Maksimov and Kolovsky, Equation (32)

Percentage Accurate: 77.0% → 97.0%

Time: 18.9s

Alternatives: 12

Speedup: 1.0×

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: 77.0% 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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (K m n M l)
 :precision binary64
 (* (cos M) (exp (- (- (fabs (- n m)) 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((n - m)) - 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((n - m)) - 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((n - m)) - 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((n - m)) - 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(n - m)) - 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((n - m)) - 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[(n - m), $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: 63.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := K \cdot \left(m \cdot 0.5\right) - M\\ \mathbf{if}\;m \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;\cos M \cdot e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -9.2 \cdot 10^{-58}:\\ \;\;\;\;\left(\cos t_0 + -0.5 \cdot \left(\left(n \cdot K\right) \cdot \sin t_0\right)\right) \cdot e^{-\ell}\\ \mathbf{elif}\;m \leq 2.7 \cdot 10^{-301}:\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (let* ((t_0 (- (* K (* m 0.5)) M)))
   (if (<= m -5.5e-10)
     (* (cos M) (exp (* (pow m 2.0) -0.25)))
     (if (<= m -9.2e-58)
       (* (+ (cos t_0) (* -0.5 (* (* n K) (sin t_0)))) (exp (- l)))
       (if (<= m 2.7e-301)
         (* (cos M) (exp (- (pow M 2.0))))
         (* (cos M) (exp (* -0.25 (pow n 2.0)))))))))

C

double code(double K, double m, double n, double M, double l) {
	double t_0 = (K * (m * 0.5)) - M;
	double tmp;
	if (m <= -5.5e-10) {
		tmp = cos(M) * exp((pow(m, 2.0) * -0.25));
	} else if (m <= -9.2e-58) {
		tmp = (cos(t_0) + (-0.5 * ((n * K) * sin(t_0)))) * exp(-l);
	} else if (m <= 2.7e-301) {
		tmp = cos(M) * exp(-pow(M, 2.0));
	} else {
		tmp = cos(M) * 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) :: t_0
    real(8) :: tmp
    t_0 = (k * (m * 0.5d0)) - m_1
    if (m <= (-5.5d-10)) then
        tmp = cos(m_1) * exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-9.2d-58)) then
        tmp = (cos(t_0) + ((-0.5d0) * ((n * k) * sin(t_0)))) * exp(-l)
    else if (m <= 2.7d-301) then
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    else
        tmp = cos(m_1) * 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 t_0 = (K * (m * 0.5)) - M;
	double tmp;
	if (m <= -5.5e-10) {
		tmp = Math.cos(M) * Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -9.2e-58) {
		tmp = (Math.cos(t_0) + (-0.5 * ((n * K) * Math.sin(t_0)))) * Math.exp(-l);
	} else if (m <= 2.7e-301) {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	} else {
		tmp = Math.cos(M) * Math.exp((-0.25 * Math.pow(n, 2.0)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	t_0 = (K * (m * 0.5)) - M
	tmp = 0
	if m <= -5.5e-10:
		tmp = math.cos(M) * math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -9.2e-58:
		tmp = (math.cos(t_0) + (-0.5 * ((n * K) * math.sin(t_0)))) * math.exp(-l)
	elif m <= 2.7e-301:
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	else:
		tmp = math.cos(M) * math.exp((-0.25 * math.pow(n, 2.0)))
	return tmp

Julia

function code(K, m, n, M, l)
	t_0 = Float64(Float64(K * Float64(m * 0.5)) - M)
	tmp = 0.0
	if (m <= -5.5e-10)
		tmp = Float64(cos(M) * exp(Float64((m ^ 2.0) * -0.25)));
	elseif (m <= -9.2e-58)
		tmp = Float64(Float64(cos(t_0) + Float64(-0.5 * Float64(Float64(n * K) * sin(t_0)))) * exp(Float64(-l)));
	elseif (m <= 2.7e-301)
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	else
		tmp = Float64(cos(M) * exp(Float64(-0.25 * (n ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(K, m, n, M, l)
	t_0 = (K * (m * 0.5)) - M;
	tmp = 0.0;
	if (m <= -5.5e-10)
		tmp = cos(M) * exp(((m ^ 2.0) * -0.25));
	elseif (m <= -9.2e-58)
		tmp = (cos(t_0) + (-0.5 * ((n * K) * sin(t_0)))) * exp(-l);
	elseif (m <= 2.7e-301)
		tmp = cos(M) * exp(-(M ^ 2.0));
	else
		tmp = cos(M) * exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := Block[{t$95$0 = N[(N[(K * N[(m * 0.5), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]}, If[LessEqual[m, -5.5e-10], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -9.2e-58], N[(N[(N[Cos[t$95$0], $MachinePrecision] + N[(-0.5 * N[(N[(n * K), $MachinePrecision] * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 2.7e-301], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 63.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.35:\\ \;\;\;\;\cos M \cdot e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -3.3 \cdot 10^{-69}:\\ \;\;\;\;e^{-\ell} \cdot \cos \left(\frac{K}{\frac{2}{n}} - M\right)\\ \mathbf{elif}\;m \leq 3.4 \cdot 10^{-298}:\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -0.35)
   (* (cos M) (exp (* (pow m 2.0) -0.25)))
   (if (<= m -3.3e-69)
     (* (exp (- l)) (cos (- (/ K (/ 2.0 n)) M)))
     (if (<= m 3.4e-298)
       (* (cos M) (exp (- (pow M 2.0))))
       (* (cos M) (exp (* -0.25 (pow n 2.0))))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.35) {
		tmp = cos(M) * exp((pow(m, 2.0) * -0.25));
	} else if (m <= -3.3e-69) {
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	} else if (m <= 3.4e-298) {
		tmp = cos(M) * exp(-pow(M, 2.0));
	} else {
		tmp = cos(M) * 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 <= (-0.35d0)) then
        tmp = cos(m_1) * exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-3.3d-69)) then
        tmp = exp(-l) * cos(((k / (2.0d0 / n)) - m_1))
    else if (m <= 3.4d-298) then
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    else
        tmp = cos(m_1) * 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 <= -0.35) {
		tmp = Math.cos(M) * Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -3.3e-69) {
		tmp = Math.exp(-l) * Math.cos(((K / (2.0 / n)) - M));
	} else if (m <= 3.4e-298) {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	} else {
		tmp = Math.cos(M) * Math.exp((-0.25 * Math.pow(n, 2.0)));
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if m <= -0.35:
		tmp = math.cos(M) * math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -3.3e-69:
		tmp = math.exp(-l) * math.cos(((K / (2.0 / n)) - M))
	elif m <= 3.4e-298:
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	else:
		tmp = math.cos(M) * math.exp((-0.25 * math.pow(n, 2.0)))
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if (m <= -0.35)
		tmp = Float64(cos(M) * exp(Float64((m ^ 2.0) * -0.25)));
	elseif (m <= -3.3e-69)
		tmp = Float64(exp(Float64(-l)) * cos(Float64(Float64(K / Float64(2.0 / n)) - M)));
	elseif (m <= 3.4e-298)
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	else
		tmp = Float64(cos(M) * 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 <= -0.35)
		tmp = cos(M) * exp(((m ^ 2.0) * -0.25));
	elseif (m <= -3.3e-69)
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	elseif (m <= 3.4e-298)
		tmp = cos(M) * exp(-(M ^ 2.0));
	else
		tmp = cos(M) * exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -0.35], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -3.3e-69], N[(N[Exp[(-l)], $MachinePrecision] * N[Cos[N[(N[(K / N[(2.0 / n), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 3.4e-298], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 63.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.35:\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -4 \cdot 10^{-69}:\\ \;\;\;\;e^{-\ell} \cdot \cos \left(\frac{K}{\frac{2}{n}} - M\right)\\ \mathbf{elif}\;m \leq 10^{-296}:\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \mathbf{else}:\\ \;\;\;\;e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -0.35)
   (exp (* (pow m 2.0) -0.25))
   (if (<= m -4e-69)
     (* (exp (- l)) (cos (- (/ K (/ 2.0 n)) M)))
     (if (<= m 1e-296)
       (* (cos M) (exp (- (pow M 2.0))))
       (exp (* -0.25 (pow n 2.0)))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.35) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} else if (m <= -4e-69) {
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	} else if (m <= 1e-296) {
		tmp = cos(M) * exp(-pow(M, 2.0));
	} 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 <= (-0.35d0)) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-4d-69)) then
        tmp = exp(-l) * cos(((k / (2.0d0 / n)) - m_1))
    else if (m <= 1d-296) then
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    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 <= -0.35) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -4e-69) {
		tmp = Math.exp(-l) * Math.cos(((K / (2.0 / n)) - M));
	} else if (m <= 1e-296) {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	} 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 <= -0.35:
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -4e-69:
		tmp = math.exp(-l) * math.cos(((K / (2.0 / n)) - M))
	elif m <= 1e-296:
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	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 <= -0.35)
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	elseif (m <= -4e-69)
		tmp = Float64(exp(Float64(-l)) * cos(Float64(Float64(K / Float64(2.0 / n)) - M)));
	elseif (m <= 1e-296)
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	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 <= -0.35)
		tmp = exp(((m ^ 2.0) * -0.25));
	elseif (m <= -4e-69)
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	elseif (m <= 1e-296)
		tmp = cos(M) * exp(-(M ^ 2.0));
	else
		tmp = exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -0.35], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], If[LessEqual[m, -4e-69], N[(N[Exp[(-l)], $MachinePrecision] * N[Cos[N[(N[(K / N[(2.0 / n), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1e-296], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $MachinePrecision])], $MachinePrecision]), $MachinePrecision], N[Exp[N[(-0.25 * N[Power[n, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 63.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.35:\\ \;\;\;\;\cos M \cdot e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -4.4 \cdot 10^{-69}:\\ \;\;\;\;e^{-\ell} \cdot \cos \left(\frac{K}{\frac{2}{n}} - M\right)\\ \mathbf{elif}\;m \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\cos M \cdot e^{-{M}^{2}}\\ \mathbf{else}:\\ \;\;\;\;e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -0.35)
   (* (cos M) (exp (* (pow m 2.0) -0.25)))
   (if (<= m -4.4e-69)
     (* (exp (- l)) (cos (- (/ K (/ 2.0 n)) M)))
     (if (<= m 4e-303)
       (* (cos M) (exp (- (pow M 2.0))))
       (exp (* -0.25 (pow n 2.0)))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.35) {
		tmp = cos(M) * exp((pow(m, 2.0) * -0.25));
	} else if (m <= -4.4e-69) {
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	} else if (m <= 4e-303) {
		tmp = cos(M) * exp(-pow(M, 2.0));
	} 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 <= (-0.35d0)) then
        tmp = cos(m_1) * exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-4.4d-69)) then
        tmp = exp(-l) * cos(((k / (2.0d0 / n)) - m_1))
    else if (m <= 4d-303) then
        tmp = cos(m_1) * exp(-(m_1 ** 2.0d0))
    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 <= -0.35) {
		tmp = Math.cos(M) * Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -4.4e-69) {
		tmp = Math.exp(-l) * Math.cos(((K / (2.0 / n)) - M));
	} else if (m <= 4e-303) {
		tmp = Math.cos(M) * Math.exp(-Math.pow(M, 2.0));
	} 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 <= -0.35:
		tmp = math.cos(M) * math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -4.4e-69:
		tmp = math.exp(-l) * math.cos(((K / (2.0 / n)) - M))
	elif m <= 4e-303:
		tmp = math.cos(M) * math.exp(-math.pow(M, 2.0))
	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 <= -0.35)
		tmp = Float64(cos(M) * exp(Float64((m ^ 2.0) * -0.25)));
	elseif (m <= -4.4e-69)
		tmp = Float64(exp(Float64(-l)) * cos(Float64(Float64(K / Float64(2.0 / n)) - M)));
	elseif (m <= 4e-303)
		tmp = Float64(cos(M) * exp(Float64(-(M ^ 2.0))));
	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 <= -0.35)
		tmp = cos(M) * exp(((m ^ 2.0) * -0.25));
	elseif (m <= -4.4e-69)
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	elseif (m <= 4e-303)
		tmp = cos(M) * exp(-(M ^ 2.0));
	else
		tmp = exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -0.35], N[(N[Cos[M], $MachinePrecision] * N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, -4.4e-69], N[(N[Exp[(-l)], $MachinePrecision] * N[Cos[N[(N[(K / N[(2.0 / n), $MachinePrecision]), $MachinePrecision] - M), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 4e-303], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-N[Power[M, 2.0], $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: 63.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.35:\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -7.4 \cdot 10^{-106}:\\ \;\;\;\;e^{-\ell} \cdot \cos \left(\frac{K}{\frac{2}{n}} - M\right)\\ \mathbf{else}:\\ \;\;\;\;e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -0.35)
   (exp (* (pow m 2.0) -0.25))
   (if (<= m -7.4e-106)
     (* (exp (- l)) (cos (- (/ K (/ 2.0 n)) M)))
     (exp (* -0.25 (pow n 2.0))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.35) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} else if (m <= -7.4e-106) {
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	} 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 <= (-0.35d0)) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-7.4d-106)) then
        tmp = exp(-l) * cos(((k / (2.0d0 / n)) - m_1))
    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 <= -0.35) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -7.4e-106) {
		tmp = Math.exp(-l) * Math.cos(((K / (2.0 / n)) - M));
	} 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 <= -0.35:
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -7.4e-106:
		tmp = math.exp(-l) * math.cos(((K / (2.0 / n)) - M))
	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 <= -0.35)
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	elseif (m <= -7.4e-106)
		tmp = Float64(exp(Float64(-l)) * cos(Float64(Float64(K / Float64(2.0 / n)) - M)));
	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 <= -0.35)
		tmp = exp(((m ^ 2.0) * -0.25));
	elseif (m <= -7.4e-106)
		tmp = exp(-l) * cos(((K / (2.0 / n)) - M));
	else
		tmp = exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -0.35], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], If[LessEqual[m, -7.4e-106], N[(N[Exp[(-l)], $MachinePrecision] * N[Cos[N[(N[(K / N[(2.0 / n), $MachinePrecision]), $MachinePrecision] - M), $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 7: 68.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.35 \lor \neg \left(m \leq 9.5 \cdot 10^{-34}\right):\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (or (<= m -0.35) (not (<= m 9.5e-34)))
   (exp (* (pow m 2.0) -0.25))
   (* (cos M) (exp (- l)))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if ((m <= -0.35) || !(m <= 9.5e-34)) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} 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 <= (-0.35d0)) .or. (.not. (m <= 9.5d-34))) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    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 <= -0.35) || !(m <= 9.5e-34)) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else {
		tmp = Math.cos(M) * Math.exp(-l);
	}
	return tmp;
}

Python

def code(K, m, n, M, l):
	tmp = 0
	if (m <= -0.35) or not (m <= 9.5e-34):
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	else:
		tmp = math.cos(M) * math.exp(-l)
	return tmp

Julia

function code(K, m, n, M, l)
	tmp = 0.0
	if ((m <= -0.35) || !(m <= 9.5e-34))
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	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 <= -0.35) || ~((m <= 9.5e-34)))
		tmp = exp(((m ^ 2.0) * -0.25));
	else
		tmp = cos(M) * exp(-l);
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[Or[LessEqual[m, -0.35], N[Not[LessEqual[m, 9.5e-34]], $MachinePrecision]], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 64.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.35:\\ \;\;\;\;e^{{m}^{2} \cdot -0.25}\\ \mathbf{elif}\;m \leq -6 \cdot 10^{-100}:\\ \;\;\;\;\cos M \cdot e^{-\ell}\\ \mathbf{else}:\\ \;\;\;\;e^{-0.25 \cdot {n}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (K m n M l)
 :precision binary64
 (if (<= m -0.35)
   (exp (* (pow m 2.0) -0.25))
   (if (<= m -6e-100) (* (cos M) (exp (- l))) (exp (* -0.25 (pow n 2.0))))))

C

double code(double K, double m, double n, double M, double l) {
	double tmp;
	if (m <= -0.35) {
		tmp = exp((pow(m, 2.0) * -0.25));
	} else if (m <= -6e-100) {
		tmp = cos(M) * exp(-l);
	} 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 <= (-0.35d0)) then
        tmp = exp(((m ** 2.0d0) * (-0.25d0)))
    else if (m <= (-6d-100)) then
        tmp = cos(m_1) * exp(-l)
    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 <= -0.35) {
		tmp = Math.exp((Math.pow(m, 2.0) * -0.25));
	} else if (m <= -6e-100) {
		tmp = Math.cos(M) * Math.exp(-l);
	} 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 <= -0.35:
		tmp = math.exp((math.pow(m, 2.0) * -0.25))
	elif m <= -6e-100:
		tmp = math.cos(M) * math.exp(-l)
	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 <= -0.35)
		tmp = exp(Float64((m ^ 2.0) * -0.25));
	elseif (m <= -6e-100)
		tmp = Float64(cos(M) * exp(Float64(-l)));
	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 <= -0.35)
		tmp = exp(((m ^ 2.0) * -0.25));
	elseif (m <= -6e-100)
		tmp = cos(M) * exp(-l);
	else
		tmp = exp((-0.25 * (n ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[K_, m_, n_, M_, l_] := If[LessEqual[m, -0.35], N[Exp[N[(N[Power[m, 2.0], $MachinePrecision] * -0.25), $MachinePrecision]], $MachinePrecision], If[LessEqual[m, -6e-100], N[(N[Cos[M], $MachinePrecision] * N[Exp[(-l)], $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: 36.2% 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: 35.8% 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

Alternative 11: 6.7% 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

Alternative 12: 6.7% accurate, 425.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (K m n M l) :precision binary64 1.0)

C

double code(double K, double m, double n, double M, double l) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double K, double m, double n, double M, double l) {
	return 1.0;
}

Python

def code(K, m, n, M, l):
	return 1.0

Julia

function code(K, m, n, M, l)
	return 1.0
end

MATLAB

function tmp = code(K, m, n, M, l)
	tmp = 1.0;
end

Wolfram

code[K_, m_, n_, M_, l_] := 1.0

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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)))))))