow(l, 3.0) * 0.3333333333333333)))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= 0.1)
		tmp = Float64(U + Float64(J * Float64(l * Float64(2.0 * cos(Float64(K * 0.5))))));
	else
		tmp = Float64(U + Float64(J * Float64(Float64(l * 2.0) + Float64((l ^ 3.0) * 0.3333333333333333))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= 0.1)
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	else
		tmp = U + (J * ((l * 2.0) + ((l ^ 3.0) * 0.3333333333333333)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], 0.1], N[(U + N[(J * N[(l * N[(2.0 * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(N[(l * 2.0), $MachinePrecision] + N[(N[Power[l, 3.0], $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 84.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.36 \cdot 10^{+204}:\\ \;\;\;\;U + J \cdot \left(\ell \cdot 2 + \left(\ell \cdot {K}^{2}\right) \cdot -0.25\right)\\ \mathbf{elif}\;\ell \leq -0.105 \lor \neg \left(\ell \leq 0.00086\right):\\ \;\;\;\;\left(e^{\ell} - e^{-\ell}\right) \cdot J + U\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(\ell \cdot \left(2 \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -2.36e+204)
   (+ U (* J (+ (* l 2.0) (* (* l (pow K 2.0)) -0.25))))
   (if (or (<= l -0.105) (not (<= l 0.00086)))
     (+ (* (- (exp l) (exp (- l))) J) U)
     (+ U (* J (* l (* 2.0 (cos (* K 0.5)))))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -2.36e+204) {
		tmp = U + (J * ((l * 2.0) + ((l * pow(K, 2.0)) * -0.25)));
	} else if ((l <= -0.105) || !(l <= 0.00086)) {
		tmp = ((exp(l) - exp(-l)) * J) + U;
	} else {
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	}
	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
    real(8) :: tmp
    if (l <= (-2.36d+204)) then
        tmp = u + (j * ((l * 2.0d0) + ((l * (k ** 2.0d0)) * (-0.25d0))))
    else if ((l <= (-0.105d0)) .or. (.not. (l <= 0.00086d0))) then
        tmp = ((exp(l) - exp(-l)) * j) + u
    else
        tmp = u + (j * (l * (2.0d0 * cos((k * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -2.36e+204) {
		tmp = U + (J * ((l * 2.0) + ((l * Math.pow(K, 2.0)) * -0.25)));
	} else if ((l <= -0.105) || !(l <= 0.00086)) {
		tmp = ((Math.exp(l) - Math.exp(-l)) * J) + U;
	} else {
		tmp = U + (J * (l * (2.0 * Math.cos((K * 0.5)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -2.36e+204:
		tmp = U + (J * ((l * 2.0) + ((l * math.pow(K, 2.0)) * -0.25)))
	elif (l <= -0.105) or not (l <= 0.00086):
		tmp = ((math.exp(l) - math.exp(-l)) * J) + U
	else:
		tmp = U + (J * (l * (2.0 * math.cos((K * 0.5)))))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -2.36e+204)
		tmp = Float64(U + Float64(J * Float64(Float64(l * 2.0) + Float64(Float64(l * (K ^ 2.0)) * -0.25))));
	elseif ((l <= -0.105) || !(l <= 0.00086))
		tmp = Float64(Float64(Float64(exp(l) - exp(Float64(-l))) * J) + U);
	else
		tmp = Float64(U + Float64(J * Float64(l * Float64(2.0 * cos(Float64(K * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -2.36e+204)
		tmp = U + (J * ((l * 2.0) + ((l * (K ^ 2.0)) * -0.25)));
	elseif ((l <= -0.105) || ~((l <= 0.00086)))
		tmp = ((exp(l) - exp(-l)) * J) + U;
	else
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -2.36e+204], N[(U + N[(J * N[(N[(l * 2.0), $MachinePrecision] + N[(N[(l * N[Power[K, 2.0], $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[l, -0.105], N[Not[LessEqual[l, 0.00086]], $MachinePrecision]], N[(N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(J * N[(l * N[(2.0 * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 64.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.8 \cdot 10^{+157} \lor \neg \left(\ell \leq -600\right):\\ \;\;\;\;U + J \cdot \left(\ell \cdot \left(2 \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{U}^{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -2.8e+157) (not (<= l -600.0)))
   (+ U (* J (* l (* 2.0 (cos (* K 0.5))))))
   (pow U -3.0)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -2.8e+157) || !(l <= -600.0)) {
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	} else {
		tmp = pow(U, -3.0);
	}
	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
    real(8) :: tmp
    if ((l <= (-2.8d+157)) .or. (.not. (l <= (-600.0d0)))) then
        tmp = u + (j * (l * (2.0d0 * cos((k * 0.5d0)))))
    else
        tmp = u ** (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -2.8e+157) || !(l <= -600.0)) {
		tmp = U + (J * (l * (2.0 * Math.cos((K * 0.5)))));
	} else {
		tmp = Math.pow(U, -3.0);
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -2.8e+157) or not (l <= -600.0):
		tmp = U + (J * (l * (2.0 * math.cos((K * 0.5)))))
	else:
		tmp = math.pow(U, -3.0)
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -2.8e+157) || !(l <= -600.0))
		tmp = Float64(U + Float64(J * Float64(l * Float64(2.0 * cos(Float64(K * 0.5))))));
	else
		tmp = U ^ -3.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -2.8e+157) || ~((l <= -600.0)))
		tmp = U + (J * (l * (2.0 * cos((K * 0.5)))));
	else
		tmp = U ^ -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -2.8e+157], N[Not[LessEqual[l, -600.0]], $MachinePrecision]], N[(U + N[(J * N[(l * N[(2.0 * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[U, -3.0], $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 53.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -780:\\ \;\;\;\;{U}^{-3}\\ \mathbf{elif}\;\ell \leq 9.2 \cdot 10^{-9} \lor \neg \left(\ell \leq 3.75 \cdot 10^{+143}\right):\\ \;\;\;\;U + J \cdot \left(\ell \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(8 - {K}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -780.0)
   (pow U -3.0)
   (if (or (<= l 9.2e-9) (not (<= l 3.75e+143)))
     (+ U (* J (* l 2.0)))
     (+ U (* J (- 8.0 (pow K 2.0)))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -780.0) {
		tmp = pow(U, -3.0);
	} else if ((l <= 9.2e-9) || !(l <= 3.75e+143)) {
		tmp = U + (J * (l * 2.0));
	} else {
		tmp = U + (J * (8.0 - pow(K, 2.0)));
	}
	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
    real(8) :: tmp
    if (l <= (-780.0d0)) then
        tmp = u ** (-3.0d0)
    else if ((l <= 9.2d-9) .or. (.not. (l <= 3.75d+143))) then
        tmp = u + (j * (l * 2.0d0))
    else
        tmp = u + (j * (8.0d0 - (k ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -780.0) {
		tmp = Math.pow(U, -3.0);
	} else if ((l <= 9.2e-9) || !(l <= 3.75e+143)) {
		tmp = U + (J * (l * 2.0));
	} else {
		tmp = U + (J * (8.0 - Math.pow(K, 2.0)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -780.0:
		tmp = math.pow(U, -3.0)
	elif (l <= 9.2e-9) or not (l <= 3.75e+143):
		tmp = U + (J * (l * 2.0))
	else:
		tmp = U + (J * (8.0 - math.pow(K, 2.0)))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -780.0)
		tmp = U ^ -3.0;
	elseif ((l <= 9.2e-9) || !(l <= 3.75e+143))
		tmp = Float64(U + Float64(J * Float64(l * 2.0)));
	else
		tmp = Float64(U + Float64(J * Float64(8.0 - (K ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -780.0)
		tmp = U ^ -3.0;
	elseif ((l <= 9.2e-9) || ~((l <= 3.75e+143)))
		tmp = U + (J * (l * 2.0));
	else
		tmp = U + (J * (8.0 - (K ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -780.0], N[Power[U, -3.0], $MachinePrecision], If[Or[LessEqual[l, 9.2e-9], N[Not[LessEqual[l, 3.75e+143]], $MachinePrecision]], N[(U + N[(J * N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(8.0 - N[Power[K, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 52.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -750:\\ \;\;\;\;{U}^{-3}\\ \mathbf{elif}\;\ell \leq 7.8 \cdot 10^{+98} \lor \neg \left(\ell \leq 9 \cdot 10^{+202}\right):\\ \;\;\;\;U + J \cdot \left(\ell \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;{U}^{-4}\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -750.0)
   (pow U -3.0)
   (if (or (<= l 7.8e+98) (not (<= l 9e+202)))
     (+ U (* J (* l 2.0)))
     (pow U -4.0))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -750.0) {
		tmp = pow(U, -3.0);
	} else if ((l <= 7.8e+98) || !(l <= 9e+202)) {
		tmp = U + (J * (l * 2.0));
	} else {
		tmp = pow(U, -4.0);
	}
	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
    real(8) :: tmp
    if (l <= (-750.0d0)) then
        tmp = u ** (-3.0d0)
    else if ((l <= 7.8d+98) .or. (.not. (l <= 9d+202))) then
        tmp = u + (j * (l * 2.0d0))
    else
        tmp = u ** (-4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -750.0) {
		tmp = Math.pow(U, -3.0);
	} else if ((l <= 7.8e+98) || !(l <= 9e+202)) {
		tmp = U + (J * (l * 2.0));
	} else {
		tmp = Math.pow(U, -4.0);
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -750.0:
		tmp = math.pow(U, -3.0)
	elif (l <= 7.8e+98) or not (l <= 9e+202):
		tmp = U + (J * (l * 2.0))
	else:
		tmp = math.pow(U, -4.0)
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -750.0)
		tmp = U ^ -3.0;
	elseif ((l <= 7.8e+98) || !(l <= 9e+202))
		tmp = Float64(U + Float64(J * Float64(l * 2.0)));
	else
		tmp = U ^ -4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -750.0)
		tmp = U ^ -3.0;
	elseif ((l <= 7.8e+98) || ~((l <= 9e+202)))
		tmp = U + (J * (l * 2.0));
	else
		tmp = U ^ -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -750.0], N[Power[U, -3.0], $MachinePrecision], If[Or[LessEqual[l, 7.8e+98], N[Not[LessEqual[l, 9e+202]], $MachinePrecision]], N[(U + N[(J * N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[U, -4.0], $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 54.1% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ U + J \cdot \left(\ell \cdot 2\right) \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 (+ U (* J (* l 2.0))))

C

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

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 = u + (j * (l * 2.0d0))
end function

Java

public static double code(double J, double l, double K, double U) {
	return U + (J * (l * 2.0));
}

Python

def code(J, l, K, U):
	return U + (J * (l * 2.0))

Julia

function code(J, l, K, U)
	return Float64(U + Float64(J * Float64(l * 2.0)))
end

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 39.6% accurate, 61.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -122000000000:\\ \;\;\;\;U \cdot U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 (if (<= l -122000000000.0) (* U U) U))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -122000000000.0) {
		tmp = U * U;
	} else {
		tmp = U;
	}
	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
    real(8) :: tmp
    if (l <= (-122000000000.0d0)) then
        tmp = u * u
    else
        tmp = u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -122000000000.0) {
		tmp = U * U;
	} else {
		tmp = U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -122000000000.0:
		tmp = U * U
	else:
		tmp = U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -122000000000.0)
		tmp = Float64(U * U);
	else
		tmp = U;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -122000000000.0)
		tmp = U * U;
	else
		tmp = U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -122000000000.0], N[(U * U), $MachinePrecision], U]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 36.8% accurate, 312.0× speedup

Math

\[\begin{array}{l} \\ U \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 U)

C

double code(double J, double l, double K, double U) {
	return U;
}

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 = u
end function

Java

public static double code(double J, double l, double K, double U) {
	return U;
}

Python

def code(J, l, K, U):
	return U

Julia

function code(J, l, K, U)
	return U
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = U;
end

Wolfram

code[J_, l_, K_, U_] := U

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023350 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))