Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 86.3% → 99.4%

Time: 10.6s

Alternatives: 11

Speedup: 1.4×

• 50.5% 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: 86.3% 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: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\cos \left(0.5 \cdot K\right) \cdot \left(J \cdot \left(2 \cdot \log \left(e^{\ell}\right)\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + \left(J \cdot \left(0.016666666666666666 \cdot {\ell}^{5} + \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- (exp l) (exp (- l)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 0.0)))
     (+ (* (cos (* 0.5 K)) (* J (* 2.0 (log (exp l))))) U)
     (+
      U
      (*
       (*
        J
        (+
         (* 0.016666666666666666 (pow l 5.0))
         (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0))))
       (cos (/ K 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 <= -((double) INFINITY)) || !(t_0 <= 0.0)) {
		tmp = (cos((0.5 * K)) * (J * (2.0 * log(exp(l))))) + U;
	} else {
		tmp = U + ((J * ((0.016666666666666666 * pow(l, 5.0)) + ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0)))) * cos((K / 2.0)));
	}
	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 <= 0.0)) {
		tmp = (Math.cos((0.5 * K)) * (J * (2.0 * Math.log(Math.exp(l))))) + U;
	} else {
		tmp = U + ((J * ((0.016666666666666666 * Math.pow(l, 5.0)) + ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0)))) * Math.cos((K / 2.0)));
	}
	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 <= 0.0):
		tmp = (math.cos((0.5 * K)) * (J * (2.0 * math.log(math.exp(l))))) + U
	else:
		tmp = U + ((J * ((0.016666666666666666 * math.pow(l, 5.0)) + ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0)))) * math.cos((K / 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 <= Float64(-Inf)) || !(t_0 <= 0.0))
		tmp = Float64(Float64(cos(Float64(0.5 * K)) * Float64(J * Float64(2.0 * log(exp(l))))) + U);
	else
		tmp = Float64(U + Float64(Float64(J * Float64(Float64(0.016666666666666666 * (l ^ 5.0)) + Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))) * cos(Float64(K / 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 <= -Inf) || ~((t_0 <= 0.0)))
		tmp = (cos((0.5 * K)) * (J * (2.0 * log(exp(l))))) + U;
	else
		tmp = U + ((J * ((0.016666666666666666 * (l ^ 5.0)) + ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0)))) * cos((K / 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, (-Infinity)], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[(N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision] * N[(J * N[(2.0 * N[Log[N[Exp[l], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(N[(J * N[(N[(0.016666666666666666 * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision] + N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 2: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\cos \left(0.5 \cdot K\right) \cdot \left(J \cdot \left(2 \cdot \log \left(e^{\ell}\right)\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- (exp l) (exp (- l)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 0.0)))
     (+ (* (cos (* 0.5 K)) (* J (* 2.0 (log (exp l))))) U)
     (+
      U
      (*
       (cos (/ K 2.0))
       (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = exp(l) - exp(-l);
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 0.0)) {
		tmp = (cos((0.5 * K)) * (J * (2.0 * log(exp(l))))) + U;
	} else {
		tmp = U + (cos((K / 2.0)) * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))));
	}
	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 <= 0.0)) {
		tmp = (Math.cos((0.5 * K)) * (J * (2.0 * Math.log(Math.exp(l))))) + U;
	} else {
		tmp = U + (Math.cos((K / 2.0)) * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	}
	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 <= 0.0):
		tmp = (math.cos((0.5 * K)) * (J * (2.0 * math.log(math.exp(l))))) + U
	else:
		tmp = U + (math.cos((K / 2.0)) * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 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 <= Float64(-Inf)) || !(t_0 <= 0.0))
		tmp = Float64(Float64(cos(Float64(0.5 * K)) * Float64(J * Float64(2.0 * log(exp(l))))) + U);
	else
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * 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 = exp(l) - exp(-l);
	tmp = 0.0;
	if ((t_0 <= -Inf) || ~((t_0 <= 0.0)))
		tmp = (cos((0.5 * K)) * (J * (2.0 * log(exp(l))))) + U;
	else
		tmp = U + (cos((K / 2.0)) * (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[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[(N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision] * N[(J * N[(2.0 * N[Log[N[Exp[l], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * 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 3: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ t_1 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;t_0 \leq -0.002:\\ \;\;\;\;U + t_1 \cdot \left(t_0 \cdot J\right)\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;U + t_1 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(0.5 \cdot K\right) \cdot \left(J \cdot \left(2 \cdot \log \left(e^{\ell}\right)\right)\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- (exp l) (exp (- l)))) (t_1 (cos (/ K 2.0))))
   (if (<= t_0 -0.002)
     (+ U (* t_1 (* t_0 J)))
     (if (<= t_0 0.0)
       (+ U (* t_1 (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))
       (+ (* (cos (* 0.5 K)) (* J (* 2.0 (log (exp l))))) U)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = exp(l) - exp(-l);
	double t_1 = cos((K / 2.0));
	double tmp;
	if (t_0 <= -0.002) {
		tmp = U + (t_1 * (t_0 * J));
	} else if (t_0 <= 0.0) {
		tmp = U + (t_1 * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))));
	} else {
		tmp = (cos((0.5 * K)) * (J * (2.0 * log(exp(l))))) + 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) :: t_1
    real(8) :: tmp
    t_0 = exp(l) - exp(-l)
    t_1 = cos((k / 2.0d0))
    if (t_0 <= (-0.002d0)) then
        tmp = u + (t_1 * (t_0 * j))
    else if (t_0 <= 0.0d0) then
        tmp = u + (t_1 * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))))
    else
        tmp = (cos((0.5d0 * k)) * (j * (2.0d0 * log(exp(l))))) + 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);
	double t_1 = Math.cos((K / 2.0));
	double tmp;
	if (t_0 <= -0.002) {
		tmp = U + (t_1 * (t_0 * J));
	} else if (t_0 <= 0.0) {
		tmp = U + (t_1 * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	} else {
		tmp = (Math.cos((0.5 * K)) * (J * (2.0 * Math.log(Math.exp(l))))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.exp(l) - math.exp(-l)
	t_1 = math.cos((K / 2.0))
	tmp = 0
	if t_0 <= -0.002:
		tmp = U + (t_1 * (t_0 * J))
	elif t_0 <= 0.0:
		tmp = U + (t_1 * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))))
	else:
		tmp = (math.cos((0.5 * K)) * (J * (2.0 * math.log(math.exp(l))))) + U
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(exp(l) - exp(Float64(-l)))
	t_1 = cos(Float64(K / 2.0))
	tmp = 0.0
	if (t_0 <= -0.002)
		tmp = Float64(U + Float64(t_1 * Float64(t_0 * J)));
	elseif (t_0 <= 0.0)
		tmp = Float64(U + Float64(t_1 * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))));
	else
		tmp = Float64(Float64(cos(Float64(0.5 * K)) * Float64(J * Float64(2.0 * log(exp(l))))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = exp(l) - exp(-l);
	t_1 = cos((K / 2.0));
	tmp = 0.0;
	if (t_0 <= -0.002)
		tmp = U + (t_1 * (t_0 * J));
	elseif (t_0 <= 0.0)
		tmp = U + (t_1 * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))));
	else
		tmp = (cos((0.5 * K)) * (J * (2.0 * log(exp(l))))) + U;
	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]}, Block[{t$95$1 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, -0.002], N[(U + N[(t$95$1 * N[(t$95$0 * J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(U + N[(t$95$1 * N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision] * N[(J * N[(2.0 * N[Log[N[Exp[l], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]]]]

Derivation

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

Alternative 4: 96.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + 0.016666666666666666 \cdot \left(J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot {\ell}^{5}\right)\right)\\ t_1 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -6.2 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -0.42:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 1000000:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 1.95 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0
         (+ U (* 0.016666666666666666 (* J (* (cos (* 0.5 K)) (pow l 5.0))))))
        (t_1 (+ U (* (- (exp l) (exp (- l))) J))))
   (if (<= l -6.2e+47)
     t_0
     (if (<= l -0.42)
       t_1
       (if (<= l 1000000.0)
         (+
          U
          (*
           (cos (/ K 2.0))
           (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))
         (if (<= l 1.95e+53) t_1 t_0))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + (0.016666666666666666 * (J * (cos((0.5 * K)) * pow(l, 5.0))));
	double t_1 = U + ((exp(l) - exp(-l)) * J);
	double tmp;
	if (l <= -6.2e+47) {
		tmp = t_0;
	} else if (l <= -0.42) {
		tmp = t_1;
	} else if (l <= 1000000.0) {
		tmp = U + (cos((K / 2.0)) * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))));
	} else if (l <= 1.95e+53) {
		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 + (0.016666666666666666d0 * (j * (cos((0.5d0 * k)) * (l ** 5.0d0))))
    t_1 = u + ((exp(l) - exp(-l)) * j)
    if (l <= (-6.2d+47)) then
        tmp = t_0
    else if (l <= (-0.42d0)) then
        tmp = t_1
    else if (l <= 1000000.0d0) then
        tmp = u + (cos((k / 2.0d0)) * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))))
    else if (l <= 1.95d+53) 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 + (0.016666666666666666 * (J * (Math.cos((0.5 * K)) * Math.pow(l, 5.0))));
	double t_1 = U + ((Math.exp(l) - Math.exp(-l)) * J);
	double tmp;
	if (l <= -6.2e+47) {
		tmp = t_0;
	} else if (l <= -0.42) {
		tmp = t_1;
	} else if (l <= 1000000.0) {
		tmp = U + (Math.cos((K / 2.0)) * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	} else if (l <= 1.95e+53) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + (0.016666666666666666 * (J * (math.cos((0.5 * K)) * math.pow(l, 5.0))))
	t_1 = U + ((math.exp(l) - math.exp(-l)) * J)
	tmp = 0
	if l <= -6.2e+47:
		tmp = t_0
	elif l <= -0.42:
		tmp = t_1
	elif l <= 1000000.0:
		tmp = U + (math.cos((K / 2.0)) * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))))
	elif l <= 1.95e+53:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(0.016666666666666666 * Float64(J * Float64(cos(Float64(0.5 * K)) * (l ^ 5.0)))))
	t_1 = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J))
	tmp = 0.0
	if (l <= -6.2e+47)
		tmp = t_0;
	elseif (l <= -0.42)
		tmp = t_1;
	elseif (l <= 1000000.0)
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))));
	elseif (l <= 1.95e+53)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + (0.016666666666666666 * (J * (cos((0.5 * K)) * (l ^ 5.0))));
	t_1 = U + ((exp(l) - exp(-l)) * J);
	tmp = 0.0;
	if (l <= -6.2e+47)
		tmp = t_0;
	elseif (l <= -0.42)
		tmp = t_1;
	elseif (l <= 1000000.0)
		tmp = U + (cos((K / 2.0)) * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))));
	elseif (l <= 1.95e+53)
		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[(0.016666666666666666 * N[(J * N[(N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision] * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -6.2e+47], t$95$0, If[LessEqual[l, -0.42], t$95$1, If[LessEqual[l, 1000000.0], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * 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, 1.95e+53], t$95$1, t$95$0]]]]]]

Derivation

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

Alternative 5: 96.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(0.5 \cdot K\right)\\ t_1 := U + 0.016666666666666666 \cdot \left(J \cdot \left(t_0 \cdot {\ell}^{5}\right)\right)\\ t_2 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -6.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq -0.0095:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq 1000000:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot t_0\right)\right)\\ \mathbf{elif}\;\ell \leq 1.95 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (* 0.5 K)))
        (t_1 (+ U (* 0.016666666666666666 (* J (* t_0 (pow l 5.0))))))
        (t_2 (+ U (* (- (exp l) (exp (- l))) J))))
   (if (<= l -6.2e+47)
     t_1
     (if (<= l -0.0095)
       t_2
       (if (<= l 1000000.0)
         (+ U (* 2.0 (* J (* l t_0))))
         (if (<= l 1.95e+53) t_2 t_1))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((0.5 * K));
	double t_1 = U + (0.016666666666666666 * (J * (t_0 * pow(l, 5.0))));
	double t_2 = U + ((exp(l) - exp(-l)) * J);
	double tmp;
	if (l <= -6.2e+47) {
		tmp = t_1;
	} else if (l <= -0.0095) {
		tmp = t_2;
	} else if (l <= 1000000.0) {
		tmp = U + (2.0 * (J * (l * t_0)));
	} else if (l <= 1.95e+53) {
		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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = cos((0.5d0 * k))
    t_1 = u + (0.016666666666666666d0 * (j * (t_0 * (l ** 5.0d0))))
    t_2 = u + ((exp(l) - exp(-l)) * j)
    if (l <= (-6.2d+47)) then
        tmp = t_1
    else if (l <= (-0.0095d0)) then
        tmp = t_2
    else if (l <= 1000000.0d0) then
        tmp = u + (2.0d0 * (j * (l * t_0)))
    else if (l <= 1.95d+53) 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) {
	double t_0 = Math.cos((0.5 * K));
	double t_1 = U + (0.016666666666666666 * (J * (t_0 * Math.pow(l, 5.0))));
	double t_2 = U + ((Math.exp(l) - Math.exp(-l)) * J);
	double tmp;
	if (l <= -6.2e+47) {
		tmp = t_1;
	} else if (l <= -0.0095) {
		tmp = t_2;
	} else if (l <= 1000000.0) {
		tmp = U + (2.0 * (J * (l * t_0)));
	} else if (l <= 1.95e+53) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((0.5 * K))
	t_1 = U + (0.016666666666666666 * (J * (t_0 * math.pow(l, 5.0))))
	t_2 = U + ((math.exp(l) - math.exp(-l)) * J)
	tmp = 0
	if l <= -6.2e+47:
		tmp = t_1
	elif l <= -0.0095:
		tmp = t_2
	elif l <= 1000000.0:
		tmp = U + (2.0 * (J * (l * t_0)))
	elif l <= 1.95e+53:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(0.5 * K))
	t_1 = Float64(U + Float64(0.016666666666666666 * Float64(J * Float64(t_0 * (l ^ 5.0)))))
	t_2 = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J))
	tmp = 0.0
	if (l <= -6.2e+47)
		tmp = t_1;
	elseif (l <= -0.0095)
		tmp = t_2;
	elseif (l <= 1000000.0)
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * t_0))));
	elseif (l <= 1.95e+53)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((0.5 * K));
	t_1 = U + (0.016666666666666666 * (J * (t_0 * (l ^ 5.0))));
	t_2 = U + ((exp(l) - exp(-l)) * J);
	tmp = 0.0;
	if (l <= -6.2e+47)
		tmp = t_1;
	elseif (l <= -0.0095)
		tmp = t_2;
	elseif (l <= 1000000.0)
		tmp = U + (2.0 * (J * (l * t_0)));
	elseif (l <= 1.95e+53)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(U + N[(0.016666666666666666 * N[(J * N[(t$95$0 * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -6.2e+47], t$95$1, If[LessEqual[l, -0.0095], t$95$2, If[LessEqual[l, 1000000.0], N[(U + N[(2.0 * N[(J * N[(l * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 1.95e+53], t$95$2, t$95$1]]]]]]]

Derivation

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

Alternative 6: 85.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -0.0029:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 1000000:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \mathbf{elif}\;\ell \leq 1.55 \cdot 10^{+255}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;U + \ell \cdot \left(2 \cdot \left(J + -0.125 \cdot \left(J \cdot {K}^{2}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (+ U (* (- (exp l) (exp (- l))) J))))
   (if (<= l -0.0029)
     t_0
     (if (<= l 1000000.0)
       (+ U (* 2.0 (* J (* l (cos (* 0.5 K))))))
       (if (<= l 1.55e+255)
         t_0
         (+ U (* l (* 2.0 (+ J (* -0.125 (* J (pow K 2.0))))))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + ((exp(l) - exp(-l)) * J);
	double tmp;
	if (l <= -0.0029) {
		tmp = t_0;
	} else if (l <= 1000000.0) {
		tmp = U + (2.0 * (J * (l * cos((0.5 * K)))));
	} else if (l <= 1.55e+255) {
		tmp = t_0;
	} else {
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * 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) :: t_0
    real(8) :: tmp
    t_0 = u + ((exp(l) - exp(-l)) * j)
    if (l <= (-0.0029d0)) then
        tmp = t_0
    else if (l <= 1000000.0d0) then
        tmp = u + (2.0d0 * (j * (l * cos((0.5d0 * k)))))
    else if (l <= 1.55d+255) then
        tmp = t_0
    else
        tmp = u + (l * (2.0d0 * (j + ((-0.125d0) * (j * (k ** 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = U + ((Math.exp(l) - Math.exp(-l)) * J);
	double tmp;
	if (l <= -0.0029) {
		tmp = t_0;
	} else if (l <= 1000000.0) {
		tmp = U + (2.0 * (J * (l * Math.cos((0.5 * K)))));
	} else if (l <= 1.55e+255) {
		tmp = t_0;
	} else {
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * Math.pow(K, 2.0))))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + ((math.exp(l) - math.exp(-l)) * J)
	tmp = 0
	if l <= -0.0029:
		tmp = t_0
	elif l <= 1000000.0:
		tmp = U + (2.0 * (J * (l * math.cos((0.5 * K)))))
	elif l <= 1.55e+255:
		tmp = t_0
	else:
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * math.pow(K, 2.0))))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J))
	tmp = 0.0
	if (l <= -0.0029)
		tmp = t_0;
	elseif (l <= 1000000.0)
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))));
	elseif (l <= 1.55e+255)
		tmp = t_0;
	else
		tmp = Float64(U + Float64(l * Float64(2.0 * Float64(J + Float64(-0.125 * Float64(J * (K ^ 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + ((exp(l) - exp(-l)) * J);
	tmp = 0.0;
	if (l <= -0.0029)
		tmp = t_0;
	elseif (l <= 1000000.0)
		tmp = U + (2.0 * (J * (l * cos((0.5 * K)))));
	elseif (l <= 1.55e+255)
		tmp = t_0;
	else
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * (K ^ 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -0.0029], t$95$0, If[LessEqual[l, 1000000.0], N[(U + N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 1.55e+255], t$95$0, N[(U + N[(l * N[(2.0 * N[(J + N[(-0.125 * N[(J * N[Power[K, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 7: 80.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + 0.016666666666666666 \cdot \left(J \cdot {\ell}^{5}\right)\\ \mathbf{if}\;\ell \leq -620000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 5800000:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \mathbf{elif}\;\ell \leq 1.4 \cdot 10^{+252}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;U + \ell \cdot \left(2 \cdot \left(J + -0.125 \cdot \left(J \cdot {K}^{2}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (+ U (* 0.016666666666666666 (* J (pow l 5.0))))))
   (if (<= l -620000000.0)
     t_0
     (if (<= l 5800000.0)
       (+ U (* 2.0 (* J (* l (cos (* 0.5 K))))))
       (if (<= l 1.4e+252)
         t_0
         (+ U (* l (* 2.0 (+ J (* -0.125 (* J (pow K 2.0))))))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + (0.016666666666666666 * (J * pow(l, 5.0)));
	double tmp;
	if (l <= -620000000.0) {
		tmp = t_0;
	} else if (l <= 5800000.0) {
		tmp = U + (2.0 * (J * (l * cos((0.5 * K)))));
	} else if (l <= 1.4e+252) {
		tmp = t_0;
	} else {
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * 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) :: t_0
    real(8) :: tmp
    t_0 = u + (0.016666666666666666d0 * (j * (l ** 5.0d0)))
    if (l <= (-620000000.0d0)) then
        tmp = t_0
    else if (l <= 5800000.0d0) then
        tmp = u + (2.0d0 * (j * (l * cos((0.5d0 * k)))))
    else if (l <= 1.4d+252) then
        tmp = t_0
    else
        tmp = u + (l * (2.0d0 * (j + ((-0.125d0) * (j * (k ** 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = U + (0.016666666666666666 * (J * Math.pow(l, 5.0)));
	double tmp;
	if (l <= -620000000.0) {
		tmp = t_0;
	} else if (l <= 5800000.0) {
		tmp = U + (2.0 * (J * (l * Math.cos((0.5 * K)))));
	} else if (l <= 1.4e+252) {
		tmp = t_0;
	} else {
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * Math.pow(K, 2.0))))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + (0.016666666666666666 * (J * math.pow(l, 5.0)))
	tmp = 0
	if l <= -620000000.0:
		tmp = t_0
	elif l <= 5800000.0:
		tmp = U + (2.0 * (J * (l * math.cos((0.5 * K)))))
	elif l <= 1.4e+252:
		tmp = t_0
	else:
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * math.pow(K, 2.0))))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(0.016666666666666666 * Float64(J * (l ^ 5.0))))
	tmp = 0.0
	if (l <= -620000000.0)
		tmp = t_0;
	elseif (l <= 5800000.0)
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))));
	elseif (l <= 1.4e+252)
		tmp = t_0;
	else
		tmp = Float64(U + Float64(l * Float64(2.0 * Float64(J + Float64(-0.125 * Float64(J * (K ^ 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + (0.016666666666666666 * (J * (l ^ 5.0)));
	tmp = 0.0;
	if (l <= -620000000.0)
		tmp = t_0;
	elseif (l <= 5800000.0)
		tmp = U + (2.0 * (J * (l * cos((0.5 * K)))));
	elseif (l <= 1.4e+252)
		tmp = t_0;
	else
		tmp = U + (l * (2.0 * (J + (-0.125 * (J * (K ^ 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(U + N[(0.016666666666666666 * N[(J * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -620000000.0], t$95$0, If[LessEqual[l, 5800000.0], N[(U + N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 1.4e+252], t$95$0, N[(U + N[(l * N[(2.0 * N[(J + N[(-0.125 * N[(J * N[Power[K, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 81.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1460000 \lor \neg \left(\ell \leq 5800000\right):\\ \;\;\;\;U + 0.016666666666666666 \cdot \left(J \cdot {\ell}^{5}\right)\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -1460000.0) (not (<= l 5800000.0)))
   (+ U (* 0.016666666666666666 (* J (pow l 5.0))))
   (+ U (* 2.0 (* J (* l (cos (* 0.5 K))))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -1460000.0) || !(l <= 5800000.0)) {
		tmp = U + (0.016666666666666666 * (J * pow(l, 5.0)));
	} else {
		tmp = U + (2.0 * (J * (l * cos((0.5 * K)))));
	}
	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 <= (-1460000.0d0)) .or. (.not. (l <= 5800000.0d0))) then
        tmp = u + (0.016666666666666666d0 * (j * (l ** 5.0d0)))
    else
        tmp = u + (2.0d0 * (j * (l * cos((0.5d0 * k)))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -1460000.0) || !(l <= 5800000.0)) {
		tmp = U + (0.016666666666666666 * (J * Math.pow(l, 5.0)));
	} else {
		tmp = U + (2.0 * (J * (l * Math.cos((0.5 * K)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -1460000.0) or not (l <= 5800000.0):
		tmp = U + (0.016666666666666666 * (J * math.pow(l, 5.0)))
	else:
		tmp = U + (2.0 * (J * (l * math.cos((0.5 * K)))))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -1460000.0) || !(l <= 5800000.0))
		tmp = Float64(U + Float64(0.016666666666666666 * Float64(J * (l ^ 5.0))));
	else
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -1460000.0) || ~((l <= 5800000.0)))
		tmp = U + (0.016666666666666666 * (J * (l ^ 5.0)));
	else
		tmp = U + (2.0 * (J * (l * cos((0.5 * K)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -1460000.0], N[Not[LessEqual[l, 5800000.0]], $MachinePrecision]], N[(U + N[(0.016666666666666666 * N[(J * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 75.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -0.0019 \lor \neg \left(\ell \leq 1000000\right):\\ \;\;\;\;U + 0.016666666666666666 \cdot \left(J \cdot {\ell}^{5}\right)\\ \mathbf{else}:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -0.0019) (not (<= l 1000000.0)))
   (+ U (* 0.016666666666666666 (* J (pow l 5.0))))
   (+ U (* l (* J 2.0)))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -0.0019) || !(l <= 1000000.0)) {
		tmp = U + (0.016666666666666666 * (J * pow(l, 5.0)));
	} 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 <= (-0.0019d0)) .or. (.not. (l <= 1000000.0d0))) then
        tmp = u + (0.016666666666666666d0 * (j * (l ** 5.0d0)))
    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 <= -0.0019) || !(l <= 1000000.0)) {
		tmp = U + (0.016666666666666666 * (J * Math.pow(l, 5.0)));
	} else {
		tmp = U + (l * (J * 2.0));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -0.0019) or not (l <= 1000000.0):
		tmp = U + (0.016666666666666666 * (J * math.pow(l, 5.0)))
	else:
		tmp = U + (l * (J * 2.0))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -0.0019) || !(l <= 1000000.0))
		tmp = Float64(U + Float64(0.016666666666666666 * Float64(J * (l ^ 5.0))));
	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 <= -0.0019) || ~((l <= 1000000.0)))
		tmp = U + (0.016666666666666666 * (J * (l ^ 5.0)));
	else
		tmp = U + (l * (J * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -0.0019], N[Not[LessEqual[l, 1000000.0]], $MachinePrecision]], N[(U + N[(0.016666666666666666 * N[(J * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 53.2% 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

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

Alternative 11: 35.9% 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 2024010 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))