Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 86.9% → 99.5%

Time: 9.9s

Alternatives: 13

Speedup: 1.3×

• 50.4% 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: 86.9% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{\ell} - e^{-\ell}\\ t_2 := \left(J \cdot t\_1\right) \cdot t\_0 + U\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\left(J \cdot \left(2 \cdot \ell\right)\right) \cdot t\_0 + U\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0)))
        (t_1 (- (exp l) (exp (- l))))
        (t_2 (+ (* (* J t_1) t_0) U)))
   (if (<= t_1 -5000000.0)
     t_2
     (if (<= t_1 0.0) (+ (* (* J (* 2.0 l)) t_0) U) t_2))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(l) - exp(-l);
	double t_2 = ((J * t_1) * t_0) + U;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((J * (2.0 * l)) * t_0) + U;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = cos((k / 2.0d0))
    t_1 = exp(l) - exp(-l)
    t_2 = ((j * t_1) * t_0) + u
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.0d0) then
        tmp = ((j * (2.0d0 * l)) * t_0) + u
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.exp(l) - Math.exp(-l);
	double t_2 = ((J * t_1) * t_0) + U;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((J * (2.0 * l)) * t_0) + U;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.exp(l) - math.exp(-l)
	t_2 = ((J * t_1) * t_0) + U
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = ((J * (2.0 * l)) * t_0) + U
	else:
		tmp = t_2
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(exp(l) - exp(Float64(-l)))
	t_2 = Float64(Float64(Float64(J * t_1) * t_0) + U)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(J * Float64(2.0 * l)) * t_0) + U);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = exp(l) - exp(-l);
	t_2 = ((J * t_1) * t_0) + U;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = ((J * (2.0 * l)) * t_0) + U;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(J * t$95$1), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000.0], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(J * N[(2.0 * l), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -5e6 or 0.0 < (-.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. Add Preprocessing

   if -5e6 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 0.0

   1. Initial program 78.1%

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

   3. Taylor expanded in l around 0 99.9%

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

Alternative 2: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.02:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot -4 + U\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(e^{\ell} - e^{-\ell}\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.02)
   (+ (* (* J (* 0.3333333333333333 (pow l 3.0))) -4.0) U)
   (+ (* J (- (exp l) (exp (- l)))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.02) {
		tmp = ((J * (0.3333333333333333 * pow(l, 3.0))) * -4.0) + U;
	} else {
		tmp = (J * (exp(l) - 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) :: tmp
    if (cos((k / 2.0d0)) <= (-0.02d0)) then
        tmp = ((j * (0.3333333333333333d0 * (l ** 3.0d0))) * (-4.0d0)) + u
    else
        tmp = (j * (exp(l) - exp(-l))) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= -0.02) {
		tmp = ((J * (0.3333333333333333 * Math.pow(l, 3.0))) * -4.0) + U;
	} else {
		tmp = (J * (Math.exp(l) - Math.exp(-l))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.02:
		tmp = ((J * (0.3333333333333333 * math.pow(l, 3.0))) * -4.0) + U
	else:
		tmp = (J * (math.exp(l) - math.exp(-l))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.02)
		tmp = Float64(Float64(Float64(J * Float64(0.3333333333333333 * (l ^ 3.0))) * -4.0) + U);
	else
		tmp = Float64(Float64(J * Float64(exp(l) - exp(Float64(-l)))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.02)
		tmp = ((J * (0.3333333333333333 * (l ^ 3.0))) * -4.0) + U;
	else
		tmp = (J * (exp(l) - exp(-l))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.02], N[(N[(N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + U), $MachinePrecision], N[(N[(J * N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.0200000000000000004

   1. Initial program 90.9%

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

   3. Taylor expanded in l around 0 83.5%

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

   4. Taylor expanded in l around inf 74.6%

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

   6. Applied egg-rr 74.6%

      \[\leadsto \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot \color{blue}{-4} + U \]

   if -0.0200000000000000004 < (cos.f64 (/.f64 K 2))

   1. Initial program 90.4%

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

   3. Taylor expanded in K around 0 90.0%

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

Alternative 3: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot t\_0 + U\\ t_2 := J \cdot \left(e^{\ell} - e^{-\ell}\right) + U\\ \mathbf{if}\;\ell \leq -3.95 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\ell \leq -0.00295:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\ell \leq 0.0058:\\ \;\;\;\;\left(J \cdot \left(2 \cdot \ell\right)\right) \cdot t\_0 + U\\ \mathbf{elif}\;\ell \leq 2.2 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0)))
        (t_1 (+ (* (* J (* 0.3333333333333333 (pow l 3.0))) t_0) U))
        (t_2 (+ (* J (- (exp l) (exp (- l)))) U)))
   (if (<= l -3.95e+102)
     t_1
     (if (<= l -0.00295)
       t_2
       (if (<= l 0.0058)
         (+ (* (* J (* 2.0 l)) t_0) U)
         (if (<= l 2.2e+89) t_2 t_1))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = ((J * (0.3333333333333333 * pow(l, 3.0))) * t_0) + U;
	double t_2 = (J * (exp(l) - exp(-l))) + U;
	double tmp;
	if (l <= -3.95e+102) {
		tmp = t_1;
	} else if (l <= -0.00295) {
		tmp = t_2;
	} else if (l <= 0.0058) {
		tmp = ((J * (2.0 * l)) * t_0) + U;
	} else if (l <= 2.2e+89) {
		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((k / 2.0d0))
    t_1 = ((j * (0.3333333333333333d0 * (l ** 3.0d0))) * t_0) + u
    t_2 = (j * (exp(l) - exp(-l))) + u
    if (l <= (-3.95d+102)) then
        tmp = t_1
    else if (l <= (-0.00295d0)) then
        tmp = t_2
    else if (l <= 0.0058d0) then
        tmp = ((j * (2.0d0 * l)) * t_0) + u
    else if (l <= 2.2d+89) 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((K / 2.0));
	double t_1 = ((J * (0.3333333333333333 * Math.pow(l, 3.0))) * t_0) + U;
	double t_2 = (J * (Math.exp(l) - Math.exp(-l))) + U;
	double tmp;
	if (l <= -3.95e+102) {
		tmp = t_1;
	} else if (l <= -0.00295) {
		tmp = t_2;
	} else if (l <= 0.0058) {
		tmp = ((J * (2.0 * l)) * t_0) + U;
	} else if (l <= 2.2e+89) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = ((J * (0.3333333333333333 * math.pow(l, 3.0))) * t_0) + U
	t_2 = (J * (math.exp(l) - math.exp(-l))) + U
	tmp = 0
	if l <= -3.95e+102:
		tmp = t_1
	elif l <= -0.00295:
		tmp = t_2
	elif l <= 0.0058:
		tmp = ((J * (2.0 * l)) * t_0) + U
	elif l <= 2.2e+89:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(Float64(Float64(J * Float64(0.3333333333333333 * (l ^ 3.0))) * t_0) + U)
	t_2 = Float64(Float64(J * Float64(exp(l) - exp(Float64(-l)))) + U)
	tmp = 0.0
	if (l <= -3.95e+102)
		tmp = t_1;
	elseif (l <= -0.00295)
		tmp = t_2;
	elseif (l <= 0.0058)
		tmp = Float64(Float64(Float64(J * Float64(2.0 * l)) * t_0) + U);
	elseif (l <= 2.2e+89)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = ((J * (0.3333333333333333 * (l ^ 3.0))) * t_0) + U;
	t_2 = (J * (exp(l) - exp(-l))) + U;
	tmp = 0.0;
	if (l <= -3.95e+102)
		tmp = t_1;
	elseif (l <= -0.00295)
		tmp = t_2;
	elseif (l <= 0.0058)
		tmp = ((J * (2.0 * l)) * t_0) + U;
	elseif (l <= 2.2e+89)
		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[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision]}, Block[{t$95$2 = N[(N[(J * N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]}, If[LessEqual[l, -3.95e+102], t$95$1, If[LessEqual[l, -0.00295], t$95$2, If[LessEqual[l, 0.0058], N[(N[(N[(J * N[(2.0 * l), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision], If[LessEqual[l, 2.2e+89], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -3.9500000000000001e102 or 2.2e89 < 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. Add Preprocessing

   3. Taylor expanded in l around 0 99.0%

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

   4. Taylor expanded in l around inf 99.0%

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

   if -3.9500000000000001e102 < l < -0.00294999999999999993 or 0.0058 < l < 2.2e89

   1. Initial program 100.0%

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

   3. Taylor expanded in K around 0 74.0%

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

   if -0.00294999999999999993 < l < 0.0058

   1. Initial program 78.1%

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

   3. Taylor expanded in l around 0 99.9%

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

Alternative 4: 59.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;t\_0 \leq -0.12:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot -1\right)\right) + U\\ \mathbf{elif}\;t\_0 \leq 0.995:\\ \;\;\;\;U \cdot \left(1 + 0.6666666666666666 \cdot \frac{J \cdot \ell}{U}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(J \cdot \ell\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))))
   (if (<= t_0 -0.12)
     (+ (* 2.0 (* J (* l -1.0))) U)
     (if (<= t_0 0.995)
       (* U (+ 1.0 (* 0.6666666666666666 (/ (* J l) U))))
       (+ (* 2.0 (* J l)) U)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double tmp;
	if (t_0 <= -0.12) {
		tmp = (2.0 * (J * (l * -1.0))) + U;
	} else if (t_0 <= 0.995) {
		tmp = U * (1.0 + (0.6666666666666666 * ((J * l) / U)));
	} else {
		tmp = (2.0 * (J * 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) :: tmp
    t_0 = cos((k / 2.0d0))
    if (t_0 <= (-0.12d0)) then
        tmp = (2.0d0 * (j * (l * (-1.0d0)))) + u
    else if (t_0 <= 0.995d0) then
        tmp = u * (1.0d0 + (0.6666666666666666d0 * ((j * l) / u)))
    else
        tmp = (2.0d0 * (j * 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.cos((K / 2.0));
	double tmp;
	if (t_0 <= -0.12) {
		tmp = (2.0 * (J * (l * -1.0))) + U;
	} else if (t_0 <= 0.995) {
		tmp = U * (1.0 + (0.6666666666666666 * ((J * l) / U)));
	} else {
		tmp = (2.0 * (J * l)) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	tmp = 0
	if t_0 <= -0.12:
		tmp = (2.0 * (J * (l * -1.0))) + U
	elif t_0 <= 0.995:
		tmp = U * (1.0 + (0.6666666666666666 * ((J * l) / U)))
	else:
		tmp = (2.0 * (J * l)) + U
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	tmp = 0.0
	if (t_0 <= -0.12)
		tmp = Float64(Float64(2.0 * Float64(J * Float64(l * -1.0))) + U);
	elseif (t_0 <= 0.995)
		tmp = Float64(U * Float64(1.0 + Float64(0.6666666666666666 * Float64(Float64(J * l) / U))));
	else
		tmp = Float64(Float64(2.0 * Float64(J * l)) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	tmp = 0.0;
	if (t_0 <= -0.12)
		tmp = (2.0 * (J * (l * -1.0))) + U;
	elseif (t_0 <= 0.995)
		tmp = U * (1.0 + (0.6666666666666666 * ((J * l) / U)));
	else
		tmp = (2.0 * (J * l)) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, -0.12], N[(N[(2.0 * N[(J * N[(l * -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], If[LessEqual[t$95$0, 0.995], N[(U * N[(1.0 + N[(0.6666666666666666 * N[(N[(J * l), $MachinePrecision] / U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(J * l), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.12

   1. Initial program 90.3%

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

   3. Taylor expanded in l around 0 66.4%

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

   5. Applied egg-rr 59.0%

      \[\leadsto 2 \cdot \left(J \cdot \left(\ell \cdot \color{blue}{-1}\right)\right) + U \]

   if -0.12 < (cos.f64 (/.f64 K 2)) < 0.994999999999999996

   1. Initial program 88.8%

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

   3. Taylor expanded in l around 0 56.4%

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

   5. Applied egg-rr 47.4%

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

   6. Taylor expanded in U around inf 53.1%

      \[\leadsto \color{blue}{U \cdot \left(1 + 0.6666666666666666 \cdot \frac{J \cdot \ell}{U}\right)} \]

   if 0.994999999999999996 < (cos.f64 (/.f64 K 2))

   1. Initial program 91.5%

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

   3. Taylor expanded in l around 0 63.5%

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

   4. Taylor expanded in K around 0 63.5%

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

Alternative 5: 82.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.02:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot -4 + U\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot {\ell}^{2}\right)\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.02)
   (+ (* (* J (* 0.3333333333333333 (pow l 3.0))) -4.0) U)
   (+ (* J (* l (+ 2.0 (* 0.3333333333333333 (pow l 2.0))))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.02) {
		tmp = ((J * (0.3333333333333333 * pow(l, 3.0))) * -4.0) + U;
	} else {
		tmp = (J * (l * (2.0 + (0.3333333333333333 * pow(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 (cos((k / 2.0d0)) <= (-0.02d0)) then
        tmp = ((j * (0.3333333333333333d0 * (l ** 3.0d0))) * (-4.0d0)) + u
    else
        tmp = (j * (l * (2.0d0 + (0.3333333333333333d0 * (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 (Math.cos((K / 2.0)) <= -0.02) {
		tmp = ((J * (0.3333333333333333 * Math.pow(l, 3.0))) * -4.0) + U;
	} else {
		tmp = (J * (l * (2.0 + (0.3333333333333333 * Math.pow(l, 2.0))))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.02:
		tmp = ((J * (0.3333333333333333 * math.pow(l, 3.0))) * -4.0) + U
	else:
		tmp = (J * (l * (2.0 + (0.3333333333333333 * math.pow(l, 2.0))))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.02)
		tmp = Float64(Float64(Float64(J * Float64(0.3333333333333333 * (l ^ 3.0))) * -4.0) + U);
	else
		tmp = Float64(Float64(J * Float64(l * Float64(2.0 + Float64(0.3333333333333333 * (l ^ 2.0))))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.02)
		tmp = ((J * (0.3333333333333333 * (l ^ 3.0))) * -4.0) + U;
	else
		tmp = (J * (l * (2.0 + (0.3333333333333333 * (l ^ 2.0))))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.02], N[(N[(N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + U), $MachinePrecision], N[(N[(J * N[(l * N[(2.0 + N[(0.3333333333333333 * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.0200000000000000004

   1. Initial program 90.9%

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

   3. Taylor expanded in l around 0 83.5%

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

   4. Taylor expanded in l around inf 74.6%

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

   6. Applied egg-rr 74.6%

      \[\leadsto \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot \color{blue}{-4} + U \]

   if -0.0200000000000000004 < (cos.f64 (/.f64 K 2))

   1. Initial program 90.4%

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

   3. Taylor expanded in l around 0 83.6%

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

   4. Taylor expanded in K around 0 80.3%

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

Alternative 6: 74.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.02:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot -4 + U\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(J \cdot {\ell}^{3}\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.02)
   (+ (* (* J (* 0.3333333333333333 (pow l 3.0))) -4.0) U)
   (+ (* 9.0 (* J (pow l 3.0))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.02) {
		tmp = ((J * (0.3333333333333333 * pow(l, 3.0))) * -4.0) + U;
	} else {
		tmp = (9.0 * (J * pow(l, 3.0))) + 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 (cos((k / 2.0d0)) <= (-0.02d0)) then
        tmp = ((j * (0.3333333333333333d0 * (l ** 3.0d0))) * (-4.0d0)) + u
    else
        tmp = (9.0d0 * (j * (l ** 3.0d0))) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= -0.02) {
		tmp = ((J * (0.3333333333333333 * Math.pow(l, 3.0))) * -4.0) + U;
	} else {
		tmp = (9.0 * (J * Math.pow(l, 3.0))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.02:
		tmp = ((J * (0.3333333333333333 * math.pow(l, 3.0))) * -4.0) + U
	else:
		tmp = (9.0 * (J * math.pow(l, 3.0))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.02)
		tmp = Float64(Float64(Float64(J * Float64(0.3333333333333333 * (l ^ 3.0))) * -4.0) + U);
	else
		tmp = Float64(Float64(9.0 * Float64(J * (l ^ 3.0))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.02)
		tmp = ((J * (0.3333333333333333 * (l ^ 3.0))) * -4.0) + U;
	else
		tmp = (9.0 * (J * (l ^ 3.0))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.02], N[(N[(N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + U), $MachinePrecision], N[(N[(9.0 * N[(J * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.0200000000000000004

   1. Initial program 90.9%

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

   3. Taylor expanded in l around 0 83.5%

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

   4. Taylor expanded in l around inf 74.6%

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

   6. Applied egg-rr 74.6%

      \[\leadsto \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot \color{blue}{-4} + U \]

   if -0.0200000000000000004 < (cos.f64 (/.f64 K 2))

   1. Initial program 90.4%

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

   3. Taylor expanded in l around 0 83.6%

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

   4. Taylor expanded in l around inf 74.2%

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

   6. Applied egg-rr 74.2%

      \[\leadsto \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot \color{blue}{27} + U \]

   7. Taylor expanded in J around 0 74.2%

      \[\leadsto \color{blue}{9 \cdot \left(J \cdot {\ell}^{3}\right)} + U \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.02:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot -1\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.02)
   (+ (* 2.0 (* J (* l -1.0))) U)
   (+ (* 0.3333333333333333 (* J (pow l 3.0))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.02) {
		tmp = (2.0 * (J * (l * -1.0))) + U;
	} else {
		tmp = (0.3333333333333333 * (J * pow(l, 3.0))) + 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 (cos((k / 2.0d0)) <= (-0.02d0)) then
        tmp = (2.0d0 * (j * (l * (-1.0d0)))) + u
    else
        tmp = (0.3333333333333333d0 * (j * (l ** 3.0d0))) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= -0.02) {
		tmp = (2.0 * (J * (l * -1.0))) + U;
	} else {
		tmp = (0.3333333333333333 * (J * Math.pow(l, 3.0))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.02:
		tmp = (2.0 * (J * (l * -1.0))) + U
	else:
		tmp = (0.3333333333333333 * (J * math.pow(l, 3.0))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.02)
		tmp = Float64(Float64(2.0 * Float64(J * Float64(l * -1.0))) + U);
	else
		tmp = Float64(Float64(0.3333333333333333 * Float64(J * (l ^ 3.0))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.02)
		tmp = (2.0 * (J * (l * -1.0))) + U;
	else
		tmp = (0.3333333333333333 * (J * (l ^ 3.0))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.02], N[(N[(2.0 * N[(J * N[(l * -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(N[(0.3333333333333333 * N[(J * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.0200000000000000004

   1. Initial program 90.9%

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

   3. Taylor expanded in l around 0 65.4%

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

   5. Applied egg-rr 58.5%

      \[\leadsto 2 \cdot \left(J \cdot \left(\ell \cdot \color{blue}{-1}\right)\right) + U \]

   if -0.0200000000000000004 < (cos.f64 (/.f64 K 2))

   1. Initial program 90.4%

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

   3. Taylor expanded in l around 0 83.6%

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

   4. Taylor expanded in l around inf 74.2%

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

   5. Taylor expanded in K around 0 74.2%

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

Alternative 8: 68.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.02:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot -1\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(J \cdot {\ell}^{3}\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.02)
   (+ (* 2.0 (* J (* l -1.0))) U)
   (+ (* 9.0 (* J (pow l 3.0))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.02) {
		tmp = (2.0 * (J * (l * -1.0))) + U;
	} else {
		tmp = (9.0 * (J * pow(l, 3.0))) + 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 (cos((k / 2.0d0)) <= (-0.02d0)) then
        tmp = (2.0d0 * (j * (l * (-1.0d0)))) + u
    else
        tmp = (9.0d0 * (j * (l ** 3.0d0))) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= -0.02) {
		tmp = (2.0 * (J * (l * -1.0))) + U;
	} else {
		tmp = (9.0 * (J * Math.pow(l, 3.0))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.02:
		tmp = (2.0 * (J * (l * -1.0))) + U
	else:
		tmp = (9.0 * (J * math.pow(l, 3.0))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.02)
		tmp = Float64(Float64(2.0 * Float64(J * Float64(l * -1.0))) + U);
	else
		tmp = Float64(Float64(9.0 * Float64(J * (l ^ 3.0))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.02)
		tmp = (2.0 * (J * (l * -1.0))) + U;
	else
		tmp = (9.0 * (J * (l ^ 3.0))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.02], N[(N[(2.0 * N[(J * N[(l * -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(N[(9.0 * N[(J * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.0200000000000000004

   1. Initial program 90.9%

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

   3. Taylor expanded in l around 0 65.4%

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

   5. Applied egg-rr 58.5%

      \[\leadsto 2 \cdot \left(J \cdot \left(\ell \cdot \color{blue}{-1}\right)\right) + U \]

   if -0.0200000000000000004 < (cos.f64 (/.f64 K 2))

   1. Initial program 90.4%

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

   3. Taylor expanded in l around 0 83.6%

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

   4. Taylor expanded in l around inf 74.2%

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

   6. Applied egg-rr 74.2%

      \[\leadsto \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot \color{blue}{27} + U \]

   7. Taylor expanded in J around 0 74.2%

      \[\leadsto \color{blue}{9 \cdot \left(J \cdot {\ell}^{3}\right)} + U \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 45.7% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.6666666666666666 \cdot \left(J \cdot \ell\right)\\ \mathbf{if}\;\ell \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\ell \leq -700:\\ \;\;\;\;U \cdot U\\ \mathbf{elif}\;\ell \leq 4.1 \cdot 10^{-26}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (* 0.6666666666666666 (* J l))))
   (if (<= l -9.5e+61)
     t_0
     (if (<= l -700.0) (* U U) (if (<= l 4.1e-26) U t_0)))))

C

double code(double J, double l, double K, double U) {
	double t_0 = 0.6666666666666666 * (J * l);
	double tmp;
	if (l <= -9.5e+61) {
		tmp = t_0;
	} else if (l <= -700.0) {
		tmp = U * U;
	} else if (l <= 4.1e-26) {
		tmp = U;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.6666666666666666d0 * (j * l)
    if (l <= (-9.5d+61)) then
        tmp = t_0
    else if (l <= (-700.0d0)) then
        tmp = u * u
    else if (l <= 4.1d-26) then
        tmp = u
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = 0.6666666666666666 * (J * l);
	double tmp;
	if (l <= -9.5e+61) {
		tmp = t_0;
	} else if (l <= -700.0) {
		tmp = U * U;
	} else if (l <= 4.1e-26) {
		tmp = U;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = 0.6666666666666666 * (J * l)
	tmp = 0
	if l <= -9.5e+61:
		tmp = t_0
	elif l <= -700.0:
		tmp = U * U
	elif l <= 4.1e-26:
		tmp = U
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(0.6666666666666666 * Float64(J * l))
	tmp = 0.0
	if (l <= -9.5e+61)
		tmp = t_0;
	elseif (l <= -700.0)
		tmp = Float64(U * U);
	elseif (l <= 4.1e-26)
		tmp = U;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = 0.6666666666666666 * (J * l);
	tmp = 0.0;
	if (l <= -9.5e+61)
		tmp = t_0;
	elseif (l <= -700.0)
		tmp = U * U;
	elseif (l <= 4.1e-26)
		tmp = U;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(0.6666666666666666 * N[(J * l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -9.5e+61], t$95$0, If[LessEqual[l, -700.0], N[(U * U), $MachinePrecision], If[LessEqual[l, 4.1e-26], U, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if l < -9.49999999999999959e61 or 4.0999999999999999e-26 < l

   1. Initial program 97.7%

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

   3. Taylor expanded in l around 0 38.7%

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

   5. Applied egg-rr 30.0%

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

   6. Taylor expanded in J around inf 30.0%

      \[\leadsto \color{blue}{0.6666666666666666 \cdot \left(J \cdot \ell\right)} \]

   if -9.49999999999999959e61 < l < -700

   1. Initial program 100.0%

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

   4. Applied egg-rr 3.2%

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

   6. Applied egg-rr 27.3%

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

   if -700 < l < 4.0999999999999999e-26

   1. Initial program 80.4%

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

   4. Applied egg-rr 56.0%

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

   5. Taylor expanded in J around 0 79.5%

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

Alternative 10: 54.9% accurate, 22.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -6.2 \cdot 10^{-28}:\\ \;\;\;\;J \cdot \left(0.6666666666666666 \cdot \ell + \frac{U}{J}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(J \cdot \ell\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -6.2e-28)
   (* J (+ (* 0.6666666666666666 l) (/ U J)))
   (+ (* 2.0 (* J l)) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -6.2e-28) {
		tmp = J * ((0.6666666666666666 * l) + (U / J));
	} else {
		tmp = (2.0 * (J * 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) :: tmp
    if (l <= (-6.2d-28)) then
        tmp = j * ((0.6666666666666666d0 * l) + (u / j))
    else
        tmp = (2.0d0 * (j * l)) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -6.2e-28) {
		tmp = J * ((0.6666666666666666 * l) + (U / J));
	} else {
		tmp = (2.0 * (J * l)) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -6.2e-28:
		tmp = J * ((0.6666666666666666 * l) + (U / J))
	else:
		tmp = (2.0 * (J * l)) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -6.2e-28)
		tmp = Float64(J * Float64(Float64(0.6666666666666666 * l) + Float64(U / J)));
	else
		tmp = Float64(Float64(2.0 * Float64(J * l)) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -6.2e-28)
		tmp = J * ((0.6666666666666666 * l) + (U / J));
	else
		tmp = (2.0 * (J * l)) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -6.2e-28], N[(J * N[(N[(0.6666666666666666 * l), $MachinePrecision] + N[(U / J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(J * l), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -6.19999999999999984e-28

   1. Initial program 97.3%

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

   3. Taylor expanded in l around 0 38.7%

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

   5. Applied egg-rr 27.6%

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

   6. Taylor expanded in J around inf 35.3%

      \[\leadsto \color{blue}{J \cdot \left(0.6666666666666666 \cdot \ell + \frac{U}{J}\right)} \]

   if -6.19999999999999984e-28 < l

   1. Initial program 87.9%

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

   3. Taylor expanded in l around 0 71.4%

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

   4. Taylor expanded in K around 0 63.8%

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

Alternative 11: 41.3% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -400:\\ \;\;\;\;U \cdot U\\ \mathbf{elif}\;\ell \leq 1.65 \cdot 10^{-20}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U \cdot U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -400.0) (* U U) (if (<= l 1.65e-20) U (* U U))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -400.0) {
		tmp = U * U;
	} else if (l <= 1.65e-20) {
		tmp = U;
	} else {
		tmp = U * U;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if (l <= (-400.0d0)) then
        tmp = u * u
    else if (l <= 1.65d-20) then
        tmp = u
    else
        tmp = u * u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -400.0) {
		tmp = U * U;
	} else if (l <= 1.65e-20) {
		tmp = U;
	} else {
		tmp = U * U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -400.0:
		tmp = U * U
	elif l <= 1.65e-20:
		tmp = U
	else:
		tmp = U * U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -400.0)
		tmp = Float64(U * U);
	elseif (l <= 1.65e-20)
		tmp = U;
	else
		tmp = Float64(U * U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -400.0)
		tmp = U * U;
	elseif (l <= 1.65e-20)
		tmp = U;
	else
		tmp = U * U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -400.0], N[(U * U), $MachinePrecision], If[LessEqual[l, 1.65e-20], U, N[(U * U), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if l < -400 or 1.65e-20 < l

   1. Initial program 98.7%

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

   4. Applied egg-rr 2.7%

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

   6. Applied egg-rr 15.4%

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

   if -400 < l < 1.65e-20

   1. Initial program 79.7%

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

   4. Applied egg-rr 55.5%

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

   5. Taylor expanded in J around 0 78.8%

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

Alternative 12: 54.2% accurate, 44.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

3. Taylor expanded in l around 0 62.2%

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

4. Taylor expanded in K around 0 53.7%

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

Alternative 13: 36.8% accurate, 312.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = u
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

4. Applied egg-rr 25.4%

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

5. Taylor expanded in J around 0 35.2%

   \[\leadsto \color{blue}{U} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024052 -o generate:simplify
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))