Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 86.6% → 99.8%

Time: 10.4s

Alternatives: 12

Speedup: 1.4×

• 49.8% 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: 86.6% 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: 99.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+167} \lor \neg \left(t_1 \leq 0.002\right):\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot J\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + t_0 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \left(0.016666666666666666 \cdot {\ell}^{5} + \ell \cdot 2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))) (t_1 (- (exp l) (exp (- l)))))
   (if (or (<= t_1 -2e+167) (not (<= t_1 0.002)))
     (+ (* t_0 (* t_1 J)) U)
     (+
      U
      (*
       t_0
       (*
        J
        (+
         (* 0.3333333333333333 (pow l 3.0))
         (+ (* 0.016666666666666666 (pow l 5.0)) (* l 2.0)))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(l) - exp(-l);
	double tmp;
	if ((t_1 <= -2e+167) || !(t_1 <= 0.002)) {
		tmp = (t_0 * (t_1 * J)) + U;
	} else {
		tmp = U + (t_0 * (J * ((0.3333333333333333 * pow(l, 3.0)) + ((0.016666666666666666 * pow(l, 5.0)) + (l * 2.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((k / 2.0d0))
    t_1 = exp(l) - exp(-l)
    if ((t_1 <= (-2d+167)) .or. (.not. (t_1 <= 0.002d0))) then
        tmp = (t_0 * (t_1 * j)) + u
    else
        tmp = u + (t_0 * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + ((0.016666666666666666d0 * (l ** 5.0d0)) + (l * 2.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.exp(l) - Math.exp(-l);
	double tmp;
	if ((t_1 <= -2e+167) || !(t_1 <= 0.002)) {
		tmp = (t_0 * (t_1 * J)) + U;
	} else {
		tmp = U + (t_0 * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + ((0.016666666666666666 * Math.pow(l, 5.0)) + (l * 2.0)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.exp(l) - math.exp(-l)
	tmp = 0
	if (t_1 <= -2e+167) or not (t_1 <= 0.002):
		tmp = (t_0 * (t_1 * J)) + U
	else:
		tmp = U + (t_0 * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + ((0.016666666666666666 * math.pow(l, 5.0)) + (l * 2.0)))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(exp(l) - exp(Float64(-l)))
	tmp = 0.0
	if ((t_1 <= -2e+167) || !(t_1 <= 0.002))
		tmp = Float64(Float64(t_0 * Float64(t_1 * J)) + U);
	else
		tmp = Float64(U + Float64(t_0 * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(Float64(0.016666666666666666 * (l ^ 5.0)) + Float64(l * 2.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = exp(l) - exp(-l);
	tmp = 0.0;
	if ((t_1 <= -2e+167) || ~((t_1 <= 0.002)))
		tmp = (t_0 * (t_1 * J)) + U;
	else
		tmp = U + (t_0 * (J * ((0.3333333333333333 * (l ^ 3.0)) + ((0.016666666666666666 * (l ^ 5.0)) + (l * 2.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+167], N[Not[LessEqual[t$95$1, 0.002]], $MachinePrecision]], N[(N[(t$95$0 * N[(t$95$1 * J), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(t$95$0 * N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(0.016666666666666666 * N[Power[l, 5.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -2.0000000000000001e167 or 2e-3 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 100.0%

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

   if -2.0000000000000001e167 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 2e-3

   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 99.9%

      \[\leadsto \left(J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3} + \left(0.016666666666666666 \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -2 \cdot 10^{+167} \lor \neg \left(e^{\ell} - e^{-\ell} \leq 0.002\right):\\ \;\;\;\;\cos \left(\frac{K}{2}\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \left(0.016666666666666666 \cdot {\ell}^{5} + \ell \cdot 2\right)\right)\right)\\ \end{array} \]

Alternative 2: 99.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{\ell} - e^{-\ell}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+167} \lor \neg \left(t_1 \leq 0.002\right):\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot J\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + t_0 \cdot \left(2 \cdot \left(\ell \cdot J\right) + 0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))) (t_1 (- (exp l) (exp (- l)))))
   (if (or (<= t_1 -2e+167) (not (<= t_1 0.002)))
     (+ (* t_0 (* t_1 J)) U)
     (+
      U
      (* t_0 (+ (* 2.0 (* l J)) (* 0.3333333333333333 (* J (pow l 3.0)))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(l) - exp(-l);
	double tmp;
	if ((t_1 <= -2e+167) || !(t_1 <= 0.002)) {
		tmp = (t_0 * (t_1 * J)) + U;
	} else {
		tmp = U + (t_0 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * pow(l, 3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((k / 2.0d0))
    t_1 = exp(l) - exp(-l)
    if ((t_1 <= (-2d+167)) .or. (.not. (t_1 <= 0.002d0))) then
        tmp = (t_0 * (t_1 * j)) + u
    else
        tmp = u + (t_0 * ((2.0d0 * (l * j)) + (0.3333333333333333d0 * (j * (l ** 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.exp(l) - Math.exp(-l);
	double tmp;
	if ((t_1 <= -2e+167) || !(t_1 <= 0.002)) {
		tmp = (t_0 * (t_1 * J)) + U;
	} else {
		tmp = U + (t_0 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * Math.pow(l, 3.0)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.exp(l) - math.exp(-l)
	tmp = 0
	if (t_1 <= -2e+167) or not (t_1 <= 0.002):
		tmp = (t_0 * (t_1 * J)) + U
	else:
		tmp = U + (t_0 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * math.pow(l, 3.0)))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(exp(l) - exp(Float64(-l)))
	tmp = 0.0
	if ((t_1 <= -2e+167) || !(t_1 <= 0.002))
		tmp = Float64(Float64(t_0 * Float64(t_1 * J)) + U);
	else
		tmp = Float64(U + Float64(t_0 * Float64(Float64(2.0 * Float64(l * J)) + Float64(0.3333333333333333 * Float64(J * (l ^ 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = exp(l) - exp(-l);
	tmp = 0.0;
	if ((t_1 <= -2e+167) || ~((t_1 <= 0.002)))
		tmp = (t_0 * (t_1 * J)) + U;
	else
		tmp = U + (t_0 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * (l ^ 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+167], N[Not[LessEqual[t$95$1, 0.002]], $MachinePrecision]], N[(N[(t$95$0 * N[(t$95$1 * J), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(t$95$0 * N[(N[(2.0 * N[(l * J), $MachinePrecision]), $MachinePrecision] + N[(0.3333333333333333 * N[(J * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -2.0000000000000001e167 or 2e-3 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 100.0%

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

   if -2.0000000000000001e167 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 2e-3

   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 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -2 \cdot 10^{+167} \lor \neg \left(e^{\ell} - e^{-\ell} \leq 0.002\right):\\ \;\;\;\;\cos \left(\frac{K}{2}\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(\ell \cdot J\right) + 0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)\right)\\ \end{array} \]

Alternative 3: 95.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5.2 \cdot 10^{+111} \lor \neg \left(\ell \leq -130 \lor \neg \left(\ell \leq 0.046\right) \land \ell \leq 5.6 \cdot 10^{+102}\right):\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -5.2e+111)
         (not (or (<= l -130.0) (and (not (<= l 0.046)) (<= l 5.6e+102)))))
   (+
    U
    (* (cos (/ K 2.0)) (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))
   (+ U (* (- (exp l) (exp (- l))) J))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -5.2e+111) || !((l <= -130.0) || (!(l <= 0.046) && (l <= 5.6e+102)))) {
		tmp = U + (cos((K / 2.0)) * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))));
	} else {
		tmp = U + ((exp(l) - exp(-l)) * J);
	}
	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 <= (-5.2d+111)) .or. (.not. (l <= (-130.0d0)) .or. (.not. (l <= 0.046d0)) .and. (l <= 5.6d+102))) then
        tmp = u + (cos((k / 2.0d0)) * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))))
    else
        tmp = u + ((exp(l) - exp(-l)) * j)
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -5.2e+111) || !((l <= -130.0) || (!(l <= 0.046) && (l <= 5.6e+102)))) {
		tmp = U + (Math.cos((K / 2.0)) * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	} else {
		tmp = U + ((Math.exp(l) - Math.exp(-l)) * J);
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -5.2e+111) or not ((l <= -130.0) or (not (l <= 0.046) and (l <= 5.6e+102))):
		tmp = U + (math.cos((K / 2.0)) * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))))
	else:
		tmp = U + ((math.exp(l) - math.exp(-l)) * J)
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -5.2e+111) || !((l <= -130.0) || (!(l <= 0.046) && (l <= 5.6e+102))))
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))));
	else
		tmp = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -5.2e+111) || ~(((l <= -130.0) || (~((l <= 0.046)) && (l <= 5.6e+102)))))
		tmp = U + (cos((K / 2.0)) * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))));
	else
		tmp = U + ((exp(l) - exp(-l)) * J);
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -5.2e+111], N[Not[Or[LessEqual[l, -130.0], And[N[Not[LessEqual[l, 0.046]], $MachinePrecision], LessEqual[l, 5.6e+102]]]], $MachinePrecision]], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -5.1999999999999997e111 or -130 < l < 0.045999999999999999 or 5.60000000000000037e102 < l

   1. Initial program 84.1%

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

   2. Taylor expanded in l around 0 99.9%

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

   if -5.1999999999999997e111 < l < -130 or 0.045999999999999999 < l < 5.60000000000000037e102

   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 73.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -5.2 \cdot 10^{+111} \lor \neg \left(\ell \leq -130 \lor \neg \left(\ell \leq 0.046\right) \land \ell \leq 5.6 \cdot 10^{+102}\right):\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \end{array} \]

Alternative 4: 95.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ t_1 := \cos \left(\frac{K}{2}\right)\\ t_2 := U + t_1 \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{if}\;\ell \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq -130:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 0.0145:\\ \;\;\;\;U + t_1 \cdot \left(2 \cdot \left(\ell \cdot J\right) + 0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)\right)\\ \mathbf{elif}\;\ell \leq 5.2 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (+ U (* (- (exp l) (exp (- l))) J)))
        (t_1 (cos (/ K 2.0)))
        (t_2
         (+ U (* t_1 (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))))
   (if (<= l -5.2e+111)
     t_2
     (if (<= l -130.0)
       t_0
       (if (<= l 0.0145)
         (+
          U
          (* t_1 (+ (* 2.0 (* l J)) (* 0.3333333333333333 (* J (pow l 3.0))))))
         (if (<= l 5.2e+102) t_0 t_2))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + ((exp(l) - exp(-l)) * J);
	double t_1 = cos((K / 2.0));
	double t_2 = U + (t_1 * (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0))));
	double tmp;
	if (l <= -5.2e+111) {
		tmp = t_2;
	} else if (l <= -130.0) {
		tmp = t_0;
	} else if (l <= 0.0145) {
		tmp = U + (t_1 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * pow(l, 3.0)))));
	} else if (l <= 5.2e+102) {
		tmp = t_0;
	} 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 = u + ((exp(l) - exp(-l)) * j)
    t_1 = cos((k / 2.0d0))
    t_2 = u + (t_1 * (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0))))
    if (l <= (-5.2d+111)) then
        tmp = t_2
    else if (l <= (-130.0d0)) then
        tmp = t_0
    else if (l <= 0.0145d0) then
        tmp = u + (t_1 * ((2.0d0 * (l * j)) + (0.3333333333333333d0 * (j * (l ** 3.0d0)))))
    else if (l <= 5.2d+102) then
        tmp = t_0
    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 = U + ((Math.exp(l) - Math.exp(-l)) * J);
	double t_1 = Math.cos((K / 2.0));
	double t_2 = U + (t_1 * (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0))));
	double tmp;
	if (l <= -5.2e+111) {
		tmp = t_2;
	} else if (l <= -130.0) {
		tmp = t_0;
	} else if (l <= 0.0145) {
		tmp = U + (t_1 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * Math.pow(l, 3.0)))));
	} else if (l <= 5.2e+102) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + ((math.exp(l) - math.exp(-l)) * J)
	t_1 = math.cos((K / 2.0))
	t_2 = U + (t_1 * (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0))))
	tmp = 0
	if l <= -5.2e+111:
		tmp = t_2
	elif l <= -130.0:
		tmp = t_0
	elif l <= 0.0145:
		tmp = U + (t_1 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * math.pow(l, 3.0)))))
	elif l <= 5.2e+102:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J))
	t_1 = cos(Float64(K / 2.0))
	t_2 = Float64(U + Float64(t_1 * Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0)))))
	tmp = 0.0
	if (l <= -5.2e+111)
		tmp = t_2;
	elseif (l <= -130.0)
		tmp = t_0;
	elseif (l <= 0.0145)
		tmp = Float64(U + Float64(t_1 * Float64(Float64(2.0 * Float64(l * J)) + Float64(0.3333333333333333 * Float64(J * (l ^ 3.0))))));
	elseif (l <= 5.2e+102)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + ((exp(l) - exp(-l)) * J);
	t_1 = cos((K / 2.0));
	t_2 = U + (t_1 * (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0))));
	tmp = 0.0;
	if (l <= -5.2e+111)
		tmp = t_2;
	elseif (l <= -130.0)
		tmp = t_0;
	elseif (l <= 0.0145)
		tmp = U + (t_1 * ((2.0 * (l * J)) + (0.3333333333333333 * (J * (l ^ 3.0)))));
	elseif (l <= 5.2e+102)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(U + N[(t$95$1 * N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -5.2e+111], t$95$2, If[LessEqual[l, -130.0], t$95$0, If[LessEqual[l, 0.0145], N[(U + N[(t$95$1 * N[(N[(2.0 * N[(l * J), $MachinePrecision]), $MachinePrecision] + N[(0.3333333333333333 * N[(J * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 5.2e+102], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -5.1999999999999997e111 or 5.20000000000000013e102 < 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 0 100.0%

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

   if -5.1999999999999997e111 < l < -130 or 0.0145000000000000007 < l < 5.20000000000000013e102

   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 73.3%

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

   if -130 < l < 0.0145000000000000007

   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 99.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq -130:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{elif}\;\ell \leq 0.0145:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(\ell \cdot J\right) + 0.3333333333333333 \cdot \left(J \cdot {\ell}^{3}\right)\right)\\ \mathbf{elif}\;\ell \leq 5.2 \cdot 10^{+102}:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\right)\\ \end{array} \]

Alternative 5: 78.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \mathbf{if}\;t_0 \leq 0.5989:\\ \;\;\;\;U + t_0 \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))))
   (if (<= t_0 0.5989)
     (+ U (* t_0 (* l (* J 2.0))))
     (+ U (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* l 2.0)))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double tmp;
	if (t_0 <= 0.5989) {
		tmp = U + (t_0 * (l * (J * 2.0)));
	} else {
		tmp = U + (J * ((0.3333333333333333 * pow(l, 3.0)) + (l * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos((k / 2.0d0))
    if (t_0 <= 0.5989d0) then
        tmp = u + (t_0 * (l * (j * 2.0d0)))
    else
        tmp = u + (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (l * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double tmp;
	if (t_0 <= 0.5989) {
		tmp = U + (t_0 * (l * (J * 2.0)));
	} else {
		tmp = U + (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (l * 2.0)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	tmp = 0
	if t_0 <= 0.5989:
		tmp = U + (t_0 * (l * (J * 2.0)))
	else:
		tmp = U + (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (l * 2.0)))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	tmp = 0.0
	if (t_0 <= 0.5989)
		tmp = Float64(U + Float64(t_0 * Float64(l * Float64(J * 2.0))));
	else
		tmp = Float64(U + Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(l * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	tmp = 0.0;
	if (t_0 <= 0.5989)
		tmp = U + (t_0 * (l * (J * 2.0)));
	else
		tmp = U + (J * ((0.3333333333333333 * (l ^ 3.0)) + (l * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, 0.5989], N[(U + N[(t$95$0 * N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(l * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < 0.59889999999999999

   1. Initial program 85.4%

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

   2. Taylor expanded in l around 0 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*l* 66.2%

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

   4. Simplified 66.2%

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

   if 0.59889999999999999 < (cos.f64 (/.f64 K 2))

   1. Initial program 88.1%

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

   2. Taylor expanded in l around 0 87.3%

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

   3. Taylor expanded in K around 0 84.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq 0.5989:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + \ell \cdot 2\right)\\ \end{array} \]

Alternative 6: 86.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{if}\;\ell \leq -130:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 0.0038:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 3.5 \cdot 10^{+255}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (+ U (* (- (exp l) (exp (- l))) J))))
   (if (<= l -130.0)
     t_0
     (if (<= l 0.0038)
       (+ U (* (cos (/ K 2.0)) (* l (* J 2.0))))
       (if (<= l 3.5e+255) t_0 (+ U (* 2.0 (* l (* J (cos (* K 0.5)))))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = U + ((exp(l) - exp(-l)) * J);
	double tmp;
	if (l <= -130.0) {
		tmp = t_0;
	} else if (l <= 0.0038) {
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	} else if (l <= 3.5e+255) {
		tmp = t_0;
	} else {
		tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    real(8) :: tmp
    t_0 = u + ((exp(l) - exp(-l)) * j)
    if (l <= (-130.0d0)) then
        tmp = t_0
    else if (l <= 0.0038d0) then
        tmp = u + (cos((k / 2.0d0)) * (l * (j * 2.0d0)))
    else if (l <= 3.5d+255) then
        tmp = t_0
    else
        tmp = u + (2.0d0 * (l * (j * cos((k * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = U + ((Math.exp(l) - Math.exp(-l)) * J);
	double tmp;
	if (l <= -130.0) {
		tmp = t_0;
	} else if (l <= 0.0038) {
		tmp = U + (Math.cos((K / 2.0)) * (l * (J * 2.0)));
	} else if (l <= 3.5e+255) {
		tmp = t_0;
	} else {
		tmp = U + (2.0 * (l * (J * Math.cos((K * 0.5)))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = U + ((math.exp(l) - math.exp(-l)) * J)
	tmp = 0
	if l <= -130.0:
		tmp = t_0
	elif l <= 0.0038:
		tmp = U + (math.cos((K / 2.0)) * (l * (J * 2.0)))
	elif l <= 3.5e+255:
		tmp = t_0
	else:
		tmp = U + (2.0 * (l * (J * math.cos((K * 0.5)))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(U + Float64(Float64(exp(l) - exp(Float64(-l))) * J))
	tmp = 0.0
	if (l <= -130.0)
		tmp = t_0;
	elseif (l <= 0.0038)
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(l * Float64(J * 2.0))));
	elseif (l <= 3.5e+255)
		tmp = t_0;
	else
		tmp = Float64(U + Float64(2.0 * Float64(l * Float64(J * cos(Float64(K * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = U + ((exp(l) - exp(-l)) * J);
	tmp = 0.0;
	if (l <= -130.0)
		tmp = t_0;
	elseif (l <= 0.0038)
		tmp = U + (cos((K / 2.0)) * (l * (J * 2.0)));
	elseif (l <= 3.5e+255)
		tmp = t_0;
	else
		tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(U + N[(N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision] * J), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -130.0], t$95$0, If[LessEqual[l, 0.0038], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 3.5e+255], t$95$0, N[(U + N[(2.0 * N[(l * N[(J * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -130 or 0.00379999999999999999 < l < 3.49999999999999986e255

   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 75.3%

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

   if -130 < l < 0.00379999999999999999

   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 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

   4. Simplified 99.4%

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

   if 3.49999999999999986e255 < 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 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-*l* 84.0%

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

      3. *-commutative 84.0%

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

   4. Simplified 84.0%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -130:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{elif}\;\ell \leq 0.0038:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\ell \cdot \left(J \cdot 2\right)\right)\\ \mathbf{elif}\;\ell \leq 3.5 \cdot 10^{+255}:\\ \;\;\;\;U + \left(e^{\ell} - e^{-\ell}\right) \cdot J\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \end{array} \]

Alternative 7: 56.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.56:\\ \;\;\;\;U + \left(\ell \cdot J\right) \cdot \left(2 + \left(K \cdot K\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot J\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.56)
   (+ U (* (* l J) (+ 2.0 (* (* K K) -0.25))))
   (+ U (* 2.0 (* l J)))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.56) {
		tmp = U + ((l * J) * (2.0 + ((K * K) * -0.25)));
	} else {
		tmp = U + (2.0 * (l * J));
	}
	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)) <= (-0.56d0)) then
        tmp = u + ((l * j) * (2.0d0 + ((k * k) * (-0.25d0))))
    else
        tmp = u + (2.0d0 * (l * j))
    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)) <= -0.56) {
		tmp = U + ((l * J) * (2.0 + ((K * K) * -0.25)));
	} else {
		tmp = U + (2.0 * (l * J));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.56:
		tmp = U + ((l * J) * (2.0 + ((K * K) * -0.25)))
	else:
		tmp = U + (2.0 * (l * J))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.56)
		tmp = Float64(U + Float64(Float64(l * J) * Float64(2.0 + Float64(Float64(K * K) * -0.25))));
	else
		tmp = Float64(U + Float64(2.0 * Float64(l * J)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.56)
		tmp = U + ((l * J) * (2.0 + ((K * K) * -0.25)));
	else
		tmp = U + (2.0 * (l * J));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.56], N[(U + N[(N[(l * J), $MachinePrecision] * N[(2.0 + N[(N[(K * K), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(2.0 * N[(l * J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.56000000000000005

   1. Initial program 82.7%

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

   2. Taylor expanded in l around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*l* 58.5%

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

      3. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in K around 0 39.6%

      \[\leadsto \color{blue}{2 \cdot \left(\ell \cdot J\right) + \left(-0.25 \cdot \left({K}^{2} \cdot \left(\ell \cdot J\right)\right) + U\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 39.6%

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

      2. +-commutative 39.6%

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

      3. associate-*r* 39.6%

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

      4. distribute-rgt-out 50.7%

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

      5. *-commutative 50.7%

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

      6. unpow2 50.7%

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

   7. Simplified 50.7%

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

   if -0.56000000000000005 < (cos.f64 (/.f64 K 2))

   1. Initial program 88.0%

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

   2. Taylor expanded in l around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*l* 65.4%

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

      3. *-commutative 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in K around 0 58.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.56:\\ \;\;\;\;U + \left(\ell \cdot J\right) \cdot \left(2 + \left(K \cdot K\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot J\right)\\ \end{array} \]

Alternative 8: 64.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right) \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+ U (* 2.0 (* l (* J (cos (* K 0.5)))))))

C

double code(double J, double l, double K, double U) {
	return U + (2.0 * (l * (J * cos((K * 0.5)))));
}

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 + (2.0d0 * (l * (j * cos((k * 0.5d0)))))
end function

Java

public static double code(double J, double l, double K, double U) {
	return U + (2.0 * (l * (J * Math.cos((K * 0.5)))));
}

Python

def code(J, l, K, U):
	return U + (2.0 * (l * (J * math.cos((K * 0.5)))))

Julia

function code(J, l, K, U)
	return Float64(U + Float64(2.0 * Float64(l * Float64(J * cos(Float64(K * 0.5))))))
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
end

Wolfram

code[J_, l_, K_, U_] := N[(U + N[(2.0 * N[(l * N[(J * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.1%

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

2. Taylor expanded in l around 0 64.2%

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

   1. *-commutative 64.2%

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

   2. associate-*l* 64.2%

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

   3. *-commutative 64.2%

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

4. Simplified 64.2%

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

5. Final simplification 64.2%

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

Alternative 9: 64.8% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

2. Taylor expanded in l around 0 64.2%

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

   1. *-commutative 64.2%

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

   2. associate-*l* 64.2%

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

4. Simplified 64.2%

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

5. Final simplification 64.2%

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

Alternative 10: 42.3% accurate, 43.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;U \cdot U\\ \mathbf{elif}\;\ell \leq 1200:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U \cdot U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -1.1e+25) (* U U) (if (<= l 1200.0) U (* U U))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -1.1e+25) {
		tmp = U * U;
	} else if (l <= 1200.0) {
		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 <= (-1.1d+25)) then
        tmp = u * u
    else if (l <= 1200.0d0) 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 <= -1.1e+25) {
		tmp = U * U;
	} else if (l <= 1200.0) {
		tmp = U;
	} else {
		tmp = U * U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -1.1e+25:
		tmp = U * U
	elif l <= 1200.0:
		tmp = U
	else:
		tmp = U * U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -1.1e+25)
		tmp = Float64(U * U);
	elseif (l <= 1200.0)
		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 <= -1.1e+25)
		tmp = U * U;
	elseif (l <= 1200.0)
		tmp = U;
	else
		tmp = U * U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -1.1e+25], N[(U * U), $MachinePrecision], If[LessEqual[l, 1200.0], U, N[(U * U), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if l < -1.1e25 or 1200 < 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. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Applied egg-rr 13.7%

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

   if -1.1e25 < l < 1200

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l* 75.3%

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

      3. fma-def 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in l around 0 70.7%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;U \cdot U\\ \mathbf{elif}\;\ell \leq 1200:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U \cdot U\\ \end{array} \]

Alternative 11: 54.8% accurate, 44.6× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

2. Taylor expanded in l around 0 64.2%

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

   1. *-commutative 64.2%

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

   2. associate-*l* 64.2%

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

   3. *-commutative 64.2%

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

4. Simplified 64.2%

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

5. Taylor expanded in K around 0 53.3%

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

6. Final simplification 53.3%

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

Alternative 12: 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 87.1%

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

   1. *-commutative 87.1%

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

   2. associate-*l* 87.1%

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

   3. fma-def 87.1%

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

3. Simplified 87.1%

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

4. Taylor expanded in l around 0 38.0%

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

5. Final simplification 38.0%

   \[\leadsto U \]

Reproduce

herbie shell --seed 2023240 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))