Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 86.3% → 99.5%

Time: 13.9s

Alternatives: 16

Speedup: 1.5×

• 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: 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: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-\ell}\\ t_1 := e^{\ell} - t_0\\ t_2 := \cos \left(0.5 \cdot K\right)\\ \mathbf{if}\;t_1 \leq -20:\\ \;\;\;\;J \cdot \left(t_1 \cdot t_2\right)\\ \mathbf{elif}\;t_1 \leq 10^{-13}:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \mathbf{else}:\\ \;\;\;\;U - J \cdot \left(t_2 \cdot \left(t_0 - e^{\ell}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (exp (- l))) (t_1 (- (exp l) t_0)) (t_2 (cos (* 0.5 K))))
   (if (<= t_1 -20.0)
     (* J (* t_1 t_2))
     (if (<= t_1 1e-13)
       (+
        (*
         (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))
         (cos (/ K 2.0)))
        U)
       (- U (* J (* t_2 (- t_0 (exp l)))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = exp(-l);
	double t_1 = exp(l) - t_0;
	double t_2 = cos((0.5 * K));
	double tmp;
	if (t_1 <= -20.0) {
		tmp = J * (t_1 * t_2);
	} else if (t_1 <= 1e-13) {
		tmp = ((J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))) * cos((K / 2.0))) + U;
	} else {
		tmp = U - (J * (t_2 * (t_0 - exp(l))));
	}
	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 = exp(-l)
    t_1 = exp(l) - t_0
    t_2 = cos((0.5d0 * k))
    if (t_1 <= (-20.0d0)) then
        tmp = j * (t_1 * t_2)
    else if (t_1 <= 1d-13) then
        tmp = ((j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))) * cos((k / 2.0d0))) + u
    else
        tmp = u - (j * (t_2 * (t_0 - exp(l))))
    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);
	double t_1 = Math.exp(l) - t_0;
	double t_2 = Math.cos((0.5 * K));
	double tmp;
	if (t_1 <= -20.0) {
		tmp = J * (t_1 * t_2);
	} else if (t_1 <= 1e-13) {
		tmp = ((J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))) * Math.cos((K / 2.0))) + U;
	} else {
		tmp = U - (J * (t_2 * (t_0 - Math.exp(l))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.exp(-l)
	t_1 = math.exp(l) - t_0
	t_2 = math.cos((0.5 * K))
	tmp = 0
	if t_1 <= -20.0:
		tmp = J * (t_1 * t_2)
	elif t_1 <= 1e-13:
		tmp = ((J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))) * math.cos((K / 2.0))) + U
	else:
		tmp = U - (J * (t_2 * (t_0 - math.exp(l))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = exp(Float64(-l))
	t_1 = Float64(exp(l) - t_0)
	t_2 = cos(Float64(0.5 * K))
	tmp = 0.0
	if (t_1 <= -20.0)
		tmp = Float64(J * Float64(t_1 * t_2));
	elseif (t_1 <= 1e-13)
		tmp = Float64(Float64(Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0))) * cos(Float64(K / 2.0))) + U);
	else
		tmp = Float64(U - Float64(J * Float64(t_2 * Float64(t_0 - exp(l)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = exp(-l);
	t_1 = exp(l) - t_0;
	t_2 = cos((0.5 * K));
	tmp = 0.0;
	if (t_1 <= -20.0)
		tmp = J * (t_1 * t_2);
	elseif (t_1 <= 1e-13)
		tmp = ((J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))) * cos((K / 2.0))) + U;
	else
		tmp = U - (J * (t_2 * (t_0 - exp(l))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Exp[(-l)], $MachinePrecision]}, Block[{t$95$1 = N[(N[Exp[l], $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$1, -20.0], N[(J * N[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-13], N[(N[(N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U - N[(J * N[(t$95$2 * N[(t$95$0 - N[Exp[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -20

   1. Initial program 100.0%

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

   2. Taylor expanded in J around 0 100.0%

      \[\leadsto \color{blue}{J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(e^{\ell} - e^{-\ell}\right)\right)} + U \]

   3. Taylor expanded in J around inf 100.0%

      \[\leadsto \color{blue}{J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(e^{\ell} - e^{-\ell}\right)\right)} \]

   if -20 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 1e-13

   1. Initial program 73.0%

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

   2. Taylor expanded in l around 0 100.0%

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

   if 1e-13 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 100.0%

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

   2. Taylor expanded in J around 0 100.0%

      \[\leadsto \color{blue}{J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(e^{\ell} - e^{-\ell}\right)\right)} + U \]
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -20:\\ \;\;\;\;J \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot \cos \left(0.5 \cdot K\right)\right)\\ \mathbf{elif}\;e^{\ell} - e^{-\ell} \leq 10^{-13}:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \mathbf{else}:\\ \;\;\;\;U - J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(e^{-\ell} - e^{\ell}\right)\right)\\ \end{array} \]

Alternative 2: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_0 \leq -20 \lor \neg \left(t_0 \leq 0.2\right):\\ \;\;\;\;J \cdot \left(t_0 \cdot \cos \left(0.5 \cdot K\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- (exp l) (exp (- l)))))
   (if (or (<= t_0 -20.0) (not (<= t_0 0.2)))
     (* J (* t_0 (cos (* 0.5 K))))
     (+
      (*
       (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))
       (cos (/ K 2.0)))
      U))))

C

double code(double J, double l, double K, double U) {
	double t_0 = exp(l) - exp(-l);
	double tmp;
	if ((t_0 <= -20.0) || !(t_0 <= 0.2)) {
		tmp = J * (t_0 * cos((0.5 * K)));
	} else {
		tmp = ((J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))) * cos((K / 2.0))) + 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)
    if ((t_0 <= (-20.0d0)) .or. (.not. (t_0 <= 0.2d0))) then
        tmp = j * (t_0 * cos((0.5d0 * k)))
    else
        tmp = ((j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))) * cos((k / 2.0d0))) + 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 tmp;
	if ((t_0 <= -20.0) || !(t_0 <= 0.2)) {
		tmp = J * (t_0 * Math.cos((0.5 * K)));
	} else {
		tmp = ((J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))) * Math.cos((K / 2.0))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.exp(l) - math.exp(-l)
	tmp = 0
	if (t_0 <= -20.0) or not (t_0 <= 0.2):
		tmp = J * (t_0 * math.cos((0.5 * K)))
	else:
		tmp = ((J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))) * math.cos((K / 2.0))) + U
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(exp(l) - exp(Float64(-l)))
	tmp = 0.0
	if ((t_0 <= -20.0) || !(t_0 <= 0.2))
		tmp = Float64(J * Float64(t_0 * cos(Float64(0.5 * K))));
	else
		tmp = Float64(Float64(Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0))) * cos(Float64(K / 2.0))) + U);
	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 <= -20.0) || ~((t_0 <= 0.2)))
		tmp = J * (t_0 * cos((0.5 * K)));
	else
		tmp = ((J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))) * cos((K / 2.0))) + 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]}, If[Or[LessEqual[t$95$0, -20.0], N[Not[LessEqual[t$95$0, 0.2]], $MachinePrecision]], N[(J * N[(t$95$0 * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -20 or 0.20000000000000001 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 100.0%

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

   2. Taylor expanded in J around 0 100.0%

      \[\leadsto \color{blue}{J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(e^{\ell} - e^{-\ell}\right)\right)} + U \]

   3. Taylor expanded in J around inf 100.0%

      \[\leadsto \color{blue}{J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(e^{\ell} - e^{-\ell}\right)\right)} \]

   if -20 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 0.20000000000000001

   1. Initial program 73.2%

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

   2. Taylor expanded in l around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -20 \lor \neg \left(e^{\ell} - e^{-\ell} \leq 0.2\right):\\ \;\;\;\;J \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot \cos \left(0.5 \cdot K\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \end{array} \]

Alternative 3: 93.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + \left(J \cdot 0.3333333333333333\right) \cdot \left(\cos \left(0.5 \cdot K\right) \cdot {\ell}^{3}\right)\\ t_1 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -2.8 \cdot 10^{+134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -3.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 0.0235:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0
         (+ U (* (* J 0.3333333333333333) (* (cos (* 0.5 K)) (pow l 3.0)))))
        (t_1 (+ U (* (- (exp l) (exp (- l))) J))))
   (if (<= l -2.8e+134)
     t_0
     (if (<= l -3.1)
       t_1
       (if (<= l 0.0235)
         (+ U (* (cos (/ K 2.0)) (* l (* J 2.0))))
         (if (<= l 2.2e+66) t_1 t_0))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + ((J * 0.3333333333333333) * (cos((0.5 * K)) * pow(l, 3.0)));
	double t_1 = U + ((exp(l) - exp(-l)) * J);
	double tmp;
	if (l <= -2.8e+134) {
		tmp = t_0;
	} else if (l <= -3.1) {
		tmp = t_1;
	} else if (l <= 0.0235) {
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	} else if (l <= 2.2e+66) {
		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 + ((j * 0.3333333333333333d0) * (cos((0.5d0 * k)) * (l ** 3.0d0)))
    t_1 = u + ((exp(l) - exp(-l)) * j)
    if (l <= (-2.8d+134)) then
        tmp = t_0
    else if (l <= (-3.1d0)) then
        tmp = t_1
    else if (l <= 0.0235d0) then
        tmp = u + (cos((k / 2.0d0)) * (l * (j * 2.0d0)))
    else if (l <= 2.2d+66) 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 + ((J * 0.3333333333333333) * (Math.cos((0.5 * K)) * Math.pow(l, 3.0)));
	double t_1 = U + ((Math.exp(l) - Math.exp(-l)) * J);
	double tmp;
	if (l <= -2.8e+134) {
		tmp = t_0;
	} else if (l <= -3.1) {
		tmp = t_1;
	} else if (l <= 0.0235) {
		tmp = U + (Math.cos((K / 2.0)) * (l * (J * 2.0)));
	} else if (l <= 2.2e+66) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + ((J * 0.3333333333333333) * (math.cos((0.5 * K)) * math.pow(l, 3.0)))
	t_1 = U + ((math.exp(l) - math.exp(-l)) * J)
	tmp = 0
	if l <= -2.8e+134:
		tmp = t_0
	elif l <= -3.1:
		tmp = t_1
	elif l <= 0.0235:
		tmp = U + (math.cos((K / 2.0)) * (l * (J * 2.0)))
	elif l <= 2.2e+66:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(Float64(J * 0.3333333333333333) * Float64(cos(Float64(0.5 * K)) * (l ^ 3.0))))
	t_1 = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J))
	tmp = 0.0
	if (l <= -2.8e+134)
		tmp = t_0;
	elseif (l <= -3.1)
		tmp = t_1;
	elseif (l <= 0.0235)
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(l * Float64(J * 2.0))));
	elseif (l <= 2.2e+66)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + ((J * 0.3333333333333333) * (cos((0.5 * K)) * (l ^ 3.0)));
	t_1 = U + ((exp(l) - exp(-l)) * J);
	tmp = 0.0;
	if (l <= -2.8e+134)
		tmp = t_0;
	elseif (l <= -3.1)
		tmp = t_1;
	elseif (l <= 0.0235)
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	elseif (l <= 2.2e+66)
		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[(J * 0.3333333333333333), $MachinePrecision] * N[(N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision] * N[Power[l, 3.0], $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, -2.8e+134], t$95$0, If[LessEqual[l, -3.1], t$95$1, If[LessEqual[l, 0.0235], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.2e+66], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -2.7999999999999999e134 or 2.1999999999999998e66 < l

   1. Initial program 100.0%

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

   2. Taylor expanded in l around 0 99.0%

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

   3. Taylor expanded in l around inf 99.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \left(J \cdot \left({\ell}^{3} \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]
   4. Step-by-step derivation

      1. associate-*r* 99.0%

         \[\leadsto \color{blue}{\left(0.3333333333333333 \cdot J\right) \cdot \left({\ell}^{3} \cdot \cos \left(0.5 \cdot K\right)\right)} + U \]

      2. *-commutative 99.0%

         \[\leadsto \color{blue}{\left(J \cdot 0.3333333333333333\right)} \cdot \left({\ell}^{3} \cdot \cos \left(0.5 \cdot K\right)\right) + U \]

   5. Simplified 99.0%

      \[\leadsto \color{blue}{\left(J \cdot 0.3333333333333333\right) \cdot \left({\ell}^{3} \cdot \cos \left(0.5 \cdot K\right)\right)} + U \]

   if -2.7999999999999999e134 < l < -3.10000000000000009 or 0.0235 < l < 2.1999999999999998e66

   1. Initial program 100.0%

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

   2. Taylor expanded in K around 0 81.8%

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

   if -3.10000000000000009 < l < 0.0235

   1. Initial program 73.2%

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

   2. Taylor expanded in l around 0 99.1%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.8 \cdot 10^{+134}:\\ \;\;\;\;U + \left(J \cdot 0.3333333333333333\right) \cdot \left(\cos \left(0.5 \cdot K\right) \cdot {\ell}^{3}\right)\\ \mathbf{elif}\;\ell \leq -3.1:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{elif}\;\ell \leq 0.0235:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + \left(J \cdot 0.3333333333333333\right) \cdot \left(\cos \left(0.5 \cdot K\right) \cdot {\ell}^{3}\right)\\ \end{array} \]

Alternative 4: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+
  (* (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0))) (cos (/ K 2.0)))
  U))

C

double code(double J, double l, double K, double U) {
	return ((J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))) * 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 * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))) * cos((k / 2.0d0))) + u
end function

Java

public static double code(double J, double l, double K, double U) {
	return ((J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))) * Math.cos((K / 2.0))) + U;
}

Python

def code(J, l, K, U):
	return ((J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))) * math.cos((K / 2.0))) + U

Julia

function code(J, l, K, U)
	return Float64(Float64(Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0))) * cos(Float64(K / 2.0))) + U)
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = ((J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))) * cos((K / 2.0))) + U;
end

Wolfram

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

Derivation

1. Initial program 86.2%

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

2. Taylor expanded in l around 0 90.7%

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

3. Final simplification 90.7%

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

Alternative 5: 87.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3.1 \lor \neg \left(\ell \leq 0.00145\right):\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -3.1) (not (<= l 0.00145)))
   (+ U (* (- (exp l) (exp (- l))) J))
   (+ U (* (cos (/ K 2.0)) (* l (* J 2.0))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -3.1) || !(l <= 0.00145)) {
		tmp = U + ((exp(l) - exp(-l)) * J);
	} else {
		tmp = U + (cos((K / 2.0)) * (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 <= (-3.1d0)) .or. (.not. (l <= 0.00145d0))) then
        tmp = u + ((exp(l) - exp(-l)) * j)
    else
        tmp = u + (cos((k / 2.0d0)) * (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 <= -3.1) || !(l <= 0.00145)) {
		tmp = U + ((Math.exp(l) - Math.exp(-l)) * J);
	} else {
		tmp = U + (Math.cos((K / 2.0)) * (l * (J * 2.0)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -3.1) or not (l <= 0.00145):
		tmp = U + ((math.exp(l) - math.exp(-l)) * J)
	else:
		tmp = U + (math.cos((K / 2.0)) * (l * (J * 2.0)))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -3.1) || !(l <= 0.00145))
		tmp = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J));
	else
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(l * Float64(J * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -3.1) || ~((l <= 0.00145)))
		tmp = U + ((exp(l) - exp(-l)) * J);
	else
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -3.1], N[Not[LessEqual[l, 0.00145]], $MachinePrecision]], N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -3.10000000000000009 or 0.00145 < l

   1. Initial program 100.0%

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

   2. Taylor expanded in K around 0 68.5%

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

   if -3.10000000000000009 < l < 0.00145

   1. Initial program 73.2%

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

   2. Taylor expanded in l around 0 99.1%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3.1 \lor \neg \left(\ell \leq 0.00145\right):\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \end{array} \]

Alternative 6: 78.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \mathbf{if}\;\ell \leq -3 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;{U}^{-4}\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;U + \ell \cdot \left(2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* J (* 0.3333333333333333 (pow l 3.0)))))
   (if (<= l -3e+81)
     t_0
     (if (<= l -1.15e+16)
       (pow U -4.0)
       (if (<= l 3.3e+34) (+ U (* l (* 2.0 (* J (cos (* 0.5 K)))))) t_0)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = J * (0.3333333333333333 * pow(l, 3.0));
	double tmp;
	if (l <= -3e+81) {
		tmp = t_0;
	} else if (l <= -1.15e+16) {
		tmp = pow(U, -4.0);
	} else if (l <= 3.3e+34) {
		tmp = U + (l * (2.0 * (J * cos((0.5 * K)))));
	} 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) :: tmp
    t_0 = j * (0.3333333333333333d0 * (l ** 3.0d0))
    if (l <= (-3d+81)) then
        tmp = t_0
    else if (l <= (-1.15d+16)) then
        tmp = u ** (-4.0d0)
    else if (l <= 3.3d+34) then
        tmp = u + (l * (2.0d0 * (j * cos((0.5d0 * k)))))
    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 = J * (0.3333333333333333 * Math.pow(l, 3.0));
	double tmp;
	if (l <= -3e+81) {
		tmp = t_0;
	} else if (l <= -1.15e+16) {
		tmp = Math.pow(U, -4.0);
	} else if (l <= 3.3e+34) {
		tmp = U + (l * (2.0 * (J * Math.cos((0.5 * K)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = J * (0.3333333333333333 * math.pow(l, 3.0))
	tmp = 0
	if l <= -3e+81:
		tmp = t_0
	elif l <= -1.15e+16:
		tmp = math.pow(U, -4.0)
	elif l <= 3.3e+34:
		tmp = U + (l * (2.0 * (J * math.cos((0.5 * K)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(J * Float64(0.3333333333333333 * (l ^ 3.0)))
	tmp = 0.0
	if (l <= -3e+81)
		tmp = t_0;
	elseif (l <= -1.15e+16)
		tmp = U ^ -4.0;
	elseif (l <= 3.3e+34)
		tmp = Float64(U + Float64(l * Float64(2.0 * Float64(J * cos(Float64(0.5 * K))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = J * (0.3333333333333333 * (l ^ 3.0));
	tmp = 0.0;
	if (l <= -3e+81)
		tmp = t_0;
	elseif (l <= -1.15e+16)
		tmp = U ^ -4.0;
	elseif (l <= 3.3e+34)
		tmp = U + (l * (2.0 * (J * cos((0.5 * K)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -3e+81], t$95$0, If[LessEqual[l, -1.15e+16], N[Power[U, -4.0], $MachinePrecision], If[LessEqual[l, 3.3e+34], N[(U + N[(l * N[(2.0 * N[(J * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if l < -2.99999999999999997e81 or 3.29999999999999988e34 < l

   1. Initial program 100.0%

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

   2. Taylor expanded in l around 0 91.1%

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

   3. Taylor expanded in K around 0 60.1%

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

   4. Taylor expanded in l around inf 60.1%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)} \]
   5. Step-by-step derivation

      1. *-commutative 60.1%

         \[\leadsto \color{blue}{\left(J \cdot {\ell}^{3}\right) \cdot 0.3333333333333333} \]

      2. associate-*r* 60.1%

         \[\leadsto \color{blue}{J \cdot \left({\ell}^{3} \cdot 0.3333333333333333\right)} \]

      3. *-commutative 60.1%

         \[\leadsto J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3}\right)} \]

   6. Simplified 60.1%

      \[\leadsto \color{blue}{J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)} \]

   if -2.99999999999999997e81 < l < -1.15e16

   1. Initial program 100.0%

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

   3. Applied egg-rr 73.0%

      \[\leadsto \color{blue}{{U}^{-4}} \]

   if -1.15e16 < l < 3.29999999999999988e34

   1. Initial program 74.3%

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

   2. Taylor expanded in l around 0 95.7%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]
   3. Step-by-step derivation

      1. associate-*r* 95.7%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)} + U \]

      2. *-commutative 95.7%

         \[\leadsto \color{blue}{\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right) \cdot \left(2 \cdot J\right)} + U \]

      3. associate-*l* 95.7%

         \[\leadsto \color{blue}{\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \left(2 \cdot J\right)\right)} + U \]

      4. *-commutative 95.7%

         \[\leadsto \ell \cdot \color{blue}{\left(\left(2 \cdot J\right) \cdot \cos \left(0.5 \cdot K\right)\right)} + U \]

      5. associate-*l* 95.7%

         \[\leadsto \ell \cdot \color{blue}{\left(2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]

   4. Simplified 95.7%

      \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3 \cdot 10^{+81}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \mathbf{elif}\;\ell \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;{U}^{-4}\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;U + \ell \cdot \left(2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \end{array} \]

Alternative 7: 78.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \mathbf{if}\;\ell \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;{U}^{-4}\\ \mathbf{elif}\;\ell \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* J (* 0.3333333333333333 (pow l 3.0)))))
   (if (<= l -1.9e+81)
     t_0
     (if (<= l -5.2e+15)
       (pow U -4.0)
       (if (<= l 4.2e+34) (+ U (* (cos (/ K 2.0)) (* l (* J 2.0)))) t_0)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = J * (0.3333333333333333 * pow(l, 3.0));
	double tmp;
	if (l <= -1.9e+81) {
		tmp = t_0;
	} else if (l <= -5.2e+15) {
		tmp = pow(U, -4.0);
	} else if (l <= 4.2e+34) {
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	} 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) :: tmp
    t_0 = j * (0.3333333333333333d0 * (l ** 3.0d0))
    if (l <= (-1.9d+81)) then
        tmp = t_0
    else if (l <= (-5.2d+15)) then
        tmp = u ** (-4.0d0)
    else if (l <= 4.2d+34) then
        tmp = u + (cos((k / 2.0d0)) * (l * (j * 2.0d0)))
    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 = J * (0.3333333333333333 * Math.pow(l, 3.0));
	double tmp;
	if (l <= -1.9e+81) {
		tmp = t_0;
	} else if (l <= -5.2e+15) {
		tmp = Math.pow(U, -4.0);
	} else if (l <= 4.2e+34) {
		tmp = U + (Math.cos((K / 2.0)) * (l * (J * 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = J * (0.3333333333333333 * math.pow(l, 3.0))
	tmp = 0
	if l <= -1.9e+81:
		tmp = t_0
	elif l <= -5.2e+15:
		tmp = math.pow(U, -4.0)
	elif l <= 4.2e+34:
		tmp = U + (math.cos((K / 2.0)) * (l * (J * 2.0)))
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(J * Float64(0.3333333333333333 * (l ^ 3.0)))
	tmp = 0.0
	if (l <= -1.9e+81)
		tmp = t_0;
	elseif (l <= -5.2e+15)
		tmp = U ^ -4.0;
	elseif (l <= 4.2e+34)
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(l * Float64(J * 2.0))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = J * (0.3333333333333333 * (l ^ 3.0));
	tmp = 0.0;
	if (l <= -1.9e+81)
		tmp = t_0;
	elseif (l <= -5.2e+15)
		tmp = U ^ -4.0;
	elseif (l <= 4.2e+34)
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -1.9e+81], t$95$0, If[LessEqual[l, -5.2e+15], N[Power[U, -4.0], $MachinePrecision], If[LessEqual[l, 4.2e+34], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if l < -1.9e81 or 4.20000000000000035e34 < l

   1. Initial program 100.0%

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

   2. Taylor expanded in l around 0 91.1%

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

   3. Taylor expanded in K around 0 60.1%

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

   4. Taylor expanded in l around inf 60.1%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)} \]
   5. Step-by-step derivation

      1. *-commutative 60.1%

         \[\leadsto \color{blue}{\left(J \cdot {\ell}^{3}\right) \cdot 0.3333333333333333} \]

      2. associate-*r* 60.1%

         \[\leadsto \color{blue}{J \cdot \left({\ell}^{3} \cdot 0.3333333333333333\right)} \]

      3. *-commutative 60.1%

         \[\leadsto J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3}\right)} \]

   6. Simplified 60.1%

      \[\leadsto \color{blue}{J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)} \]

   if -1.9e81 < l < -5.2e15

   1. Initial program 100.0%

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

   3. Applied egg-rr 73.0%

      \[\leadsto \color{blue}{{U}^{-4}} \]

   if -5.2e15 < l < 4.20000000000000035e34

   1. Initial program 74.3%

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

   2. Taylor expanded in l around 0 95.7%

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

      1. associate-*r* 95.7%

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

      2. *-commutative 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \mathbf{elif}\;\ell \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;{U}^{-4}\\ \mathbf{elif}\;\ell \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \end{array} \]

Alternative 8: 77.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;J \leq -6.9 \cdot 10^{+90} \lor \neg \left(J \leq 1.1 \cdot 10^{+112}\right):\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= J -6.9e+90) (not (<= J 1.1e+112)))
   (+ U (* (cos (/ K 2.0)) (* l (* J 2.0))))
   (+ (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((J <= -6.9e+90) || !(J <= 1.1e+112)) {
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	} else {
		tmp = (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))) + 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) :: tmp
    if ((j <= (-6.9d+90)) .or. (.not. (j <= 1.1d+112))) then
        tmp = u + (cos((k / 2.0d0)) * (l * (j * 2.0d0)))
    else
        tmp = (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((J <= -6.9e+90) || !(J <= 1.1e+112)) {
		tmp = U + (Math.cos((K / 2.0)) * (l * (J * 2.0)));
	} else {
		tmp = (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (J <= -6.9e+90) or not (J <= 1.1e+112):
		tmp = U + (math.cos((K / 2.0)) * (l * (J * 2.0)))
	else:
		tmp = (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((J <= -6.9e+90) || !(J <= 1.1e+112))
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(l * Float64(J * 2.0))));
	else
		tmp = Float64(Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((J <= -6.9e+90) || ~((J <= 1.1e+112)))
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	else
		tmp = (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[J, -6.9e+90], N[Not[LessEqual[J, 1.1e+112]], $MachinePrecision]], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if J < -6.89999999999999955e90 or 1.1e112 < J

   1. Initial program 72.8%

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

   2. Taylor expanded in l around 0 88.3%

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

      1. associate-*r* 88.3%

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

      2. *-commutative 88.3%

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

   4. Simplified 88.3%

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

   if -6.89999999999999955e90 < J < 1.1e112

   1. Initial program 94.3%

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

   2. Taylor expanded in l around 0 89.0%

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

   3. Taylor expanded in K around 0 74.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;J \leq -6.9 \cdot 10^{+90} \lor \neg \left(J \leq 1.1 \cdot 10^{+112}\right):\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right) + U\\ \end{array} \]

Alternative 9: 72.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \mathbf{if}\;\ell \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;{U}^{-4}\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* J (* 0.3333333333333333 (pow l 3.0)))))
   (if (<= l -1.26e+82)
     t_0
     (if (<= l -5.2e+15)
       (pow U -4.0)
       (if (<= l 3.3e+34) (+ U (* l (* J 2.0))) t_0)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = J * (0.3333333333333333 * pow(l, 3.0));
	double tmp;
	if (l <= -1.26e+82) {
		tmp = t_0;
	} else if (l <= -5.2e+15) {
		tmp = pow(U, -4.0);
	} else if (l <= 3.3e+34) {
		tmp = U + (l * (J * 2.0));
	} 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) :: tmp
    t_0 = j * (0.3333333333333333d0 * (l ** 3.0d0))
    if (l <= (-1.26d+82)) then
        tmp = t_0
    else if (l <= (-5.2d+15)) then
        tmp = u ** (-4.0d0)
    else if (l <= 3.3d+34) then
        tmp = u + (l * (j * 2.0d0))
    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 = J * (0.3333333333333333 * Math.pow(l, 3.0));
	double tmp;
	if (l <= -1.26e+82) {
		tmp = t_0;
	} else if (l <= -5.2e+15) {
		tmp = Math.pow(U, -4.0);
	} else if (l <= 3.3e+34) {
		tmp = U + (l * (J * 2.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = J * (0.3333333333333333 * math.pow(l, 3.0))
	tmp = 0
	if l <= -1.26e+82:
		tmp = t_0
	elif l <= -5.2e+15:
		tmp = math.pow(U, -4.0)
	elif l <= 3.3e+34:
		tmp = U + (l * (J * 2.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(J * Float64(0.3333333333333333 * (l ^ 3.0)))
	tmp = 0.0
	if (l <= -1.26e+82)
		tmp = t_0;
	elseif (l <= -5.2e+15)
		tmp = U ^ -4.0;
	elseif (l <= 3.3e+34)
		tmp = Float64(U + Float64(l * Float64(J * 2.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = J * (0.3333333333333333 * (l ^ 3.0));
	tmp = 0.0;
	if (l <= -1.26e+82)
		tmp = t_0;
	elseif (l <= -5.2e+15)
		tmp = U ^ -4.0;
	elseif (l <= 3.3e+34)
		tmp = U + (l * (J * 2.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -1.26e+82], t$95$0, If[LessEqual[l, -5.2e+15], N[Power[U, -4.0], $MachinePrecision], If[LessEqual[l, 3.3e+34], N[(U + N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if l < -1.2600000000000001e82 or 3.29999999999999988e34 < l

   1. Initial program 100.0%

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

   2. Taylor expanded in l around 0 91.1%

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

   3. Taylor expanded in K around 0 60.1%

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

   4. Taylor expanded in l around inf 60.1%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)} \]
   5. Step-by-step derivation

      1. *-commutative 60.1%

         \[\leadsto \color{blue}{\left(J \cdot {\ell}^{3}\right) \cdot 0.3333333333333333} \]

      2. associate-*r* 60.1%

         \[\leadsto \color{blue}{J \cdot \left({\ell}^{3} \cdot 0.3333333333333333\right)} \]

      3. *-commutative 60.1%

         \[\leadsto J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3}\right)} \]

   6. Simplified 60.1%

      \[\leadsto \color{blue}{J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)} \]

   if -1.2600000000000001e82 < l < -5.2e15

   1. Initial program 100.0%

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

   3. Applied egg-rr 73.0%

      \[\leadsto \color{blue}{{U}^{-4}} \]

   if -5.2e15 < l < 3.29999999999999988e34

   1. Initial program 74.3%

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

   2. Taylor expanded in l around 0 95.9%

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

   3. Taylor expanded in K around 0 83.2%

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

   4. Taylor expanded in l around 0 83.2%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right)} + U \]
   5. Step-by-step derivation

      1. associate-*r* 83.2%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

   6. Simplified 83.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \mathbf{elif}\;\ell \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;{U}^{-4}\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\\ \end{array} \]

Alternative 10: 54.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -9.5 \cdot 10^{+82} \lor \neg \left(\ell \leq -5.2 \cdot 10^{+15}\right) \land \ell \leq 850:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;{U}^{-4}\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -9.5e+82) (and (not (<= l -5.2e+15)) (<= l 850.0)))
   (+ U (* l (* J 2.0)))
   (pow U -4.0)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -9.5e+82) || (!(l <= -5.2e+15) && (l <= 850.0))) {
		tmp = U + (l * (J * 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 <= (-9.5d+82)) .or. (.not. (l <= (-5.2d+15))) .and. (l <= 850.0d0)) then
        tmp = u + (l * (j * 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 <= -9.5e+82) || (!(l <= -5.2e+15) && (l <= 850.0))) {
		tmp = U + (l * (J * 2.0));
	} else {
		tmp = Math.pow(U, -4.0);
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -9.5e+82) or (not (l <= -5.2e+15) and (l <= 850.0)):
		tmp = U + (l * (J * 2.0))
	else:
		tmp = math.pow(U, -4.0)
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -9.5e+82) || (!(l <= -5.2e+15) && (l <= 850.0)))
		tmp = Float64(U + Float64(l * Float64(J * 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 <= -9.5e+82) || (~((l <= -5.2e+15)) && (l <= 850.0)))
		tmp = U + (l * (J * 2.0));
	else
		tmp = U ^ -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -9.5e+82], And[N[Not[LessEqual[l, -5.2e+15]], $MachinePrecision], LessEqual[l, 850.0]]], N[(U + N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[U, -4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -9.50000000000000049e82 or -5.2e15 < l < 850

   1. Initial program 80.0%

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

   2. Taylor expanded in l around 0 97.9%

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

   3. Taylor expanded in K around 0 81.8%

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

   4. Taylor expanded in l around 0 72.1%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right)} + U \]
   5. Step-by-step derivation

      1. associate-*r* 72.1%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

   6. Simplified 72.1%

      \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

   if -9.50000000000000049e82 < l < -5.2e15 or 850 < l

   1. Initial program 100.0%

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

   3. Applied egg-rr 31.1%

      \[\leadsto \color{blue}{{U}^{-4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -9.5 \cdot 10^{+82} \lor \neg \left(\ell \leq -5.2 \cdot 10^{+15}\right) \land \ell \leq 850:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;{U}^{-4}\\ \end{array} \]

Alternative 11: 52.8% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 - K \cdot -0.03125\\ \mathbf{if}\;\ell \leq 0.05:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;U + \left(\frac{K \cdot -0.03125 - t_0 \cdot t_0}{K \cdot -0.03125 + \left(K \cdot -0.03125 - -4\right)} + J \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (- -4.0 (* K -0.03125))))
   (if (<= l 0.05)
     (+ U (* l (* J 2.0)))
     (+
      U
      (+
       (/
        (- (* K -0.03125) (* t_0 t_0))
        (+ (* K -0.03125) (- (* K -0.03125) -4.0)))
       (* J 0.25))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = -4.0 - (K * -0.03125);
	double tmp;
	if (l <= 0.05) {
		tmp = U + (l * (J * 2.0));
	} else {
		tmp = U + ((((K * -0.03125) - (t_0 * t_0)) / ((K * -0.03125) + ((K * -0.03125) - -4.0))) + (J * 0.25));
	}
	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 = (-4.0d0) - (k * (-0.03125d0))
    if (l <= 0.05d0) then
        tmp = u + (l * (j * 2.0d0))
    else
        tmp = u + ((((k * (-0.03125d0)) - (t_0 * t_0)) / ((k * (-0.03125d0)) + ((k * (-0.03125d0)) - (-4.0d0)))) + (j * 0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = -4.0 - (K * -0.03125);
	double tmp;
	if (l <= 0.05) {
		tmp = U + (l * (J * 2.0));
	} else {
		tmp = U + ((((K * -0.03125) - (t_0 * t_0)) / ((K * -0.03125) + ((K * -0.03125) - -4.0))) + (J * 0.25));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = -4.0 - (K * -0.03125)
	tmp = 0
	if l <= 0.05:
		tmp = U + (l * (J * 2.0))
	else:
		tmp = U + ((((K * -0.03125) - (t_0 * t_0)) / ((K * -0.03125) + ((K * -0.03125) - -4.0))) + (J * 0.25))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(-4.0 - Float64(K * -0.03125))
	tmp = 0.0
	if (l <= 0.05)
		tmp = Float64(U + Float64(l * Float64(J * 2.0)));
	else
		tmp = Float64(U + Float64(Float64(Float64(Float64(K * -0.03125) - Float64(t_0 * t_0)) / Float64(Float64(K * -0.03125) + Float64(Float64(K * -0.03125) - -4.0))) + Float64(J * 0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = -4.0 - (K * -0.03125);
	tmp = 0.0;
	if (l <= 0.05)
		tmp = U + (l * (J * 2.0));
	else
		tmp = U + ((((K * -0.03125) - (t_0 * t_0)) / ((K * -0.03125) + ((K * -0.03125) - -4.0))) + (J * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(-4.0 - N[(K * -0.03125), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, 0.05], N[(U + N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(N[(N[(N[(K * -0.03125), $MachinePrecision] - N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(N[(K * -0.03125), $MachinePrecision] + N[(N[(K * -0.03125), $MachinePrecision] - -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(J * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if l < 0.050000000000000003

   1. Initial program 81.1%

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

   2. Taylor expanded in l around 0 93.4%

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

   3. Taylor expanded in K around 0 78.1%

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

   4. Taylor expanded in l around 0 68.9%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right)} + U \]
   5. Step-by-step derivation

      1. associate-*r* 68.9%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

   6. Simplified 68.9%

      \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

   if 0.050000000000000003 < l

   1. Initial program 100.0%

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

   3. Applied egg-rr 4.7%

      \[\leadsto \left(J \cdot \color{blue}{0.25}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   4. Taylor expanded in K around 0 25.2%

      \[\leadsto \color{blue}{\left(-0.03125 \cdot \left(J \cdot {K}^{2}\right) + 0.25 \cdot J\right)} + U \]

   6. Applied egg-rr 18.9%

      \[\leadsto \left(\color{blue}{\frac{K \cdot -0.03125 - \left(-4 - K \cdot -0.03125\right) \cdot \left(-4 - K \cdot -0.03125\right)}{K \cdot -0.03125 - \left(-4 - K \cdot -0.03125\right)}} + 0.25 \cdot J\right) + U \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq 0.05:\\ \;\;\;\;U + \ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;U + \left(\frac{K \cdot -0.03125 - \left(-4 - K \cdot -0.03125\right) \cdot \left(-4 - K \cdot -0.03125\right)}{K \cdot -0.03125 + \left(K \cdot -0.03125 - -4\right)} + J \cdot 0.25\right)\\ \end{array} \]

Alternative 12: 42.4% accurate, 34.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3:\\ \;\;\;\;U \cdot U\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;-4 - U \cdot U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -3.0) (* U U) (if (<= l 3.3e+34) U (- -4.0 (* U U)))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -3.0) {
		tmp = U * U;
	} else if (l <= 3.3e+34) {
		tmp = U;
	} else {
		tmp = -4.0 - (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 <= (-3.0d0)) then
        tmp = u * u
    else if (l <= 3.3d+34) then
        tmp = u
    else
        tmp = (-4.0d0) - (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 <= -3.0) {
		tmp = U * U;
	} else if (l <= 3.3e+34) {
		tmp = U;
	} else {
		tmp = -4.0 - (U * U);
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -3.0:
		tmp = U * U
	elif l <= 3.3e+34:
		tmp = U
	else:
		tmp = -4.0 - (U * U)
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -3.0)
		tmp = Float64(U * U);
	elseif (l <= 3.3e+34)
		tmp = U;
	else
		tmp = Float64(-4.0 - Float64(U * U));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -3.0)
		tmp = U * U;
	elseif (l <= 3.3e+34)
		tmp = U;
	else
		tmp = -4.0 - (U * U);
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -3.0], N[(U * U), $MachinePrecision], If[LessEqual[l, 3.3e+34], U, N[(-4.0 - N[(U * U), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -3

   1. Initial program 100.0%

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

   3. Applied egg-rr 15.8%

      \[\leadsto \color{blue}{U \cdot U} \]

   if -3 < l < 3.29999999999999988e34

   1. Initial program 73.8%

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

   2. Taylor expanded in J around 0 70.3%

      \[\leadsto \color{blue}{U} \]

   if 3.29999999999999988e34 < l

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(J, \left(e^{\ell} - e^{-\ell}\right) \cdot \cos \left(\frac{K}{2}\right), U\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(J, \left(e^{\ell} - e^{-\ell}\right) \cdot \cos \left(\frac{K}{2}\right), U\right)} \]

   5. Applied egg-rr 14.2%

      \[\leadsto \color{blue}{-4 + \left(-U\right) \cdot U} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 14.2%

         \[\leadsto \color{blue}{-4 - U \cdot U} \]

   7. Simplified 14.2%

      \[\leadsto \color{blue}{-4 - U \cdot U} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3:\\ \;\;\;\;U \cdot U\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;-4 - U \cdot U\\ \end{array} \]

Alternative 13: 42.1% accurate, 43.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3 \lor \neg \left(\ell \leq 1.9 \cdot 10^{+58}\right):\\ \;\;\;\;U \cdot U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -3.0) (not (<= l 1.9e+58))) (* U U) U))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -3.0) || !(l <= 1.9e+58)) {
		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 <= (-3.0d0)) .or. (.not. (l <= 1.9d+58))) 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 <= -3.0) || !(l <= 1.9e+58)) {
		tmp = U * U;
	} else {
		tmp = U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -3.0) or not (l <= 1.9e+58):
		tmp = U * U
	else:
		tmp = U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -3.0) || !(l <= 1.9e+58))
		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 <= -3.0) || ~((l <= 1.9e+58)))
		tmp = U * U;
	else
		tmp = U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -3.0], N[Not[LessEqual[l, 1.9e+58]], $MachinePrecision]], N[(U * U), $MachinePrecision], U]

Derivation

1. Split input into 2 regimes

2. if l < -3 or 1.8999999999999999e58 < l

   1. Initial program 100.0%

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

   3. Applied egg-rr 13.7%

      \[\leadsto \color{blue}{U \cdot U} \]

   if -3 < l < 1.8999999999999999e58

   1. Initial program 75.1%

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

   2. Taylor expanded in J around 0 67.0%

      \[\leadsto \color{blue}{U} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3 \lor \neg \left(\ell \leq 1.9 \cdot 10^{+58}\right):\\ \;\;\;\;U \cdot U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]

Alternative 14: 55.1% 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

1. Initial program 86.2%

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

2. Taylor expanded in l around 0 90.7%

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

3. Taylor expanded in K around 0 70.9%

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

4. Taylor expanded in l around 0 54.1%

   \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right)} + U \]
5. Step-by-step derivation

   1. associate-*r* 54.1%

      \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

6. Simplified 54.1%

   \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

7. Final simplification 54.1%

   \[\leadsto U + \ell \cdot \left(J \cdot 2\right) \]

Alternative 15: 2.7% accurate, 312.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 1.0)

C

double code(double J, double l, double K, double U) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double J, double l, double K, double U) {
	return 1.0;
}

Python

def code(J, l, K, U):
	return 1.0

Julia

function code(J, l, K, U)
	return 1.0
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = 1.0;
end

Wolfram

code[J_, l_, K_, U_] := 1.0

Derivation

1. Initial program 86.2%

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

3. Applied egg-rr 2.7%

   \[\leadsto \color{blue}{\frac{U}{U}} \]
4. Step-by-step derivation

   1. *-inverses 2.7%

      \[\leadsto \color{blue}{1} \]

5. Simplified 2.7%

   \[\leadsto \color{blue}{1} \]

6. Final simplification 2.7%

   \[\leadsto 1 \]

Alternative 16: 37.0% 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

1. Initial program 86.2%

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

2. Taylor expanded in J around 0 38.1%

   \[\leadsto \color{blue}{U} \]

3. Final simplification 38.1%

   \[\leadsto U \]

Reproduce

herbie shell --seed 2023306 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))