Maksimov and Kolovsky, Equation (32)

Percentage Accurate: 75.8% → 96.5%

Time: 22.2s

Alternatives: 9

Speedup: 2.0×

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: 75.8% 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: 96.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (K m n M l)
 :precision binary64
 (* (cos M) (exp (- (- (fabs (- m n)) l) (pow (- (* 0.5 (+ m n)) 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(((0.5 * (m + n)) - 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) - (((0.5d0 * (m + n)) - 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(((0.5 * (m + n)) - M), 2.0)));
}

Python

def code(K, m, n, M, l):
	return math.cos(M) * math.exp(((math.fabs((m - n)) - l) - math.pow(((0.5 * (m + n)) - 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(0.5 * Float64(m + n)) - M) ^ 2.0))))
end

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = cos(M) * exp(((abs((m - n)) - l) - (((0.5 * (m + n)) - 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[(0.5 * N[(m + n), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 90.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|m - n\right|\\ \mathbf{if}\;M \leq -1.6 \cdot 10^{+154}:\\ \;\;\;\;\cos M \cdot e^{\left(t_0 + M \cdot \left(m - M\right)\right) - \ell}\\ \mathbf{elif}\;M \leq 82:\\ \;\;\;\;e^{t_0 - \left(0.25 \cdot \left(\left(m + n\right) \cdot \left(m + n\right)\right) + \ell\right)}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{t_0 + \left(n \cdot 0.5 - M\right) \cdot \left(\left(M - n \cdot 0.5\right) - m\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (fabs (- m n))))
   (if (<= M -1.6e+154)
     (* (cos M) (exp (- (+ t_0 (* M (- m M))) l)))
     (if (<= M 82.0)
       (exp (- t_0 (+ (* 0.25 (* (+ m n) (+ m n))) l)))
       (* (cos M) (exp (+ t_0 (* (- (* n 0.5) M) (- (- M (* n 0.5)) m)))))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = fabs((m - n));
	double tmp;
	if (M <= -1.6e+154) {
		tmp = cos(M) * exp(((t_0 + (M * (m - M))) - l));
	} else if (M <= 82.0) {
		tmp = exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	} else {
		tmp = cos(M) * exp((t_0 + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))));
	}
	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) :: tmp
    t_0 = abs((m - n))
    if (m_1 <= (-1.6d+154)) then
        tmp = cos(m_1) * exp(((t_0 + (m_1 * (m - m_1))) - l))
    else if (m_1 <= 82.0d0) then
        tmp = exp((t_0 - ((0.25d0 * ((m + n) * (m + n))) + l)))
    else
        tmp = cos(m_1) * exp((t_0 + (((n * 0.5d0) - m_1) * ((m_1 - (n * 0.5d0)) - m))))
    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));
	double tmp;
	if (M <= -1.6e+154) {
		tmp = Math.cos(M) * Math.exp(((t_0 + (M * (m - M))) - l));
	} else if (M <= 82.0) {
		tmp = Math.exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	} else {
		tmp = Math.cos(M) * Math.exp((t_0 + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.fabs((m - n))
	tmp = 0
	if M <= -1.6e+154:
		tmp = math.cos(M) * math.exp(((t_0 + (M * (m - M))) - l))
	elif M <= 82.0:
		tmp = math.exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)))
	else:
		tmp = math.cos(M) * math.exp((t_0 + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))))
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = abs(Float64(m - n))
	tmp = 0.0
	if (M <= -1.6e+154)
		tmp = Float64(cos(M) * exp(Float64(Float64(t_0 + Float64(M * Float64(m - M))) - l)));
	elseif (M <= 82.0)
		tmp = exp(Float64(t_0 - Float64(Float64(0.25 * Float64(Float64(m + n) * Float64(m + n))) + l)));
	else
		tmp = Float64(cos(M) * exp(Float64(t_0 + Float64(Float64(Float64(n * 0.5) - M) * Float64(Float64(M - Float64(n * 0.5)) - m)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = abs((m - n));
	tmp = 0.0;
	if (M <= -1.6e+154)
		tmp = cos(M) * exp(((t_0 + (M * (m - M))) - l));
	elseif (M <= 82.0)
		tmp = exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	else
		tmp = cos(M) * exp((t_0 + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[M, -1.6e+154], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(t$95$0 + N[(M * N[(m - M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[M, 82.0], N[Exp[N[(t$95$0 - N[(N[(0.25 * N[(N[(m + n), $MachinePrecision] * N[(m + n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(t$95$0 + N[(N[(N[(n * 0.5), $MachinePrecision] - M), $MachinePrecision] * N[(N[(M - N[(n * 0.5), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 3: 86.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|m - n\right|\\ \mathbf{if}\;m \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;e^{t_0 - \left(0.25 \cdot \left(\left(m + n\right) \cdot \left(m + n\right)\right) + \ell\right)}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{\left(t_0 - \ell\right) + \left(n \cdot 0.5 - M\right) \cdot \left(\left(M - n \cdot 0.5\right) - m\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (fabs (- m n))))
   (if (<= m -2.7e+24)
     (exp (- t_0 (+ (* 0.25 (* (+ m n) (+ m n))) l)))
     (*
      (cos M)
      (exp (+ (- t_0 l) (* (- (* n 0.5) M) (- (- M (* n 0.5)) m))))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = fabs((m - n));
	double tmp;
	if (m <= -2.7e+24) {
		tmp = exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	} else {
		tmp = cos(M) * exp(((t_0 - l) + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))));
	}
	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) :: tmp
    t_0 = abs((m - n))
    if (m <= (-2.7d+24)) then
        tmp = exp((t_0 - ((0.25d0 * ((m + n) * (m + n))) + l)))
    else
        tmp = cos(m_1) * exp(((t_0 - l) + (((n * 0.5d0) - m_1) * ((m_1 - (n * 0.5d0)) - m))))
    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));
	double tmp;
	if (m <= -2.7e+24) {
		tmp = Math.exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	} else {
		tmp = Math.cos(M) * Math.exp(((t_0 - l) + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.fabs((m - n))
	tmp = 0
	if m <= -2.7e+24:
		tmp = math.exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)))
	else:
		tmp = math.cos(M) * math.exp(((t_0 - l) + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))))
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = abs(Float64(m - n))
	tmp = 0.0
	if (m <= -2.7e+24)
		tmp = exp(Float64(t_0 - Float64(Float64(0.25 * Float64(Float64(m + n) * Float64(m + n))) + l)));
	else
		tmp = Float64(cos(M) * exp(Float64(Float64(t_0 - l) + Float64(Float64(Float64(n * 0.5) - M) * Float64(Float64(M - Float64(n * 0.5)) - m)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = abs((m - n));
	tmp = 0.0;
	if (m <= -2.7e+24)
		tmp = exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	else
		tmp = cos(M) * exp(((t_0 - l) + (((n * 0.5) - M) * ((M - (n * 0.5)) - m))));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[m, -2.7e+24], N[Exp[N[(t$95$0 - N[(N[(0.25 * N[(N[(m + n), $MachinePrecision] * N[(m + n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(t$95$0 - l), $MachinePrecision] + N[(N[(N[(n * 0.5), $MachinePrecision] - M), $MachinePrecision] * N[(N[(M - N[(n * 0.5), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 89.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|m - n\right|\\ \mathbf{if}\;M \leq -3.6 \cdot 10^{+152} \lor \neg \left(M \leq 1.25 \cdot 10^{+40}\right):\\ \;\;\;\;\cos M \cdot e^{\left(t_0 + M \cdot \left(m - M\right)\right) - \ell}\\ \mathbf{else}:\\ \;\;\;\;e^{t_0 - \left(0.25 \cdot \left(\left(m + n\right) \cdot \left(m + n\right)\right) + \ell\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (fabs (- m n))))
   (if (or (<= M -3.6e+152) (not (<= M 1.25e+40)))
     (* (cos M) (exp (- (+ t_0 (* M (- m M))) l)))
     (exp (- t_0 (+ (* 0.25 (* (+ m n) (+ m n))) l))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = fabs((m - n));
	double tmp;
	if ((M <= -3.6e+152) || !(M <= 1.25e+40)) {
		tmp = cos(M) * exp(((t_0 + (M * (m - M))) - l));
	} else {
		tmp = exp((t_0 - ((0.25 * ((m + n) * (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) :: t_0
    real(8) :: tmp
    t_0 = abs((m - n))
    if ((m_1 <= (-3.6d+152)) .or. (.not. (m_1 <= 1.25d+40))) then
        tmp = cos(m_1) * exp(((t_0 + (m_1 * (m - m_1))) - l))
    else
        tmp = exp((t_0 - ((0.25d0 * ((m + n) * (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 t_0 = Math.abs((m - n));
	double tmp;
	if ((M <= -3.6e+152) || !(M <= 1.25e+40)) {
		tmp = Math.cos(M) * Math.exp(((t_0 + (M * (m - M))) - l));
	} else {
		tmp = Math.exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = math.fabs((m - n))
	tmp = 0
	if (M <= -3.6e+152) or not (M <= 1.25e+40):
		tmp = math.cos(M) * math.exp(((t_0 + (M * (m - M))) - l))
	else:
		tmp = math.exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)))
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = abs(Float64(m - n))
	tmp = 0.0
	if ((M <= -3.6e+152) || !(M <= 1.25e+40))
		tmp = Float64(cos(M) * exp(Float64(Float64(t_0 + Float64(M * Float64(m - M))) - l)));
	else
		tmp = exp(Float64(t_0 - Float64(Float64(0.25 * Float64(Float64(m + n) * Float64(m + n))) + l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = abs((m - n));
	tmp = 0.0;
	if ((M <= -3.6e+152) || ~((M <= 1.25e+40)))
		tmp = cos(M) * exp(((t_0 + (M * (m - M))) - l));
	else
		tmp = exp((t_0 - ((0.25 * ((m + n) * (m + n))) + l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[M, -3.6e+152], N[Not[LessEqual[M, 1.25e+40]], $MachinePrecision]], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[(t$95$0 + N[(M * N[(m - M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(t$95$0 - N[(N[(0.25 * N[(N[(m + n), $MachinePrecision] * N[(m + n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 5: 63.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -104000000:\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -3.1 \cdot 10^{-186}:\\ \;\;\;\;\cos \left(0.5 \cdot \left(n \cdot K\right) - M\right) \cdot e^{\left(-\ell\right) - n}\\ \mathbf{else}:\\ \;\;\;\;e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -104000000.0)
   (exp (* (pow m 2.0) -0.25))
   (if (<= m -3.1e-186)
     (* (cos (- (* 0.5 (* n K)) M)) (exp (- (- l) n)))
     (exp (* -0.25 (pow n 2.0))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -104000000.0) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} else if (m <= -3.1e-186) {
		tmp = cos(((0.5 * (n * K)) - M)) * exp((-l - n));
	} else {
		tmp = exp((-0.25 * pow(n, 2.0)));
	}
	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) :: tmp
    if (m <= (-104000000.0d0)) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-3.1d-186)) then
        tmp = cos(((0.5d0 * (n * k)) - m_1)) * exp((-l - n))
    else
        tmp = exp(((-0.25d0) * (n ** 2.0d0)))
    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 <= -104000000.0) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -3.1e-186) {
		tmp = Math.cos(((0.5 * (n * K)) - M)) * Math.exp((-l - n));
	} else {
		tmp = Math.exp((-0.25 * Math.pow(n, 2.0)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if m <= -104000000.0:
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -3.1e-186:
		tmp = math.cos(((0.5 * (n * K)) - M)) * math.exp((-l - n))
	else:
		tmp = math.exp((-0.25 * math.pow(n, 2.0)))
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if (m <= -104000000.0)
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	elseif (m <= -3.1e-186)
		tmp = Float64(cos(Float64(Float64(0.5 * Float64(n * K)) - M)) * exp(Float64(Float64(-l) - n)));
	else
		tmp = exp(Float64(-0.25 * (n ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (m <= -104000000.0)
		tmp = exp(((m ^ 2.0) * -0.25));
	elseif (m <= -3.1e-186)
		tmp = cos(((0.5 * (n * K)) - M)) * exp((-l - n));
	else
		tmp = exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -104000000.0], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], If[LessEqual[m, -3.1e-186], N[(N[Cos[N[(N[(0.5 * N[(n * K), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision] * N[Exp[N[((-l) - n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 6: 86.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{\left|m - n\right| - \left(0.25 \cdot \left(\left(m + n\right) \cdot \left(m + n\right)\right) + \ell\right)} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (exp (- (fabs (- m n)) (+ (* 0.25 (* (+ m n) (+ m n))) l))))

C

double code(double K, double m, double n, double M, double l) {
	return exp((fabs((m - n)) - ((0.25 * ((m + n) * (m + n))) + 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 = exp((abs((m - n)) - ((0.25d0 * ((m + n) * (m + n))) + l)))
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	return Math.exp((Math.abs((m - n)) - ((0.25 * ((m + n) * (m + n))) + l)));
}

Python

def code(K, m, n, M, l):
	return math.exp((math.fabs((m - n)) - ((0.25 * ((m + n) * (m + n))) + l)))

Julia

function code(K, m, n, M, l)
	return exp(Float64(abs(Float64(m - n)) - Float64(Float64(0.25 * Float64(Float64(m + n) * Float64(m + n))) + l)))
end

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = exp((abs((m - n)) - ((0.25 * ((m + n) * (m + n))) + l)));
end

Wolfram

code[K_, m_, n_, M_, l_] := N[Exp[N[(N[Abs[N[(m - n), $MachinePrecision]], $MachinePrecision] - N[(N[(0.25 * N[(N[(m + n), $MachinePrecision] * N[(m + n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 7: 68.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -2200000000 \lor \neg \left(m \leq 0.023\right):\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;e^{-\ell}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (or (<= m -2200000000.0) (not (<= m 0.023)))
   (exp (* (pow m 2.0) -0.25))
   (exp (- l))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((m <= -2200000000.0) || !(m <= 0.023)) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} else {
		tmp = 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 <= (-2200000000.0d0)) .or. (.not. (m <= 0.023d0))) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    else
        tmp = 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 <= -2200000000.0) || !(m <= 0.023)) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else {
		tmp = Math.exp(-l);
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if (m <= -2200000000.0) or not (m <= 0.023):
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	else:
		tmp = math.exp(-l)
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if ((m <= -2200000000.0) || !(m <= 0.023))
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	else
		tmp = exp(Float64(-l));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if ((m <= -2200000000.0) || ~((m <= 0.023)))
		tmp = exp(((m ^ 2.0) * -0.25));
	else
		tmp = exp(-l);
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[Or[LessEqual[m, -2200000000.0], N[Not[LessEqual[m, 0.023]], $MachinePrecision]], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], N[Exp[(-l)], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 64.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -8 \cdot 10^{+17}:\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -8e+17) (exp (* (pow m 2.0) -0.25)) (exp (* -0.25 (pow n 2.0)))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -8e+17) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} else {
		tmp = exp((-0.25 * pow(n, 2.0)));
	}
	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) :: tmp
    if (m <= (-8d+17)) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    else
        tmp = exp(((-0.25d0) * (n ** 2.0d0)))
    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 <= -8e+17) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else {
		tmp = Math.exp((-0.25 * Math.pow(n, 2.0)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if m <= -8e+17:
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	else:
		tmp = math.exp((-0.25 * math.pow(n, 2.0)))
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if (m <= -8e+17)
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	else
		tmp = exp(Float64(-0.25 * (n ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	tmp = 0.0;
	if (m <= -8e+17)
		tmp = exp(((m ^ 2.0) * -0.25));
	else
		tmp = exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -8e+17], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 9: 35.4% accurate, 4.2× speedup

Math

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

FPCore

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

C

double code(double K, double m, double n, double M, double l) {
	return 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 = exp(-l)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[K_, m_, n_, M_, l_] := N[Exp[(-l)], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023347 
(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)))))))