Maksimov and Kolovsky, Equation (32)

Percentage Accurate: 76.3% → 96.9%

Time: 17.6s

Alternatives: 10

Speedup: 1.4×

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: 76.3% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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(m_1) * exp(((abs((m - n)) - l) - ((((m + n) / 2.0d0) - m_1) ** 2.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 73.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|m - n\right| - \ell\\ t_1 := {m}^{2} \cdot -0.25\\ \mathbf{if}\;m \leq -55:\\ \;\;\;\;\cos M \cdot e^{t_1}\\ \mathbf{elif}\;m \leq -1.28 \cdot 10^{-23}:\\ \;\;\;\;\cos M \cdot e^{-0.25 \cdot {n}^{2}}\\ \mathbf{elif}\;m \leq -1.95 \cdot 10^{-147}:\\ \;\;\;\;\cos M \cdot e^{M \cdot \left(m - M\right) + t_0}\\ \mathbf{elif}\;m \leq -2.2 \cdot 10^{-278} \lor \neg \left(m \leq 1.22 \cdot 10^{-253}\right):\\ \;\;\;\;\cos M \cdot e^{t_0 - \left(n \cdot 0.5\right) \cdot \left(m + n \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \cos \left(0.5 \cdot \left(m \cdot K\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (- (fabs (- m n)) l)) (t_1 (* (pow m 2.0) -0.25)))
   (if (<= m -55.0)
     (* (cos M) (exp t_1))
     (if (<= m -1.28e-23)
       (* (cos M) (exp (* -0.25 (pow n 2.0))))
       (if (<= m -1.95e-147)
         (* (cos M) (exp (+ (* M (- m M)) t_0)))
         (if (or (<= m -2.2e-278) (not (<= m 1.22e-253)))
           (* (cos M) (exp (- t_0 (* (* n 0.5) (+ m (* n 0.5))))))
           (* t_1 (cos (* 0.5 (* m K))))))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = fabs((m - n)) - l;
	double t_1 = pow(m, 2.0) * -0.25;
	double tmp;
	if (m <= -55.0) {
		tmp = cos(M) * exp(t_1);
	} else if (m <= -1.28e-23) {
		tmp = cos(M) * exp((-0.25 * pow(n, 2.0)));
	} else if (m <= -1.95e-147) {
		tmp = cos(M) * exp(((M * (m - M)) + t_0));
	} else if ((m <= -2.2e-278) || !(m <= 1.22e-253)) {
		tmp = cos(M) * exp((t_0 - ((n * 0.5) * (m + (n * 0.5)))));
	} else {
		tmp = t_1 * cos((0.5 * (m * K)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = abs((m - n)) - l
    t_1 = (m ** 2.0d0) * (-0.25d0)
    if (m <= (-55.0d0)) then
        tmp = cos(m_1) * exp(t_1)
    else if (m <= (-1.28d-23)) then
        tmp = cos(m_1) * exp(((-0.25d0) * (n ** 2.0d0)))
    else if (m <= (-1.95d-147)) then
        tmp = cos(m_1) * exp(((m_1 * (m - m_1)) + t_0))
    else if ((m <= (-2.2d-278)) .or. (.not. (m <= 1.22d-253))) then
        tmp = cos(m_1) * exp((t_0 - ((n * 0.5d0) * (m + (n * 0.5d0)))))
    else
        tmp = t_1 * cos((0.5d0 * (m * k)))
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double t_0 = Math.abs((m - n)) - l;
	double t_1 = Math.pow(m, 2.0) * -0.25;
	double tmp;
	if (m <= -55.0) {
		tmp = Math.cos(M) * Math.exp(t_1);
	} else if (m <= -1.28e-23) {
		tmp = Math.cos(M) * Math.exp((-0.25 * Math.pow(n, 2.0)));
	} else if (m <= -1.95e-147) {
		tmp = Math.cos(M) * Math.exp(((M * (m - M)) + t_0));
	} else if ((m <= -2.2e-278) || !(m <= 1.22e-253)) {
		tmp = Math.cos(M) * Math.exp((t_0 - ((n * 0.5) * (m + (n * 0.5)))));
	} else {
		tmp = t_1 * Math.cos((0.5 * (m * K)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.fabs((m - n)) - l
	t_1 = math.pow(m, 2.0) * -0.25
	tmp = 0
	if m <= -55.0:
		tmp = math.cos(M) * math.exp(t_1)
	elif m <= -1.28e-23:
		tmp = math.cos(M) * math.exp((-0.25 * math.pow(n, 2.0)))
	elif m <= -1.95e-147:
		tmp = math.cos(M) * math.exp(((M * (m - M)) + t_0))
	elif (m <= -2.2e-278) or not (m <= 1.22e-253):
		tmp = math.cos(M) * math.exp((t_0 - ((n * 0.5) * (m + (n * 0.5)))))
	else:
		tmp = t_1 * math.cos((0.5 * (m * K)))
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = Float64(abs(Float64(m - n)) - l)
	t_1 = Float64((m ^ 2.0) * -0.25)
	tmp = 0.0
	if (m <= -55.0)
		tmp = Float64(cos(M) * exp(t_1));
	elseif (m <= -1.28e-23)
		tmp = Float64(cos(M) * exp(Float64(-0.25 * (n ^ 2.0))));
	elseif (m <= -1.95e-147)
		tmp = Float64(cos(M) * exp(Float64(Float64(M * Float64(m - M)) + t_0)));
	elseif ((m <= -2.2e-278) || !(m <= 1.22e-253))
		tmp = Float64(cos(M) * exp(Float64(t_0 - Float64(Float64(n * 0.5) * Float64(m + Float64(n * 0.5))))));
	else
		tmp = Float64(t_1 * cos(Float64(0.5 * Float64(m * K))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = abs((m - n)) - l;
	t_1 = (m ^ 2.0) * -0.25;
	tmp = 0.0;
	if (m <= -55.0)
		tmp = cos(M) * exp(t_1);
	elseif (m <= -1.28e-23)
		tmp = cos(M) * exp((-0.25 * (n ^ 2.0)));
	elseif (m <= -1.95e-147)
		tmp = cos(M) * exp(((M * (m - M)) + t_0));
	elseif ((m <= -2.2e-278) || ~((m <= 1.22e-253)))
		tmp = cos(M) * exp((t_0 - ((n * 0.5) * (m + (n * 0.5)))));
	else
		tmp = t_1 * cos((0.5 * (m * K)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[(N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision] - l), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[m, -55.0], N[(N[Cos[M], $MachinePrecision] * N[Exp[t$95$1], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -1.28e-23], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -1.95e-147], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(M * N[(m - M), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[m, -2.2e-278], N[Not[LessEqual[m, 1.22e-253]], $MachinePrecision]], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(t$95$0 - N[(N[(n * 0.5), $MachinePrecision] * N[(m + N[(n * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[Cos[N[(0.5 * N[(m * K), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 3: 71.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos M \cdot e^{-0.25 \cdot {n}^{2}}\\ t_1 := \cos M \cdot e^{M \cdot \left(m - M\right) + \left(\left|m - n\right| - \ell\right)}\\ t_2 := {m}^{2} \cdot -0.25\\ \mathbf{if}\;m \leq -55:\\ \;\;\;\;\cos M \cdot e^{t_2}\\ \mathbf{elif}\;m \leq -2.8 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;m \leq 3.6 \cdot 10^{-260}:\\ \;\;\;\;t_2 \cdot \cos \left(0.5 \cdot \left(m \cdot K\right)\right)\\ \mathbf{elif}\;m \leq 1.05 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (* (cos M) (exp (* -0.25 (pow n 2.0)))))
        (t_1 (* (cos M) (exp (+ (* M (- m M)) (- (fabs (- m n)) l)))))
        (t_2 (* (pow m 2.0) -0.25)))
   (if (<= m -55.0)
     (* (cos M) (exp t_2))
     (if (<= m -2.8e-23)
       t_0
       (if (<= m -3.1e-165)
         t_1
         (if (<= m 3.6e-260)
           (* t_2 (cos (* 0.5 (* m K))))
           (if (<= m 1.05e-150) t_1 t_0)))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = cos(M) * exp((-0.25 * pow(n, 2.0)));
	double t_1 = cos(M) * exp(((M * (m - M)) + (fabs((m - n)) - l)));
	double t_2 = pow(m, 2.0) * -0.25;
	double tmp;
	if (m <= -55.0) {
		tmp = cos(M) * exp(t_2);
	} else if (m <= -2.8e-23) {
		tmp = t_0;
	} else if (m <= -3.1e-165) {
		tmp = t_1;
	} else if (m <= 3.6e-260) {
		tmp = t_2 * cos((0.5 * (m * K)));
	} else if (m <= 1.05e-150) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = cos(m_1) * exp(((-0.25d0) * (n ** 2.0d0)))
    t_1 = cos(m_1) * exp(((m_1 * (m - m_1)) + (abs((m - n)) - l)))
    t_2 = (m ** 2.0d0) * (-0.25d0)
    if (m <= (-55.0d0)) then
        tmp = cos(m_1) * exp(t_2)
    else if (m <= (-2.8d-23)) then
        tmp = t_0
    else if (m <= (-3.1d-165)) then
        tmp = t_1
    else if (m <= 3.6d-260) then
        tmp = t_2 * cos((0.5d0 * (m * k)))
    else if (m <= 1.05d-150) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double t_0 = Math.cos(M) * Math.exp((-0.25 * Math.pow(n, 2.0)));
	double t_1 = Math.cos(M) * Math.exp(((M * (m - M)) + (Math.abs((m - n)) - l)));
	double t_2 = Math.pow(m, 2.0) * -0.25;
	double tmp;
	if (m <= -55.0) {
		tmp = Math.cos(M) * Math.exp(t_2);
	} else if (m <= -2.8e-23) {
		tmp = t_0;
	} else if (m <= -3.1e-165) {
		tmp = t_1;
	} else if (m <= 3.6e-260) {
		tmp = t_2 * Math.cos((0.5 * (m * K)));
	} else if (m <= 1.05e-150) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.cos(M) * math.exp((-0.25 * math.pow(n, 2.0)))
	t_1 = math.cos(M) * math.exp(((M * (m - M)) + (math.fabs((m - n)) - l)))
	t_2 = math.pow(m, 2.0) * -0.25
	tmp = 0
	if m <= -55.0:
		tmp = math.cos(M) * math.exp(t_2)
	elif m <= -2.8e-23:
		tmp = t_0
	elif m <= -3.1e-165:
		tmp = t_1
	elif m <= 3.6e-260:
		tmp = t_2 * math.cos((0.5 * (m * K)))
	elif m <= 1.05e-150:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = Float64(cos(M) * exp(Float64(-0.25 * (n ^ 2.0))))
	t_1 = Float64(cos(M) * exp(Float64(Float64(M * Float64(m - M)) + Float64(abs(Float64(m - n)) - l))))
	t_2 = Float64((m ^ 2.0) * -0.25)
	tmp = 0.0
	if (m <= -55.0)
		tmp = Float64(cos(M) * exp(t_2));
	elseif (m <= -2.8e-23)
		tmp = t_0;
	elseif (m <= -3.1e-165)
		tmp = t_1;
	elseif (m <= 3.6e-260)
		tmp = Float64(t_2 * cos(Float64(0.5 * Float64(m * K))));
	elseif (m <= 1.05e-150)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = cos(M) * exp((-0.25 * (n ^ 2.0)));
	t_1 = cos(M) * exp(((M * (m - M)) + (abs((m - n)) - l)));
	t_2 = (m ^ 2.0) * -0.25;
	tmp = 0.0;
	if (m <= -55.0)
		tmp = cos(M) * exp(t_2);
	elseif (m <= -2.8e-23)
		tmp = t_0;
	elseif (m <= -3.1e-165)
		tmp = t_1;
	elseif (m <= 3.6e-260)
		tmp = t_2 * cos((0.5 * (m * K)));
	elseif (m <= 1.05e-150)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(M * N[(m - M), $MachinePrecision]), $MachinePrecision] + N[(N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[m, -55.0], N[(N[Cos[M], $MachinePrecision] * N[Exp[t$95$2], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -2.8e-23], t$95$0, If[LessEqual[m, -3.1e-165], t$95$1, If[LessEqual[m, 3.6e-260], N[(t$95$2 * N[Cos[N[(0.5 * N[(m * K), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.05e-150], t$95$1, t$95$0]]]]]]]]

Derivation

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

Alternative 4: 87.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -56:\\ \;\;\;\;\cos M \cdot e^{{m}^{2} \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{\left(n \cdot 0.5 - M\right) \cdot \left(\left(M - n \cdot 0.5\right) - m\right) + \left(\left|m - n\right| - \ell\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -56.0)
   (* (cos M) (exp (* (pow m 2.0) -0.25)))
   (*
    (cos M)
    (exp (+ (* (- (* n 0.5) M) (- (- M (* n 0.5)) m)) (- (fabs (- m n)) l))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -56.0) {
		tmp = cos(M) * exp((pow(m, 2.0) * -0.25));
	} else {
		tmp = cos(M) * exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (fabs((m - n)) - l)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (m <= (-56.0d0)) then
        tmp = cos(m_1) * exp(((m ** 2.0d0) * (-0.25d0)))
    else
        tmp = cos(m_1) * exp(((((n * 0.5d0) - m_1) * ((m_1 - (n * 0.5d0)) - m)) + (abs((m - n)) - l)))
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -56.0) {
		tmp = Math.cos(M) * Math.exp((Math.pow(m, 2.0) * -0.25));
	} else {
		tmp = Math.cos(M) * Math.exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (Math.abs((m - n)) - l)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if m <= -56.0:
		tmp = math.cos(M) * math.exp((math.pow(m, 2.0) * -0.25))
	else:
		tmp = math.cos(M) * math.exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (math.fabs((m - n)) - l)))
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if (m <= -56.0)
		tmp = Float64(cos(M) * exp(Float64((m ^ 2.0) * -0.25)));
	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(m - n)) - l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (m <= -56.0)
		tmp = cos(M) * exp(((m ^ 2.0) * -0.25));
	else
		tmp = cos(M) * exp(((((n * 0.5) - M) * ((M - (n * 0.5)) - m)) + (abs((m - n)) - l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -56.0], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $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[(m - n), $MachinePrecision]], $MachinePrecision] - l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 80.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos M \cdot e^{-{M}^{2}}\\ t_1 := {m}^{2} \cdot -0.25\\ t_2 := \cos M \cdot e^{t_1}\\ \mathbf{if}\;m \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;m \leq -6 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 4.6 \cdot 10^{-213}:\\ \;\;\;\;t_1 \cdot \cos \left(0.5 \cdot \left(m \cdot K\right)\right)\\ \mathbf{elif}\;m \leq 16:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (* (cos M) (exp (- (pow M 2.0)))))
        (t_1 (* (pow m 2.0) -0.25))
        (t_2 (* (cos M) (exp t_1))))
   (if (<= m -1.45e-12)
     t_2
     (if (<= m -6e-160)
       t_0
       (if (<= m 4.6e-213)
         (* t_1 (cos (* 0.5 (* m K))))
         (if (<= m 16.0) t_0 t_2))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = cos(M) * exp(-pow(M, 2.0));
	double t_1 = pow(m, 2.0) * -0.25;
	double t_2 = cos(M) * exp(t_1);
	double tmp;
	if (m <= -1.45e-12) {
		tmp = t_2;
	} else if (m <= -6e-160) {
		tmp = t_0;
	} else if (m <= 4.6e-213) {
		tmp = t_1 * cos((0.5 * (m * K)));
	} else if (m <= 16.0) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = cos(m_1) * exp(-(m_1 ** 2.0d0))
    t_1 = (m ** 2.0d0) * (-0.25d0)
    t_2 = cos(m_1) * exp(t_1)
    if (m <= (-1.45d-12)) then
        tmp = t_2
    else if (m <= (-6d-160)) then
        tmp = t_0
    else if (m <= 4.6d-213) then
        tmp = t_1 * cos((0.5d0 * (m * k)))
    else if (m <= 16.0d0) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double t_0 = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	double t_1 = Math.pow(m, 2.0) * -0.25;
	double t_2 = Math.cos(M) * Math.exp(t_1);
	double tmp;
	if (m <= -1.45e-12) {
		tmp = t_2;
	} else if (m <= -6e-160) {
		tmp = t_0;
	} else if (m <= 4.6e-213) {
		tmp = t_1 * Math.cos((0.5 * (m * K)));
	} else if (m <= 16.0) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.cos(M) * math.exp(-math.pow(M, 2.0))
	t_1 = math.pow(m, 2.0) * -0.25
	t_2 = math.cos(M) * math.exp(t_1)
	tmp = 0
	if m <= -1.45e-12:
		tmp = t_2
	elif m <= -6e-160:
		tmp = t_0
	elif m <= 4.6e-213:
		tmp = t_1 * math.cos((0.5 * (m * K)))
	elif m <= 16.0:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = Float64(cos(M) * exp(Float64(-(M ^ 2.0))))
	t_1 = Float64((m ^ 2.0) * -0.25)
	t_2 = Float64(cos(M) * exp(t_1))
	tmp = 0.0
	if (m <= -1.45e-12)
		tmp = t_2;
	elseif (m <= -6e-160)
		tmp = t_0;
	elseif (m <= 4.6e-213)
		tmp = Float64(t_1 * cos(Float64(0.5 * Float64(m * K))));
	elseif (m <= 16.0)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = cos(M) * exp(-(M ^ 2.0));
	t_1 = (m ^ 2.0) * -0.25;
	t_2 = cos(M) * exp(t_1);
	tmp = 0.0;
	if (m <= -1.45e-12)
		tmp = t_2;
	elseif (m <= -6e-160)
		tmp = t_0;
	elseif (m <= 4.6e-213)
		tmp = t_1 * cos((0.5 * (m * K)));
	elseif (m <= 16.0)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[Cos[M], $MachinePrecision] * N[Exp[t$95$1], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[m, -1.45e-12], t$95$2, If[LessEqual[m, -6e-160], t$95$0, If[LessEqual[m, 4.6e-213], N[(t$95$1 * N[Cos[N[(0.5 * N[(m * K), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 16.0], t$95$0, t$95$2]]]]]]]

Derivation

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

Alternative 6: 70.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos M \cdot e^{-0.25 \cdot {n}^{2}}\\ t_1 := {m}^{2} \cdot -0.25\\ \mathbf{if}\;m \leq -55:\\ \;\;\;\;\cos M \cdot e^{t_1}\\ \mathbf{elif}\;m \leq -9.6 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq -3.85 \cdot 10^{-160}:\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \mathbf{elif}\;m \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;t_1 \cdot \cos \left(0.5 \cdot \left(m \cdot K\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (* (cos M) (exp (* -0.25 (pow n 2.0)))))
        (t_1 (* (pow m 2.0) -0.25)))
   (if (<= m -55.0)
     (* (cos M) (exp t_1))
     (if (<= m -9.6e-19)
       t_0
       (if (<= m -3.85e-160)
         (* (cos M) (exp (- (pow M 2.0))))
         (if (<= m 1.4e-207) (* t_1 (cos (* 0.5 (* m K)))) t_0))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = cos(M) * exp((-0.25 * pow(n, 2.0)));
	double t_1 = pow(m, 2.0) * -0.25;
	double tmp;
	if (m <= -55.0) {
		tmp = cos(M) * exp(t_1);
	} else if (m <= -9.6e-19) {
		tmp = t_0;
	} else if (m <= -3.85e-160) {
		tmp = cos(M) * exp(-pow(M, 2.0));
	} else if (m <= 1.4e-207) {
		tmp = t_1 * cos((0.5 * (m * K)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos(m_1) * exp(((-0.25d0) * (n ** 2.0d0)))
    t_1 = (m ** 2.0d0) * (-0.25d0)
    if (m <= (-55.0d0)) then
        tmp = cos(m_1) * exp(t_1)
    else if (m <= (-9.6d-19)) then
        tmp = t_0
    else if (m <= (-3.85d-160)) then
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    else if (m <= 1.4d-207) then
        tmp = t_1 * cos((0.5d0 * (m * k)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double t_0 = Math.cos(M) * Math.exp((-0.25 * Math.pow(n, 2.0)));
	double t_1 = Math.pow(m, 2.0) * -0.25;
	double tmp;
	if (m <= -55.0) {
		tmp = Math.cos(M) * Math.exp(t_1);
	} else if (m <= -9.6e-19) {
		tmp = t_0;
	} else if (m <= -3.85e-160) {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	} else if (m <= 1.4e-207) {
		tmp = t_1 * Math.cos((0.5 * (m * K)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.cos(M) * math.exp((-0.25 * math.pow(n, 2.0)))
	t_1 = math.pow(m, 2.0) * -0.25
	tmp = 0
	if m <= -55.0:
		tmp = math.cos(M) * math.exp(t_1)
	elif m <= -9.6e-19:
		tmp = t_0
	elif m <= -3.85e-160:
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	elif m <= 1.4e-207:
		tmp = t_1 * math.cos((0.5 * (m * K)))
	else:
		tmp = t_0
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = Float64(cos(M) * exp(Float64(-0.25 * (n ^ 2.0))))
	t_1 = Float64((m ^ 2.0) * -0.25)
	tmp = 0.0
	if (m <= -55.0)
		tmp = Float64(cos(M) * exp(t_1));
	elseif (m <= -9.6e-19)
		tmp = t_0;
	elseif (m <= -3.85e-160)
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	elseif (m <= 1.4e-207)
		tmp = Float64(t_1 * cos(Float64(0.5 * Float64(m * K))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = cos(M) * exp((-0.25 * (n ^ 2.0)));
	t_1 = (m ^ 2.0) * -0.25;
	tmp = 0.0;
	if (m <= -55.0)
		tmp = cos(M) * exp(t_1);
	elseif (m <= -9.6e-19)
		tmp = t_0;
	elseif (m <= -3.85e-160)
		tmp = cos(M) * exp(-(M ^ 2.0));
	elseif (m <= 1.4e-207)
		tmp = t_1 * cos((0.5 * (m * K)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[m, -55.0], N[(N[Cos[M], $MachinePrecision] * N[Exp[t$95$1], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -9.6e-19], t$95$0, If[LessEqual[m, -3.85e-160], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.4e-207], N[(t$95$1 * N[Cos[N[(0.5 * N[(m * K), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

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

Alternative 7: 68.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq -1.4 \cdot 10^{-16} \lor \neg \left(M \leq 0.00135\right):\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (or (<= M -1.4e-16) (not (<= M 0.00135)))
   (* (cos M) (exp (- (pow M 2.0))))
   (* (cos M) (exp (- l)))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((M <= -1.4e-16) || !(M <= 0.00135)) {
		tmp = cos(M) * exp(-pow(M, 2.0));
	} else {
		tmp = cos(M) * exp(-l);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((m_1 <= (-1.4d-16)) .or. (.not. (m_1 <= 0.00135d0))) then
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    else
        tmp = cos(m_1) * exp(-l)
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((M <= -1.4e-16) || !(M <= 0.00135)) {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	} else {
		tmp = Math.cos(M) * Math.exp(-l);
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if (M <= -1.4e-16) or not (M <= 0.00135):
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	else:
		tmp = math.cos(M) * math.exp(-l)
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if ((M <= -1.4e-16) || !(M <= 0.00135))
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	else
		tmp = Float64(cos(M) * exp(Float64(-l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if ((M <= -1.4e-16) || ~((M <= 0.00135)))
		tmp = cos(M) * exp(-(M ^ 2.0));
	else
		tmp = cos(M) * exp(-l);
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[Or[LessEqual[M, -1.4e-16], N[Not[LessEqual[M, 0.00135]], $MachinePrecision]], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 41.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -6.5 \cdot 10^{-158} \lor \neg \left(m \leq 3.1 \cdot 10^{-231}\right):\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \mathbf{else}:\\ \;\;\;\;\left({m}^{2} \cdot -0.25\right) \cdot \cos \left(0.5 \cdot \left(m \cdot K\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (or (<= m -6.5e-158) (not (<= m 3.1e-231)))
   (* (cos M) (exp (- l)))
   (* (* (pow m 2.0) -0.25) (cos (* 0.5 (* m K))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((m <= -6.5e-158) || !(m <= 3.1e-231)) {
		tmp = cos(M) * exp(-l);
	} else {
		tmp = (pow(m, 2.0) * -0.25) * cos((0.5 * (m * K)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((m <= (-6.5d-158)) .or. (.not. (m <= 3.1d-231))) then
        tmp = cos(m_1) * exp(-l)
    else
        tmp = ((m ** 2.0d0) * (-0.25d0)) * cos((0.5d0 * (m * k)))
    end if
    code = tmp
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((m <= -6.5e-158) || !(m <= 3.1e-231)) {
		tmp = Math.cos(M) * Math.exp(-l);
	} else {
		tmp = (Math.pow(m, 2.0) * -0.25) * Math.cos((0.5 * (m * K)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if (m <= -6.5e-158) or not (m <= 3.1e-231):
		tmp = math.cos(M) * math.exp(-l)
	else:
		tmp = (math.pow(m, 2.0) * -0.25) * math.cos((0.5 * (m * K)))
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if ((m <= -6.5e-158) || !(m <= 3.1e-231))
		tmp = Float64(cos(M) * exp(Float64(-l)));
	else
		tmp = Float64(Float64((m ^ 2.0) * -0.25) * cos(Float64(0.5 * Float64(m * K))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if ((m <= -6.5e-158) || ~((m <= 3.1e-231)))
		tmp = cos(M) * exp(-l);
	else
		tmp = ((m ^ 2.0) * -0.25) * cos((0.5 * (m * K)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[Or[LessEqual[m, -6.5e-158], N[Not[LessEqual[m, 3.1e-231]], $MachinePrecision]], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision] * N[Cos[N[(0.5 * N[(m * K), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 35.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \cos M \cdot e^{-\ell} \end{array} \]

FPCore

(FPCore (K m n M l) :precision binary64 (* (cos M) (exp (- l))))

C

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

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(m_1) * exp(-l)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = cos(M) * exp(-l);
end

Wolfram

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 10: 7.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \cos M \end{array} \]

FPCore

(FPCore (K m n M l) :precision binary64 (cos M))

C

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

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(m_1)
end function

Java

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

Python

def code(K, m, n, M, l):
	return math.cos(M)

Julia

function code(K, m, n, M, l)
	return cos(M)
end

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = cos(M);
end

Wolfram

code[K_, m_, n_, M_, l_] := N[Cos[M], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024008 
(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)))))))