Maksimov and Kolovsky, Equation (32)

Percentage Accurate: 75.7% → 95.7%

Time: 24.4s

Alternatives: 11

Speedup: 1.9×

Specification

Math

\[\begin{array}{l} \\ \cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (*
  (cos (- (/ (* K (+ m n)) 2.0) M))
  (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))

C

double code(double K, double m, double n, double M, double l) {
	return cos((((K * (m + n)) / 2.0) - M)) * exp((-pow((((m + n) / 2.0) - M), 2.0) - (l - fabs((m - n)))));
}

Fortran

real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    code = cos((((k * (m + n)) / 2.0d0) - m_1)) * exp((-((((m + n) / 2.0d0) - m_1) ** 2.0d0) - (l - abs((m - n)))))
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	return Math.cos((((K * (m + n)) / 2.0) - M)) * Math.exp((-Math.pow((((m + n) / 2.0) - M), 2.0) - (l - Math.abs((m - n)))));
}

Python

def code(K, m, n, M, l):
	return math.cos((((K * (m + n)) / 2.0) - M)) * math.exp((-math.pow((((m + n) / 2.0) - M), 2.0) - (l - math.fabs((m - n)))))

Julia

function code(K, m, n, M, l)
	return Float64(cos(Float64(Float64(Float64(K * Float64(m + n)) / 2.0) - M)) * exp(Float64(Float64(-(Float64(Float64(Float64(m + n) / 2.0) - M) ^ 2.0)) - Float64(l - abs(Float64(m - n))))))
end

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = cos((((K * (m + n)) / 2.0) - M)) * exp((-((((m + n) / 2.0) - M) ^ 2.0) - (l - abs((m - n)))));
end

Wolfram

code[K_, m_, n_, M_, l_] := N[(N[Cos[N[(N[(N[(K * N[(m + n), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision] * N[Exp[N[((-N[Power[N[(N[(N[(m + n), $MachinePrecision] / 2.0), $MachinePrecision] - M), $MachinePrecision], 2.0], $MachinePrecision]) - N[(l - N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (*
  (cos (- (/ (* K (+ m n)) 2.0) M))
  (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))

C

double code(double K, double m, double n, double M, double l) {
	return cos((((K * (m + n)) / 2.0) - M)) * exp((-pow((((m + n) / 2.0) - M), 2.0) - (l - fabs((m - n)))));
}

Fortran

real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    code = cos((((k * (m + n)) / 2.0d0) - m_1)) * exp((-((((m + n) / 2.0d0) - m_1) ** 2.0d0) - (l - abs((m - n)))))
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	return Math.cos((((K * (m + n)) / 2.0) - M)) * Math.exp((-Math.pow((((m + n) / 2.0) - M), 2.0) - (l - Math.abs((m - n)))));
}

Python

def code(K, m, n, M, l):
	return math.cos((((K * (m + n)) / 2.0) - M)) * math.exp((-math.pow((((m + n) / 2.0) - M), 2.0) - (l - math.fabs((m - n)))))

Julia

function code(K, m, n, M, l)
	return Float64(cos(Float64(Float64(Float64(K * Float64(m + n)) / 2.0) - M)) * exp(Float64(Float64(-(Float64(Float64(Float64(m + n) / 2.0) - M) ^ 2.0)) - Float64(l - abs(Float64(m - n))))))
end

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = cos((((K * (m + n)) / 2.0) - M)) * exp((-((((m + n) / 2.0) - M) ^ 2.0) - (l - abs((m - n)))));
end

Wolfram

code[K_, m_, n_, M_, l_] := N[(N[Cos[N[(N[(N[(K * N[(m + n), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision] * N[Exp[N[((-N[Power[N[(N[(N[(m + n), $MachinePrecision] / 2.0), $MachinePrecision] - M), $MachinePrecision], 2.0], $MachinePrecision]) - N[(l - N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} \mathbf{if}\;m \leq -1200000000000:\\ \;\;\;\;\cos M \cdot e^{-0.25 \cdot {m}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{\left(n \cdot 0.5 - M\right) \cdot \left(\left(M - n \cdot 0.5\right) - m\right) + \left(\left|n - m\right| - \ell\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (if (<= m -1200000000000.0)
   (* (cos M) (exp (* -0.25 (pow m 2.0))))
   (*
    (cos M)
    (exp (+ (* (- (* n 0.5) M) (- (- M (* n 0.5)) m)) (- (fabs (- n m)) l))))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -1200000000000.0) {
		tmp = cos(M) * exp((-0.25 * pow(m, 2.0)));
	} else {
		tmp = cos(M) * exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (fabs((n - m)) - l)));
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: tmp
    if (m <= (-1200000000000.0d0)) then
        tmp = cos(m_1) * exp(((-0.25d0) * (m ** 2.0d0)))
    else
        tmp = cos(m_1) * exp(((((n * 0.5d0) - m_1) * ((m_1 - (n * 0.5d0)) - m)) + (abs((n - m)) - l)))
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -1200000000000.0) {
		tmp = Math.cos(M) * Math.exp((-0.25 * Math.pow(m, 2.0)));
	} else {
		tmp = Math.cos(M) * Math.exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (Math.abs((n - m)) - l)));
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	tmp = 0
	if m <= -1200000000000.0:
		tmp = math.cos(M) * math.exp((-0.25 * math.pow(m, 2.0)))
	else:
		tmp = math.cos(M) * math.exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (math.fabs((n - m)) - l)))
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	tmp = 0.0
	if (m <= -1200000000000.0)
		tmp = Float64(cos(M) * exp(Float64(-0.25 * (m ^ 2.0))));
	else
		tmp = Float64(cos(M) * exp(Float64(Float64(Float64(Float64(n * 0.5) - M) * Float64(Float64(M - Float64(n * 0.5)) - m)) + Float64(abs(Float64(n - m)) - l))));
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (m <= -1200000000000.0)
		tmp = cos(M) * exp((-0.25 * (m ^ 2.0)));
	else
		tmp = cos(M) * exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (abs((n - m)) - l)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := If[LessEqual[m, -1200000000000.0], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[m, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(N[(N[(n * 0.5), $MachinePrecision] - M), $MachinePrecision] * N[(N[(M - N[(n * 0.5), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision]), $MachinePrecision] + N[(N[Abs[N[(n - m), $MachinePrecision]], $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \cos M \cdot e^{\left(\left|n - m\right| - \ell\right) - {\left(\left(n + m\right) \cdot 0.5 - M\right)}^{2}} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (* (cos M) (exp (- (- (fabs (- n m)) l) (pow (- (* (+ n m) 0.5) M) 2.0)))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	return cos(M) * exp(((fabs((n - m)) - l) - pow((((n + m) * 0.5) - M), 2.0)));
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    code = cos(m_1) * exp(((abs((n - m)) - l) - ((((n + m) * 0.5d0) - m_1) ** 2.0d0)))
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	return Math.cos(M) * Math.exp(((Math.abs((n - m)) - l) - Math.pow((((n + m) * 0.5) - M), 2.0)));
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	return math.cos(M) * math.exp(((math.fabs((n - m)) - l) - math.pow((((n + m) * 0.5) - M), 2.0)))

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	return Float64(cos(M) * exp(Float64(Float64(abs(Float64(n - m)) - l) - (Float64(Float64(Float64(n + m) * 0.5) - M) ^ 2.0))))
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp = code(K, m, n, M, l)
	tmp = cos(M) * exp(((abs((n - m)) - l) - ((((n + m) * 0.5) - M) ^ 2.0)));
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(N[Abs[N[(n - m), $MachinePrecision]], $MachinePrecision] - l), $MachinePrecision] - N[Power[N[(N[(N[(n + m), $MachinePrecision] * 0.5), $MachinePrecision] - M), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 82.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} \mathbf{if}\;m \leq -0.0116:\\ \;\;\;\;\cos M \cdot e^{-0.25 \cdot {m}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{\left(n - m\right) + \left(\left(m \cdot 0.5 - M\right) \cdot \left(\left(M - n\right) - m \cdot 0.5\right) - \ell\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (if (<= m -0.0116)
   (* (cos M) (exp (* -0.25 (pow m 2.0))))
   (*
    (cos M)
    (exp (+ (- n m) (- (* (- (* m 0.5) M) (- (- M n) (* m 0.5))) l))))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.0116) {
		tmp = cos(M) * exp((-0.25 * pow(m, 2.0)));
	} else {
		tmp = cos(M) * exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: tmp
    if (m <= (-0.0116d0)) then
        tmp = cos(m_1) * exp(((-0.25d0) * (m ** 2.0d0)))
    else
        tmp = cos(m_1) * exp(((n - m) + ((((m * 0.5d0) - m_1) * ((m_1 - n) - (m * 0.5d0))) - l)))
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.0116) {
		tmp = Math.cos(M) * Math.exp((-0.25 * Math.pow(m, 2.0)));
	} else {
		tmp = Math.cos(M) * Math.exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	tmp = 0
	if m <= -0.0116:
		tmp = math.cos(M) * math.exp((-0.25 * math.pow(m, 2.0)))
	else:
		tmp = math.cos(M) * math.exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)))
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	tmp = 0.0
	if (m <= -0.0116)
		tmp = Float64(cos(M) * exp(Float64(-0.25 * (m ^ 2.0))));
	else
		tmp = Float64(cos(M) * exp(Float64(Float64(n - m) + Float64(Float64(Float64(Float64(m * 0.5) - M) * Float64(Float64(M - n) - Float64(m * 0.5))) - l))));
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (m <= -0.0116)
		tmp = cos(M) * exp((-0.25 * (m ^ 2.0)));
	else
		tmp = cos(M) * exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := If[LessEqual[m, -0.0116], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[m, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(n - m), $MachinePrecision] + N[(N[(N[(N[(m * 0.5), $MachinePrecision] - M), $MachinePrecision] * N[(N[(M - n), $MachinePrecision] - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 82.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} \mathbf{if}\;M \leq 0.057:\\ \;\;\;\;\cos M \cdot e^{\left(n - m\right) + \left(\left(m \cdot 0.5 - M\right) \cdot \left(\left(M - n\right) - m \cdot 0.5\right) - \ell\right)}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (if (<= M 0.057)
   (*
    (cos M)
    (exp (+ (- n m) (- (* (- (* m 0.5) M) (- (- M n) (* m 0.5))) l))))
   (* (cos M) (exp (- (pow M 2.0))))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (M <= 0.057) {
		tmp = cos(M) * exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
	} else {
		tmp = cos(M) * exp(-pow(M, 2.0));
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: tmp
    if (m_1 <= 0.057d0) then
        tmp = cos(m_1) * exp(((n - m) + ((((m * 0.5d0) - m_1) * ((m_1 - n) - (m * 0.5d0))) - l)))
    else
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (M <= 0.057) {
		tmp = Math.cos(M) * Math.exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
	} else {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	tmp = 0
	if M <= 0.057:
		tmp = math.cos(M) * math.exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)))
	else:
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	tmp = 0.0
	if (M <= 0.057)
		tmp = Float64(cos(M) * exp(Float64(Float64(n - m) + Float64(Float64(Float64(Float64(m * 0.5) - M) * Float64(Float64(M - n) - Float64(m * 0.5))) - l))));
	else
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (M <= 0.057)
		tmp = cos(M) * exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
	else
		tmp = cos(M) * exp(-(M ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := If[LessEqual[M, 0.057], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(n - m), $MachinePrecision] + N[(N[(N[(N[(m * 0.5), $MachinePrecision] - M), $MachinePrecision] * N[(N[(M - n), $MachinePrecision] - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 58.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} t_0 := \cos M \cdot e^{n \cdot \left(M - m \cdot 0.5\right)}\\ t_1 := \cos M \cdot e^{\left(n - m\right) + \left(n \cdot \left(m \cdot 0.5 - M\right) - \ell\right)}\\ \mathbf{if}\;\ell \leq -4.9 \cdot 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;\cos \left(\left(n + m\right) \cdot \frac{K}{2} - M\right) \cdot e^{\ell}\\ \mathbf{elif}\;\ell \leq 2.8 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 1.18 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (* (cos M) (exp (* n (- M (* m 0.5))))))
        (t_1 (* (cos M) (exp (+ (- n m) (- (* n (- (* m 0.5) M)) l))))))
   (if (<= l -4.9e+250)
     t_1
     (if (<= l -1.2e+17)
       (* (cos (- (* (+ n m) (/ K 2.0)) M)) (exp l))
       (if (<= l 2.8e-282)
         t_0
         (if (<= l 5.8e-229)
           t_1
           (if (<= l 1.18e-30) t_0 (* (cos M) (exp (- l))))))))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double t_0 = cos(M) * exp((n * (M - (m * 0.5))));
	double t_1 = cos(M) * exp(((n - m) + ((n * ((m * 0.5) - M)) - l)));
	double tmp;
	if (l <= -4.9e+250) {
		tmp = t_1;
	} else if (l <= -1.2e+17) {
		tmp = cos((((n + m) * (K / 2.0)) - M)) * exp(l);
	} else if (l <= 2.8e-282) {
		tmp = t_0;
	} else if (l <= 5.8e-229) {
		tmp = t_1;
	} else if (l <= 1.18e-30) {
		tmp = t_0;
	} else {
		tmp = cos(M) * exp(-l);
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos(m_1) * exp((n * (m_1 - (m * 0.5d0))))
    t_1 = cos(m_1) * exp(((n - m) + ((n * ((m * 0.5d0) - m_1)) - l)))
    if (l <= (-4.9d+250)) then
        tmp = t_1
    else if (l <= (-1.2d+17)) then
        tmp = cos((((n + m) * (k / 2.0d0)) - m_1)) * exp(l)
    else if (l <= 2.8d-282) then
        tmp = t_0
    else if (l <= 5.8d-229) then
        tmp = t_1
    else if (l <= 1.18d-30) then
        tmp = t_0
    else
        tmp = cos(m_1) * exp(-l)
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double t_0 = Math.cos(M) * Math.exp((n * (M - (m * 0.5))));
	double t_1 = Math.cos(M) * Math.exp(((n - m) + ((n * ((m * 0.5) - M)) - l)));
	double tmp;
	if (l <= -4.9e+250) {
		tmp = t_1;
	} else if (l <= -1.2e+17) {
		tmp = Math.cos((((n + m) * (K / 2.0)) - M)) * Math.exp(l);
	} else if (l <= 2.8e-282) {
		tmp = t_0;
	} else if (l <= 5.8e-229) {
		tmp = t_1;
	} else if (l <= 1.18e-30) {
		tmp = t_0;
	} else {
		tmp = Math.cos(M) * Math.exp(-l);
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	t_0 = math.cos(M) * math.exp((n * (M - (m * 0.5))))
	t_1 = math.cos(M) * math.exp(((n - m) + ((n * ((m * 0.5) - M)) - l)))
	tmp = 0
	if l <= -4.9e+250:
		tmp = t_1
	elif l <= -1.2e+17:
		tmp = math.cos((((n + m) * (K / 2.0)) - M)) * math.exp(l)
	elif l <= 2.8e-282:
		tmp = t_0
	elif l <= 5.8e-229:
		tmp = t_1
	elif l <= 1.18e-30:
		tmp = t_0
	else:
		tmp = math.cos(M) * math.exp(-l)
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	t_0 = Float64(cos(M) * exp(Float64(n * Float64(M - Float64(m * 0.5)))))
	t_1 = Float64(cos(M) * exp(Float64(Float64(n - m) + Float64(Float64(n * Float64(Float64(m * 0.5) - M)) - l))))
	tmp = 0.0
	if (l <= -4.9e+250)
		tmp = t_1;
	elseif (l <= -1.2e+17)
		tmp = Float64(cos(Float64(Float64(Float64(n + m) * Float64(K / 2.0)) - M)) * exp(l));
	elseif (l <= 2.8e-282)
		tmp = t_0;
	elseif (l <= 5.8e-229)
		tmp = t_1;
	elseif (l <= 1.18e-30)
		tmp = t_0;
	else
		tmp = Float64(cos(M) * exp(Float64(-l)));
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	t_0 = cos(M) * exp((n * (M - (m * 0.5))));
	t_1 = cos(M) * exp(((n - m) + ((n * ((m * 0.5) - M)) - l)));
	tmp = 0.0;
	if (l <= -4.9e+250)
		tmp = t_1;
	elseif (l <= -1.2e+17)
		tmp = cos((((n + m) * (K / 2.0)) - M)) * exp(l);
	elseif (l <= 2.8e-282)
		tmp = t_0;
	elseif (l <= 5.8e-229)
		tmp = t_1;
	elseif (l <= 1.18e-30)
		tmp = t_0;
	else
		tmp = cos(M) * exp(-l);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(n * N[(M - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(n - m), $MachinePrecision] + N[(N[(n * N[(N[(m * 0.5), $MachinePrecision] - M), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -4.9e+250], t$95$1, If[LessEqual[l, -1.2e+17], N[(N[Cos[N[(N[(N[(n + m), $MachinePrecision] * N[(K / 2.0), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision] * N[Exp[l], $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.8e-282], t$95$0, If[LessEqual[l, 5.8e-229], t$95$1, If[LessEqual[l, 1.18e-30], t$95$0, N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 6: 78.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \cos M \cdot e^{\left(n - m\right) + \left(\left(m \cdot 0.5 - M\right) \cdot \left(\left(M - n\right) - m \cdot 0.5\right) - \ell\right)} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (* (cos M) (exp (+ (- n m) (- (* (- (* m 0.5) M) (- (- M n) (* m 0.5))) l)))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	return cos(M) * exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    code = cos(m_1) * exp(((n - m) + ((((m * 0.5d0) - m_1) * ((m_1 - n) - (m * 0.5d0))) - l)))
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	return Math.cos(M) * Math.exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	return math.cos(M) * math.exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)))

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	return Float64(cos(M) * exp(Float64(Float64(n - m) + Float64(Float64(Float64(Float64(m * 0.5) - M) * Float64(Float64(M - n) - Float64(m * 0.5))) - l))))
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp = code(K, m, n, M, l)
	tmp = cos(M) * exp(((n - m) + ((((m * 0.5) - M) * ((M - n) - (m * 0.5))) - l)));
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(n - m), $MachinePrecision] + N[(N[(N[(N[(m * 0.5), $MachinePrecision] - M), $MachinePrecision] * N[(N[(M - n), $MachinePrecision] - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 7: 53.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.4 \cdot 10^{+251} \lor \neg \left(\ell \leq 1.18 \cdot 10^{-30}\right):\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{n \cdot \left(M - m \cdot 0.5\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (if (or (<= l -2.4e+251) (not (<= l 1.18e-30)))
   (* (cos M) (exp (- l)))
   (* (cos M) (exp (* n (- M (* m 0.5)))))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((l <= -2.4e+251) || !(l <= 1.18e-30)) {
		tmp = cos(M) * exp(-l);
	} else {
		tmp = cos(M) * exp((n * (M - (m * 0.5))));
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: tmp
    if ((l <= (-2.4d+251)) .or. (.not. (l <= 1.18d-30))) then
        tmp = cos(m_1) * exp(-l)
    else
        tmp = cos(m_1) * exp((n * (m_1 - (m * 0.5d0))))
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((l <= -2.4e+251) || !(l <= 1.18e-30)) {
		tmp = Math.cos(M) * Math.exp(-l);
	} else {
		tmp = Math.cos(M) * Math.exp((n * (M - (m * 0.5))));
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	tmp = 0
	if (l <= -2.4e+251) or not (l <= 1.18e-30):
		tmp = math.cos(M) * math.exp(-l)
	else:
		tmp = math.cos(M) * math.exp((n * (M - (m * 0.5))))
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	tmp = 0.0
	if ((l <= -2.4e+251) || !(l <= 1.18e-30))
		tmp = Float64(cos(M) * exp(Float64(-l)));
	else
		tmp = Float64(cos(M) * exp(Float64(n * Float64(M - Float64(m * 0.5)))));
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if ((l <= -2.4e+251) || ~((l <= 1.18e-30)))
		tmp = cos(M) * exp(-l);
	else
		tmp = cos(M) * exp((n * (M - (m * 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := If[Or[LessEqual[l, -2.4e+251], N[Not[LessEqual[l, 1.18e-30]], $MachinePrecision]], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(n * N[(M - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 53.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} t_0 := e^{-\ell}\\ \mathbf{if}\;\ell \leq -1.12 \cdot 10^{+252}:\\ \;\;\;\;t_0 \cdot \cos \left(\frac{K}{\frac{2}{n}} - M\right)\\ \mathbf{elif}\;\ell \leq 1.18 \cdot 10^{-30}:\\ \;\;\;\;\cos M \cdot e^{n \cdot \left(M - m \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot t_0\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (exp (- l))))
   (if (<= l -1.12e+252)
     (* t_0 (cos (- (/ K (/ 2.0 n)) M)))
     (if (<= l 1.18e-30)
       (* (cos M) (exp (* n (- M (* m 0.5)))))
       (* (cos M) t_0)))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double t_0 = exp(-l);
	double tmp;
	if (l <= -1.12e+252) {
		tmp = t_0 * cos(((K / (2.0 / n)) - M));
	} else if (l <= 1.18e-30) {
		tmp = cos(M) * exp((n * (M - (m * 0.5))));
	} else {
		tmp = cos(M) * t_0;
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(-l)
    if (l <= (-1.12d+252)) then
        tmp = t_0 * cos(((k / (2.0d0 / n)) - m_1))
    else if (l <= 1.18d-30) then
        tmp = cos(m_1) * exp((n * (m_1 - (m * 0.5d0))))
    else
        tmp = cos(m_1) * t_0
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double t_0 = Math.exp(-l);
	double tmp;
	if (l <= -1.12e+252) {
		tmp = t_0 * Math.cos(((K / (2.0 / n)) - M));
	} else if (l <= 1.18e-30) {
		tmp = Math.cos(M) * Math.exp((n * (M - (m * 0.5))));
	} else {
		tmp = Math.cos(M) * t_0;
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	t_0 = math.exp(-l)
	tmp = 0
	if l <= -1.12e+252:
		tmp = t_0 * math.cos(((K / (2.0 / n)) - M))
	elif l <= 1.18e-30:
		tmp = math.cos(M) * math.exp((n * (M - (m * 0.5))))
	else:
		tmp = math.cos(M) * t_0
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	t_0 = exp(Float64(-l))
	tmp = 0.0
	if (l <= -1.12e+252)
		tmp = Float64(t_0 * cos(Float64(Float64(K / Float64(2.0 / n)) - M)));
	elseif (l <= 1.18e-30)
		tmp = Float64(cos(M) * exp(Float64(n * Float64(M - Float64(m * 0.5)))));
	else
		tmp = Float64(cos(M) * t_0);
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	t_0 = exp(-l);
	tmp = 0.0;
	if (l <= -1.12e+252)
		tmp = t_0 * cos(((K / (2.0 / n)) - M));
	elseif (l <= 1.18e-30)
		tmp = cos(M) * exp((n * (M - (m * 0.5))));
	else
		tmp = cos(M) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[Exp[(-l)], $MachinePrecision]}, If[LessEqual[l, -1.12e+252], N[(t$95$0 * N[Cos[N[(N[(K / N[(2.0 / n), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 1.18e-30], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(n * N[(M - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

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

Alternative 9: 58.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;\cos \left(\left(n + m\right) \cdot \frac{K}{2} - M\right) \cdot e^{\ell}\\ \mathbf{elif}\;\ell \leq 1.18 \cdot 10^{-30}:\\ \;\;\;\;\cos M \cdot e^{n \cdot \left(M - m \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \end{array} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l)
 :precision binary64
 (if (<= l -2.5e+16)
   (* (cos (- (* (+ n m) (/ K 2.0)) M)) (exp l))
   (if (<= l 1.18e-30)
     (* (cos M) (exp (* n (- M (* m 0.5)))))
     (* (cos M) (exp (- l))))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (l <= -2.5e+16) {
		tmp = cos((((n + m) * (K / 2.0)) - M)) * exp(l);
	} else if (l <= 1.18e-30) {
		tmp = cos(M) * exp((n * (M - (m * 0.5))));
	} else {
		tmp = cos(M) * exp(-l);
	}
	return tmp;
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    real(8) :: tmp
    if (l <= (-2.5d+16)) then
        tmp = cos((((n + m) * (k / 2.0d0)) - m_1)) * exp(l)
    else if (l <= 1.18d-30) then
        tmp = cos(m_1) * exp((n * (m_1 - (m * 0.5d0))))
    else
        tmp = cos(m_1) * exp(-l)
    end if
    code = tmp
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (l <= -2.5e+16) {
		tmp = Math.cos((((n + m) * (K / 2.0)) - M)) * Math.exp(l);
	} else if (l <= 1.18e-30) {
		tmp = Math.cos(M) * Math.exp((n * (M - (m * 0.5))));
	} else {
		tmp = Math.cos(M) * Math.exp(-l);
	}
	return tmp;
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	tmp = 0
	if l <= -2.5e+16:
		tmp = math.cos((((n + m) * (K / 2.0)) - M)) * math.exp(l)
	elif l <= 1.18e-30:
		tmp = math.cos(M) * math.exp((n * (M - (m * 0.5))))
	else:
		tmp = math.cos(M) * math.exp(-l)
	return tmp

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	tmp = 0.0
	if (l <= -2.5e+16)
		tmp = Float64(cos(Float64(Float64(Float64(n + m) * Float64(K / 2.0)) - M)) * exp(l));
	elseif (l <= 1.18e-30)
		tmp = Float64(cos(M) * exp(Float64(n * Float64(M - Float64(m * 0.5)))));
	else
		tmp = Float64(cos(M) * exp(Float64(-l)));
	end
	return tmp
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (l <= -2.5e+16)
		tmp = cos((((n + m) * (K / 2.0)) - M)) * exp(l);
	elseif (l <= 1.18e-30)
		tmp = cos(M) * exp((n * (M - (m * 0.5))));
	else
		tmp = cos(M) * exp(-l);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := If[LessEqual[l, -2.5e+16], N[(N[Cos[N[(N[(N[(n + m), $MachinePrecision] * N[(K / 2.0), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision] * N[Exp[l], $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 1.18e-30], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(n * N[(M - N[(m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 10: 35.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \cos M \cdot e^{-\ell} \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l) :precision binary64 (* (cos M) (exp (- l))))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	return cos(M) * exp(-l);
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    code = cos(m_1) * exp(-l)
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	return Math.cos(M) * Math.exp(-l);
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	return math.cos(M) * math.exp(-l)

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	return Float64(cos(M) * exp(Float64(-l)))
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp = code(K, m, n, M, l)
	tmp = cos(M) * exp(-l);
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 7.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} [K, m, n, M, l] = \mathsf{sort}([K, m, n, M, l])\\ \\ \cos M \end{array} \]

FPCore

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
(FPCore (K m n M l) :precision binary64 (cos M))

C

assert(K < m && m < n && n < M && M < l);
double code(double K, double m, double n, double M, double l) {
	return cos(M);
}

Fortran

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
real(8) function code(k, m, n, m_1, l)
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8), intent (in) :: n
    real(8), intent (in) :: m_1
    real(8), intent (in) :: l
    code = cos(m_1)
end function

Java

assert K < m && m < n && n < M && M < l;
public static double code(double K, double m, double n, double M, double l) {
	return Math.cos(M);
}

Python

[K, m, n, M, l] = sort([K, m, n, M, l])
def code(K, m, n, M, l):
	return math.cos(M)

Julia

K, m, n, M, l = sort([K, m, n, M, l])
function code(K, m, n, M, l)
	return cos(M)
end

MATLAB

K, m, n, M, l = num2cell(sort([K, m, n, M, l])){:}
function tmp = code(K, m, n, M, l)
	tmp = cos(M);
end

Wolfram

NOTE: K, m, n, M, and l should be sorted in increasing order before calling this function.
code[K_, m_, n_, M_, l_] := N[Cos[M], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023340 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))