Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 86.1% → 99.6%

Time: 13.1s

Alternatives: 17

Speedup: 1.5×

• 50.1% 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: 86.1% 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: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+90} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\left(t_1 \cdot J\right) \cdot t_0 + U\\ \mathbf{else}:\\ \;\;\;\;U + t_0 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))) (t_1 (- (exp l) (exp (- l)))))
   (if (or (<= t_1 -1e+90) (not (<= t_1 0.0)))
     (+ (* (* t_1 J) t_0) U)
     (+ U (* t_0 (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(l) - exp(-l);
	double tmp;
	if ((t_1 <= -1e+90) || !(t_1 <= 0.0)) {
		tmp = ((t_1 * J) * t_0) + U;
	} else {
		tmp = U + (t_0 * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((k / 2.0d0))
    t_1 = exp(l) - exp(-l)
    if ((t_1 <= (-1d+90)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = ((t_1 * j) * t_0) + u
    else
        tmp = u + (t_0 * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.exp(l) - Math.exp(-l);
	double tmp;
	if ((t_1 <= -1e+90) || !(t_1 <= 0.0)) {
		tmp = ((t_1 * J) * t_0) + U;
	} else {
		tmp = U + (t_0 * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.exp(l) - math.exp(-l)
	tmp = 0
	if (t_1 <= -1e+90) or not (t_1 <= 0.0):
		tmp = ((t_1 * J) * t_0) + U
	else:
		tmp = U + (t_0 * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(exp(l) - exp(Float64(-l)))
	tmp = 0.0
	if ((t_1 <= -1e+90) || !(t_1 <= 0.0))
		tmp = Float64(Float64(Float64(t_1 * J) * t_0) + U);
	else
		tmp = Float64(U + Float64(t_0 * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = exp(l) - exp(-l);
	tmp = 0.0;
	if ((t_1 <= -1e+90) || ~((t_1 <= 0.0)))
		tmp = ((t_1 * J) * t_0) + U;
	else
		tmp = U + (t_0 * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+90], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(t$95$1 * J), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision], N[(U + 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]), $MachinePrecision]]]]

Derivation

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

Alternative 2: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+90} \lor \neg \left(t_0 \leq 10^{-5}\right):\\ \;\;\;\;t_0 \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + \ell \cdot \left(\cos \left(K \cdot 0.5\right) \cdot \left(J \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- (exp l) (exp (- l)))))
   (if (or (<= t_0 -1e+90) (not (<= t_0 1e-5)))
     (* t_0 J)
     (+ U (* l (* (cos (* K 0.5)) (* J 2.0)))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = exp(l) - exp(-l);
	double tmp;
	if ((t_0 <= -1e+90) || !(t_0 <= 1e-5)) {
		tmp = t_0 * J;
	} else {
		tmp = U + (l * (cos((K * 0.5)) * (J * 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) :: t_0
    real(8) :: tmp
    t_0 = exp(l) - exp(-l)
    if ((t_0 <= (-1d+90)) .or. (.not. (t_0 <= 1d-5))) then
        tmp = t_0 * j
    else
        tmp = u + (l * (cos((k * 0.5d0)) * (j * 2.0d0)))
    end if
    code = tmp
end function

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 <= -1e+90) || !(t_0 <= 1e-5)) {
		tmp = t_0 * J;
	} else {
		tmp = U + (l * (Math.cos((K * 0.5)) * (J * 2.0)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.exp(l) - math.exp(-l)
	tmp = 0
	if (t_0 <= -1e+90) or not (t_0 <= 1e-5):
		tmp = t_0 * J
	else:
		tmp = U + (l * (math.cos((K * 0.5)) * (J * 2.0)))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(exp(l) - exp(Float64(-l)))
	tmp = 0.0
	if ((t_0 <= -1e+90) || !(t_0 <= 1e-5))
		tmp = Float64(t_0 * J);
	else
		tmp = Float64(U + Float64(l * Float64(cos(Float64(K * 0.5)) * Float64(J * 2.0))));
	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 <= -1e+90) || ~((t_0 <= 1e-5)))
		tmp = t_0 * J;
	else
		tmp = U + (l * (cos((K * 0.5)) * (J * 2.0)));
	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, -1e+90], N[Not[LessEqual[t$95$0, 1e-5]], $MachinePrecision]], N[(t$95$0 * J), $MachinePrecision], N[(U + N[(l * N[(N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision] * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 94.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := U + t_0 \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ t_2 := \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -4.2 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq -150:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;U + t_0 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 1.56 \cdot 10^{+100}:\\ \;\;\;\;t_2 + U\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(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 (* (- (exp l) (exp (- l))) J)))
   (if (<= l -4.2e+151)
     t_1
     (if (<= l -150.0)
       t_2
       (if (<= l 2.6e-30)
         (+ U (* t_0 (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))
         (if (<= l 1.56e+100) (+ t_2 U) t_1))))))

C

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 = (exp(l) - exp(-l)) * J;
	double tmp;
	if (l <= -4.2e+151) {
		tmp = t_1;
	} else if (l <= -150.0) {
		tmp = t_2;
	} else if (l <= 2.6e-30) {
		tmp = U + (t_0 * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))));
	} else if (l <= 1.56e+100) {
		tmp = t_2 + U;
	} 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
    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 = (exp(l) - exp(-l)) * j
    if (l <= (-4.2d+151)) then
        tmp = t_1
    else if (l <= (-150.0d0)) then
        tmp = t_2
    else if (l <= 2.6d-30) then
        tmp = u + (t_0 * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))))
    else if (l <= 1.56d+100) then
        tmp = t_2 + u
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 = (Math.exp(l) - Math.exp(-l)) * J;
	double tmp;
	if (l <= -4.2e+151) {
		tmp = t_1;
	} else if (l <= -150.0) {
		tmp = t_2;
	} else if (l <= 2.6e-30) {
		tmp = U + (t_0 * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	} else if (l <= 1.56e+100) {
		tmp = t_2 + U;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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 = (math.exp(l) - math.exp(-l)) * J
	tmp = 0
	if l <= -4.2e+151:
		tmp = t_1
	elif l <= -150.0:
		tmp = t_2
	elif l <= 2.6e-30:
		tmp = U + (t_0 * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))))
	elif l <= 1.56e+100:
		tmp = t_2 + U
	else:
		tmp = t_1
	return tmp

Julia

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(Float64(exp(l) - exp(Float64(-l))) * J)
	tmp = 0.0
	if (l <= -4.2e+151)
		tmp = t_1;
	elseif (l <= -150.0)
		tmp = t_2;
	elseif (l <= 2.6e-30)
		tmp = Float64(U + Float64(t_0 * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))));
	elseif (l <= 1.56e+100)
		tmp = Float64(t_2 + U);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 = (exp(l) - exp(-l)) * J;
	tmp = 0.0;
	if (l <= -4.2e+151)
		tmp = t_1;
	elseif (l <= -150.0)
		tmp = t_2;
	elseif (l <= 2.6e-30)
		tmp = U + (t_0 * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))));
	elseif (l <= 1.56e+100)
		tmp = t_2 + U;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]}, If[LessEqual[l, -4.2e+151], t$95$1, If[LessEqual[l, -150.0], t$95$2, If[LessEqual[l, 2.6e-30], N[(U + 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]), $MachinePrecision], If[LessEqual[l, 1.56e+100], N[(t$95$2 + U), $MachinePrecision], t$95$1]]]]]]]

Derivation

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

Alternative 4: 94.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + \cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\right)\\ t_1 := \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -4.2 \cdot 10^{+151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -190:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;U + \ell \cdot \left(\cos \left(K \cdot 0.5\right) \cdot \left(J \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 1.56 \cdot 10^{+100}:\\ \;\;\;\;t_1 + U\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

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)))
   (if (<= l -4.2e+151)
     t_0
     (if (<= l -190.0)
       t_1
       (if (<= l 2.6e-30)
         (+ U (* l (* (cos (* K 0.5)) (* J 2.0))))
         (if (<= l 1.56e+100) (+ t_1 U) 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;
	double tmp;
	if (l <= -4.2e+151) {
		tmp = t_0;
	} else if (l <= -190.0) {
		tmp = t_1;
	} else if (l <= 2.6e-30) {
		tmp = U + (l * (cos((K * 0.5)) * (J * 2.0)));
	} else if (l <= 1.56e+100) {
		tmp = t_1 + U;
	} 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
    if (l <= (-4.2d+151)) then
        tmp = t_0
    else if (l <= (-190.0d0)) then
        tmp = t_1
    else if (l <= 2.6d-30) then
        tmp = u + (l * (cos((k * 0.5d0)) * (j * 2.0d0)))
    else if (l <= 1.56d+100) then
        tmp = t_1 + u
    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;
	double tmp;
	if (l <= -4.2e+151) {
		tmp = t_0;
	} else if (l <= -190.0) {
		tmp = t_1;
	} else if (l <= 2.6e-30) {
		tmp = U + (l * (Math.cos((K * 0.5)) * (J * 2.0)));
	} else if (l <= 1.56e+100) {
		tmp = t_1 + U;
	} 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
	tmp = 0
	if l <= -4.2e+151:
		tmp = t_0
	elif l <= -190.0:
		tmp = t_1
	elif l <= 2.6e-30:
		tmp = U + (l * (math.cos((K * 0.5)) * (J * 2.0)))
	elif l <= 1.56e+100:
		tmp = t_1 + U
	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(exp(l) - exp(Float64(-l))) * J)
	tmp = 0.0
	if (l <= -4.2e+151)
		tmp = t_0;
	elseif (l <= -190.0)
		tmp = t_1;
	elseif (l <= 2.6e-30)
		tmp = Float64(U + Float64(l * Float64(cos(Float64(K * 0.5)) * Float64(J * 2.0))));
	elseif (l <= 1.56e+100)
		tmp = Float64(t_1 + U);
	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;
	tmp = 0.0;
	if (l <= -4.2e+151)
		tmp = t_0;
	elseif (l <= -190.0)
		tmp = t_1;
	elseif (l <= 2.6e-30)
		tmp = U + (l * (cos((K * 0.5)) * (J * 2.0)));
	elseif (l <= 1.56e+100)
		tmp = t_1 + U;
	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[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]}, If[LessEqual[l, -4.2e+151], t$95$0, If[LessEqual[l, -190.0], t$95$1, If[LessEqual[l, 2.6e-30], N[(U + N[(l * N[(N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision] * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 1.56e+100], N[(t$95$1 + U), $MachinePrecision], t$95$0]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 77.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.117:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.117)
   (+ U (* 2.0 (* J (* l (cos (* K 0.5))))))
   (+ U (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.117) {
		tmp = U + (2.0 * (J * (l * cos((K * 0.5)))));
	} else {
		tmp = U + (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 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 (cos((k / 2.0d0)) <= (-0.117d0)) then
        tmp = u + (2.0d0 * (j * (l * cos((k * 0.5d0)))))
    else
        tmp = u + (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0)))
    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)) <= -0.117) {
		tmp = U + (2.0 * (J * (l * Math.cos((K * 0.5)))));
	} else {
		tmp = U + (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.117:
		tmp = U + (2.0 * (J * (l * math.cos((K * 0.5)))))
	else:
		tmp = U + (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0)))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.117)
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * cos(Float64(K * 0.5))))));
	else
		tmp = Float64(U + Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.117)
		tmp = U + (2.0 * (J * (l * cos((K * 0.5)))));
	else
		tmp = U + (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.117], N[(U + N[(2.0 * N[(J * N[(l * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 86.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -0.0295:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;U + \ell \cdot \left(\cos \left(K \cdot 0.5\right) \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* (- (exp l) (exp (- l))) J)))
   (if (<= l -0.0295)
     t_0
     (if (<= l 2.6e-30) (+ U (* l (* (cos (* K 0.5)) (* J 2.0)))) (+ t_0 U)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = (exp(l) - exp(-l)) * J;
	double tmp;
	if (l <= -0.0295) {
		tmp = t_0;
	} else if (l <= 2.6e-30) {
		tmp = U + (l * (cos((K * 0.5)) * (J * 2.0)));
	} else {
		tmp = t_0 + 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) :: t_0
    real(8) :: tmp
    t_0 = (exp(l) - exp(-l)) * j
    if (l <= (-0.0295d0)) then
        tmp = t_0
    else if (l <= 2.6d-30) then
        tmp = u + (l * (cos((k * 0.5d0)) * (j * 2.0d0)))
    else
        tmp = t_0 + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = (Math.exp(l) - Math.exp(-l)) * J;
	double tmp;
	if (l <= -0.0295) {
		tmp = t_0;
	} else if (l <= 2.6e-30) {
		tmp = U + (l * (Math.cos((K * 0.5)) * (J * 2.0)));
	} else {
		tmp = t_0 + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = (math.exp(l) - math.exp(-l)) * J
	tmp = 0
	if l <= -0.0295:
		tmp = t_0
	elif l <= 2.6e-30:
		tmp = U + (l * (math.cos((K * 0.5)) * (J * 2.0)))
	else:
		tmp = t_0 + U
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(Float64(exp(l) - exp(Float64(-l))) * J)
	tmp = 0.0
	if (l <= -0.0295)
		tmp = t_0;
	elseif (l <= 2.6e-30)
		tmp = Float64(U + Float64(l * Float64(cos(Float64(K * 0.5)) * Float64(J * 2.0))));
	else
		tmp = Float64(t_0 + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = (exp(l) - exp(-l)) * J;
	tmp = 0.0;
	if (l <= -0.0295)
		tmp = t_0;
	elseif (l <= 2.6e-30)
		tmp = U + (l * (cos((K * 0.5)) * (J * 2.0)));
	else
		tmp = t_0 + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]}, If[LessEqual[l, -0.0295], t$95$0, If[LessEqual[l, 2.6e-30], N[(U + N[(l * N[(N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision] * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + U), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 7: 70.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.75 \cdot 10^{+84}:\\ \;\;\;\;{\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;\ell \leq -205:\\ \;\;\;\;{U}^{-3}\\ \mathbf{elif}\;\ell \leq 0.44:\\ \;\;\;\;\mathsf{fma}\left(\ell \cdot 2, J, U\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -1.75e+84)
   (* (pow l 3.0) (* J 0.3333333333333333))
   (if (<= l -205.0)
     (pow U -3.0)
     (if (<= l 0.44)
       (fma (* l 2.0) J U)
       (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -1.75e+84) {
		tmp = pow(l, 3.0) * (J * 0.3333333333333333);
	} else if (l <= -205.0) {
		tmp = pow(U, -3.0);
	} else if (l <= 0.44) {
		tmp = fma((l * 2.0), J, U);
	} else {
		tmp = J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0));
	}
	return tmp;
}

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -1.75e+84)
		tmp = Float64((l ^ 3.0) * Float64(J * 0.3333333333333333));
	elseif (l <= -205.0)
		tmp = U ^ -3.0;
	elseif (l <= 0.44)
		tmp = fma(Float64(l * 2.0), J, U);
	else
		tmp = Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)));
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -1.75e+84], N[(N[Power[l, 3.0], $MachinePrecision] * N[(J * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, -205.0], N[Power[U, -3.0], $MachinePrecision], If[LessEqual[l, 0.44], N[(N[(l * 2.0), $MachinePrecision] * J + U), $MachinePrecision], N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 77.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.9 \cdot 10^{+67} \lor \neg \left(\ell \leq 2.5 \cdot 10^{+61}\right):\\ \;\;\;\;{\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -2.9e+67) (not (<= l 2.5e+61)))
   (* (pow l 3.0) (* J 0.3333333333333333))
   (+ U (* 2.0 (* J (* l (cos (* K 0.5))))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -2.9e+67) || !(l <= 2.5e+61)) {
		tmp = pow(l, 3.0) * (J * 0.3333333333333333);
	} else {
		tmp = U + (2.0 * (J * (l * 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 <= (-2.9d+67)) .or. (.not. (l <= 2.5d+61))) then
        tmp = (l ** 3.0d0) * (j * 0.3333333333333333d0)
    else
        tmp = u + (2.0d0 * (j * (l * 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 <= -2.9e+67) || !(l <= 2.5e+61)) {
		tmp = Math.pow(l, 3.0) * (J * 0.3333333333333333);
	} else {
		tmp = U + (2.0 * (J * (l * Math.cos((K * 0.5)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -2.9e+67) or not (l <= 2.5e+61):
		tmp = math.pow(l, 3.0) * (J * 0.3333333333333333)
	else:
		tmp = U + (2.0 * (J * (l * math.cos((K * 0.5)))))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -2.9e+67) || !(l <= 2.5e+61))
		tmp = Float64((l ^ 3.0) * Float64(J * 0.3333333333333333));
	else
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * cos(Float64(K * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -2.9e+67) || ~((l <= 2.5e+61)))
		tmp = (l ^ 3.0) * (J * 0.3333333333333333);
	else
		tmp = U + (2.0 * (J * (l * cos((K * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -2.9e+67], N[Not[LessEqual[l, 2.5e+61]], $MachinePrecision]], N[(N[Power[l, 3.0], $MachinePrecision] * N[(J * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(U + N[(2.0 * N[(J * N[(l * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 77.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -4.8 \cdot 10^{+69} \lor \neg \left(\ell \leq 4.6 \cdot 10^{+58}\right):\\ \;\;\;\;{\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;U + \ell \cdot \left(\cos \left(K \cdot 0.5\right) \cdot \left(J \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -4.8e+69) (not (<= l 4.6e+58)))
   (* (pow l 3.0) (* J 0.3333333333333333))
   (+ U (* l (* (cos (* K 0.5)) (* J 2.0))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -4.8e+69) || !(l <= 4.6e+58)) {
		tmp = pow(l, 3.0) * (J * 0.3333333333333333);
	} else {
		tmp = U + (l * (cos((K * 0.5)) * (J * 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 <= (-4.8d+69)) .or. (.not. (l <= 4.6d+58))) then
        tmp = (l ** 3.0d0) * (j * 0.3333333333333333d0)
    else
        tmp = u + (l * (cos((k * 0.5d0)) * (j * 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 <= -4.8e+69) || !(l <= 4.6e+58)) {
		tmp = Math.pow(l, 3.0) * (J * 0.3333333333333333);
	} else {
		tmp = U + (l * (Math.cos((K * 0.5)) * (J * 2.0)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -4.8e+69) or not (l <= 4.6e+58):
		tmp = math.pow(l, 3.0) * (J * 0.3333333333333333)
	else:
		tmp = U + (l * (math.cos((K * 0.5)) * (J * 2.0)))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -4.8e+69) || !(l <= 4.6e+58))
		tmp = Float64((l ^ 3.0) * Float64(J * 0.3333333333333333));
	else
		tmp = Float64(U + Float64(l * Float64(cos(Float64(K * 0.5)) * Float64(J * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -4.8e+69) || ~((l <= 4.6e+58)))
		tmp = (l ^ 3.0) * (J * 0.3333333333333333);
	else
		tmp = U + (l * (cos((K * 0.5)) * (J * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -4.8e+69], N[Not[LessEqual[l, 4.6e+58]], $MachinePrecision]], N[(N[Power[l, 3.0], $MachinePrecision] * N[(J * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(U + N[(l * N[(N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision] * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 70.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\ell}^{3} \cdot \left(J \cdot 0.3333333333333333\right)\\ \mathbf{if}\;\ell \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -205:\\ \;\;\;\;{U}^{-3}\\ \mathbf{elif}\;\ell \leq 1.4:\\ \;\;\;\;\mathsf{fma}\left(\ell \cdot 2, J, U\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* (pow l 3.0) (* J 0.3333333333333333))))
   (if (<= l -7.5e+86)
     t_0
     (if (<= l -205.0) (pow U -3.0) (if (<= l 1.4) (fma (* l 2.0) J U) t_0)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = pow(l, 3.0) * (J * 0.3333333333333333);
	double tmp;
	if (l <= -7.5e+86) {
		tmp = t_0;
	} else if (l <= -205.0) {
		tmp = pow(U, -3.0);
	} else if (l <= 1.4) {
		tmp = fma((l * 2.0), J, U);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(J, l, K, U)
	t_0 = Float64((l ^ 3.0) * Float64(J * 0.3333333333333333))
	tmp = 0.0
	if (l <= -7.5e+86)
		tmp = t_0;
	elseif (l <= -205.0)
		tmp = U ^ -3.0;
	elseif (l <= 1.4)
		tmp = fma(Float64(l * 2.0), J, U);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(N[Power[l, 3.0], $MachinePrecision] * N[(J * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -7.5e+86], t$95$0, If[LessEqual[l, -205.0], N[Power[U, -3.0], $MachinePrecision], If[LessEqual[l, 1.4], N[(N[(l * 2.0), $MachinePrecision] * J + U), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 11: 55.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -820000000 \lor \neg \left(\ell \leq 1.4\right):\\ \;\;\;\;{U}^{-64}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\ell \cdot 2, J, U\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -820000000.0) (not (<= l 1.4)))
   (pow U -64.0)
   (fma (* l 2.0) J U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -820000000.0) || !(l <= 1.4)) {
		tmp = pow(U, -64.0);
	} else {
		tmp = fma((l * 2.0), J, U);
	}
	return tmp;
}

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -820000000.0) || !(l <= 1.4))
		tmp = U ^ -64.0;
	else
		tmp = fma(Float64(l * 2.0), J, U);
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -820000000.0], N[Not[LessEqual[l, 1.4]], $MachinePrecision]], N[Power[U, -64.0], $MachinePrecision], N[(N[(l * 2.0), $MachinePrecision] * J + U), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 12: 55.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -820000000 \lor \neg \left(\ell \leq 1.4\right):\\ \;\;\;\;{U}^{-64}\\ \mathbf{else}:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -820000000.0) (not (<= l 1.4)))
   (pow U -64.0)
   (+ U (* l (* J 2.0)))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -820000000.0) || !(l <= 1.4)) {
		tmp = pow(U, -64.0);
	} else {
		tmp = U + (l * (J * 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 <= (-820000000.0d0)) .or. (.not. (l <= 1.4d0))) then
        tmp = u ** (-64.0d0)
    else
        tmp = u + (l * (j * 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 <= -820000000.0) || !(l <= 1.4)) {
		tmp = Math.pow(U, -64.0);
	} else {
		tmp = U + (l * (J * 2.0));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -820000000.0) or not (l <= 1.4):
		tmp = math.pow(U, -64.0)
	else:
		tmp = U + (l * (J * 2.0))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -820000000.0) || !(l <= 1.4))
		tmp = U ^ -64.0;
	else
		tmp = Float64(U + Float64(l * Float64(J * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -820000000.0) || ~((l <= 1.4)))
		tmp = U ^ -64.0;
	else
		tmp = U + (l * (J * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -820000000.0], N[Not[LessEqual[l, 1.4]], $MachinePrecision]], N[Power[U, -64.0], $MachinePrecision], N[(U + N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 13: 42.2% accurate, 23.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := J \cdot \left(\ell \cdot 2\right)\\ \mathbf{if}\;J \leq -9.2 \cdot 10^{+212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J \leq -5.4 \cdot 10^{+166}:\\ \;\;\;\;U + 4096\\ \mathbf{elif}\;J \leq -1.95 \cdot 10^{+73} \lor \neg \left(J \leq 1.2 \cdot 10^{+78}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* J (* l 2.0))))
   (if (<= J -9.2e+212)
     t_0
     (if (<= J -5.4e+166)
       (+ U 4096.0)
       (if (or (<= J -1.95e+73) (not (<= J 1.2e+78))) t_0 U)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = J * (l * 2.0);
	double tmp;
	if (J <= -9.2e+212) {
		tmp = t_0;
	} else if (J <= -5.4e+166) {
		tmp = U + 4096.0;
	} else if ((J <= -1.95e+73) || !(J <= 1.2e+78)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = j * (l * 2.0d0)
    if (j <= (-9.2d+212)) then
        tmp = t_0
    else if (j <= (-5.4d+166)) then
        tmp = u + 4096.0d0
    else if ((j <= (-1.95d+73)) .or. (.not. (j <= 1.2d+78))) then
        tmp = t_0
    else
        tmp = u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = J * (l * 2.0);
	double tmp;
	if (J <= -9.2e+212) {
		tmp = t_0;
	} else if (J <= -5.4e+166) {
		tmp = U + 4096.0;
	} else if ((J <= -1.95e+73) || !(J <= 1.2e+78)) {
		tmp = t_0;
	} else {
		tmp = U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = J * (l * 2.0)
	tmp = 0
	if J <= -9.2e+212:
		tmp = t_0
	elif J <= -5.4e+166:
		tmp = U + 4096.0
	elif (J <= -1.95e+73) or not (J <= 1.2e+78):
		tmp = t_0
	else:
		tmp = U
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(J * Float64(l * 2.0))
	tmp = 0.0
	if (J <= -9.2e+212)
		tmp = t_0;
	elseif (J <= -5.4e+166)
		tmp = Float64(U + 4096.0);
	elseif ((J <= -1.95e+73) || !(J <= 1.2e+78))
		tmp = t_0;
	else
		tmp = U;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = J * (l * 2.0);
	tmp = 0.0;
	if (J <= -9.2e+212)
		tmp = t_0;
	elseif (J <= -5.4e+166)
		tmp = U + 4096.0;
	elseif ((J <= -1.95e+73) || ~((J <= 1.2e+78)))
		tmp = t_0;
	else
		tmp = U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(J * N[(l * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[J, -9.2e+212], t$95$0, If[LessEqual[J, -5.4e+166], N[(U + 4096.0), $MachinePrecision], If[Or[LessEqual[J, -1.95e+73], N[Not[LessEqual[J, 1.2e+78]], $MachinePrecision]], t$95$0, U]]]]

Derivation

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1. Add Preprocessing

Alternative 14: 53.5% accurate, 44.6× speedup

Math

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

FPCore

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

C

double code(double J, double l, double K, double U) {
	return U + (l * (J * 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 + (l * (j * 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 15: 38.5% accurate, 61.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U \cdot U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 (if (<= l 2.6e+80) U (* U U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= 2.6e+80) {
		tmp = U;
	} else {
		tmp = U * 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 <= 2.6d+80) then
        tmp = u
    else
        tmp = u * u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= 2.6e+80) {
		tmp = U;
	} else {
		tmp = U * U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= 2.6e+80:
		tmp = U
	else:
		tmp = U * U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= 2.6e+80)
		tmp = U;
	else
		tmp = Float64(U * U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= 2.6e+80)
		tmp = U;
	else
		tmp = U * U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, 2.6e+80], U, N[(U * U), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 16: 2.8% accurate, 312.0× speedup

Math

\[\begin{array}{l} \\ -64 \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 -64.0)

C

double code(double J, double l, double K, double U) {
	return -64.0;
}

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 = -64.0d0
end function

Java

public static double code(double J, double l, double K, double U) {
	return -64.0;
}

Python

def code(J, l, K, U):
	return -64.0

Julia

function code(J, l, K, U)
	return -64.0
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = -64.0;
end

Wolfram

code[J_, l_, K_, U_] := -64.0

Derivation

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

Alternative 17: 36.2% 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 2023364 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))