Henrywood and Agarwal, Equation (12)

Percentage Accurate: 65.2% → 76.3%

Time: 25.5s

Alternatives: 20

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (*
  (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0)))
  (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))

C

double code(double d, double h, double l, double M, double D) {
	return (pow((d / h), (1.0 / 2.0)) * pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)));
}

Fortran

real(8) function code(d, h, l, m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m
    real(8), intent (in) :: d_1
    code = (((d / h) ** (1.0d0 / 2.0d0)) * ((d / l) ** (1.0d0 / 2.0d0))) * (1.0d0 - (((1.0d0 / 2.0d0) * (((m * d_1) / (2.0d0 * d)) ** 2.0d0)) * (h / l)))
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	return (Math.pow((d / h), (1.0 / 2.0)) * Math.pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * Math.pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)));
}

Python

def code(d, h, l, M, D):
	return (math.pow((d / h), (1.0 / 2.0)) * math.pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * math.pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)))

Julia

function code(d, h, l, M, D)
	return Float64(Float64((Float64(d / h) ^ Float64(1.0 / 2.0)) * (Float64(d / l) ^ Float64(1.0 / 2.0))) * Float64(1.0 - Float64(Float64(Float64(1.0 / 2.0) * (Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0)) * Float64(h / l))))
end

MATLAB

function tmp = code(d, h, l, M, D)
	tmp = (((d / h) ^ (1.0 / 2.0)) * ((d / l) ^ (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * (((M * D) / (2.0 * d)) ^ 2.0)) * (h / l)));
end

Wolfram

code[d_, h_, l_, M_, D_] := N[(N[(N[Power[N[(d / h), $MachinePrecision], N[(1.0 / 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(d / l), $MachinePrecision], N[(1.0 / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(N[(N[(1.0 / 2.0), $MachinePrecision] * N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (*
  (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0)))
  (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))

C

double code(double d, double h, double l, double M, double D) {
	return (pow((d / h), (1.0 / 2.0)) * pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)));
}

Fortran

real(8) function code(d, h, l, m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m
    real(8), intent (in) :: d_1
    code = (((d / h) ** (1.0d0 / 2.0d0)) * ((d / l) ** (1.0d0 / 2.0d0))) * (1.0d0 - (((1.0d0 / 2.0d0) * (((m * d_1) / (2.0d0 * d)) ** 2.0d0)) * (h / l)))
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	return (Math.pow((d / h), (1.0 / 2.0)) * Math.pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * Math.pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)));
}

Python

def code(d, h, l, M, D):
	return (math.pow((d / h), (1.0 / 2.0)) * math.pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * math.pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)))

Julia

function code(d, h, l, M, D)
	return Float64(Float64((Float64(d / h) ^ Float64(1.0 / 2.0)) * (Float64(d / l) ^ Float64(1.0 / 2.0))) * Float64(1.0 - Float64(Float64(Float64(1.0 / 2.0) * (Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0)) * Float64(h / l))))
end

MATLAB

function tmp = code(d, h, l, M, D)
	tmp = (((d / h) ^ (1.0 / 2.0)) * ((d / l) ^ (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * (((M * D) / (2.0 * d)) ^ 2.0)) * (h / l)));
end

Wolfram

code[d_, h_, l_, M_, D_] := N[(N[(N[Power[N[(d / h), $MachinePrecision], N[(1.0 / 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(d / l), $MachinePrecision], N[(1.0 / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(N[(N[(1.0 / 2.0), $MachinePrecision] * N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{-d}\\ \mathbf{if}\;h \leq -3.1 \cdot 10^{+238}:\\ \;\;\;\;\frac{t_1}{\sqrt{-h}} \cdot \left(t_0 \cdot \left(1 + \frac{h}{\ell} \cdot \left({\left(\frac{M_m}{2} \cdot \frac{D}{d}\right)}^{2} \cdot -0.5\right)\right)\right)\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(\sqrt{\frac{d}{h}} \cdot \frac{t_1}{\sqrt{-\ell}}\right) \cdot \left(1 + 0.5 \cdot \frac{h \cdot {\left(D \cdot \frac{M_m}{d \cdot 2}\right)}^{2}}{-\ell}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{d}}{\sqrt{h}} \cdot \left(t_0 \cdot \left(1 + \frac{h \cdot \left(-0.5 \cdot {\left(\frac{D}{d} \cdot \left(M_m \cdot 0.5\right)\right)}^{2}\right)}{\ell}\right)\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (let* ((t_0 (sqrt (/ d l))) (t_1 (sqrt (- d))))
   (if (<= h -3.1e+238)
     (*
      (/ t_1 (sqrt (- h)))
      (* t_0 (+ 1.0 (* (/ h l) (* (pow (* (/ M_m 2.0) (/ D d)) 2.0) -0.5)))))
     (if (<= h -5e-310)
       (*
        (* (sqrt (/ d h)) (/ t_1 (sqrt (- l))))
        (+ 1.0 (* 0.5 (/ (* h (pow (* D (/ M_m (* d 2.0))) 2.0)) (- l)))))
       (*
        (/ (sqrt d) (sqrt h))
        (*
         t_0
         (+ 1.0 (/ (* h (* -0.5 (pow (* (/ D d) (* M_m 0.5)) 2.0))) l))))))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double t_0 = sqrt((d / l));
	double t_1 = sqrt(-d);
	double tmp;
	if (h <= -3.1e+238) {
		tmp = (t_1 / sqrt(-h)) * (t_0 * (1.0 + ((h / l) * (pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5))));
	} else if (h <= -5e-310) {
		tmp = (sqrt((d / h)) * (t_1 / sqrt(-l))) * (1.0 + (0.5 * ((h * pow((D * (M_m / (d * 2.0))), 2.0)) / -l)));
	} else {
		tmp = (sqrt(d) / sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * pow(((D / d) * (M_m * 0.5)), 2.0))) / l)));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt((d / l))
    t_1 = sqrt(-d)
    if (h <= (-3.1d+238)) then
        tmp = (t_1 / sqrt(-h)) * (t_0 * (1.0d0 + ((h / l) * ((((m_m / 2.0d0) * (d_1 / d)) ** 2.0d0) * (-0.5d0)))))
    else if (h <= (-5d-310)) then
        tmp = (sqrt((d / h)) * (t_1 / sqrt(-l))) * (1.0d0 + (0.5d0 * ((h * ((d_1 * (m_m / (d * 2.0d0))) ** 2.0d0)) / -l)))
    else
        tmp = (sqrt(d) / sqrt(h)) * (t_0 * (1.0d0 + ((h * ((-0.5d0) * (((d_1 / d) * (m_m * 0.5d0)) ** 2.0d0))) / l)))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double t_0 = Math.sqrt((d / l));
	double t_1 = Math.sqrt(-d);
	double tmp;
	if (h <= -3.1e+238) {
		tmp = (t_1 / Math.sqrt(-h)) * (t_0 * (1.0 + ((h / l) * (Math.pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5))));
	} else if (h <= -5e-310) {
		tmp = (Math.sqrt((d / h)) * (t_1 / Math.sqrt(-l))) * (1.0 + (0.5 * ((h * Math.pow((D * (M_m / (d * 2.0))), 2.0)) / -l)));
	} else {
		tmp = (Math.sqrt(d) / Math.sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * Math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	t_0 = math.sqrt((d / l))
	t_1 = math.sqrt(-d)
	tmp = 0
	if h <= -3.1e+238:
		tmp = (t_1 / math.sqrt(-h)) * (t_0 * (1.0 + ((h / l) * (math.pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5))))
	elif h <= -5e-310:
		tmp = (math.sqrt((d / h)) * (t_1 / math.sqrt(-l))) * (1.0 + (0.5 * ((h * math.pow((D * (M_m / (d * 2.0))), 2.0)) / -l)))
	else:
		tmp = (math.sqrt(d) / math.sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	t_0 = sqrt(Float64(d / l))
	t_1 = sqrt(Float64(-d))
	tmp = 0.0
	if (h <= -3.1e+238)
		tmp = Float64(Float64(t_1 / sqrt(Float64(-h))) * Float64(t_0 * Float64(1.0 + Float64(Float64(h / l) * Float64((Float64(Float64(M_m / 2.0) * Float64(D / d)) ^ 2.0) * -0.5)))));
	elseif (h <= -5e-310)
		tmp = Float64(Float64(sqrt(Float64(d / h)) * Float64(t_1 / sqrt(Float64(-l)))) * Float64(1.0 + Float64(0.5 * Float64(Float64(h * (Float64(D * Float64(M_m / Float64(d * 2.0))) ^ 2.0)) / Float64(-l)))));
	else
		tmp = Float64(Float64(sqrt(d) / sqrt(h)) * Float64(t_0 * Float64(1.0 + Float64(Float64(h * Float64(-0.5 * (Float64(Float64(D / d) * Float64(M_m * 0.5)) ^ 2.0))) / l))));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	t_0 = sqrt((d / l));
	t_1 = sqrt(-d);
	tmp = 0.0;
	if (h <= -3.1e+238)
		tmp = (t_1 / sqrt(-h)) * (t_0 * (1.0 + ((h / l) * ((((M_m / 2.0) * (D / d)) ^ 2.0) * -0.5))));
	elseif (h <= -5e-310)
		tmp = (sqrt((d / h)) * (t_1 / sqrt(-l))) * (1.0 + (0.5 * ((h * ((D * (M_m / (d * 2.0))) ^ 2.0)) / -l)));
	else
		tmp = (sqrt(d) / sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * (((D / d) * (M_m * 0.5)) ^ 2.0))) / l)));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := Block[{t$95$0 = N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[(-d)], $MachinePrecision]}, If[LessEqual[h, -3.1e+238], N[(N[(t$95$1 / N[Sqrt[(-h)], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(1.0 + N[(N[(h / l), $MachinePrecision] * N[(N[Power[N[(N[(M$95$m / 2.0), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[h, -5e-310], N[(N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(N[(h * N[Power[N[(D * N[(M$95$m / N[(d * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / (-l)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(1.0 + N[(N[(h * N[(-0.5 * N[Power[N[(N[(D / d), $MachinePrecision] * N[(M$95$m * 0.5), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 2: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\left({\left(\frac{d}{h}\right)}^{0.5} \cdot {\left(\frac{d}{\ell}\right)}^{0.5}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M_m \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \leq \infty:\\ \;\;\;\;\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - 0.5 \cdot {\left(D \cdot \left(\left(M_m \cdot \frac{0.5}{d}\right) \cdot \sqrt{\frac{h}{\ell}}\right)\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot \left(\frac{{\left(M_m \cdot D\right)}^{2}}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<=
      (*
       (* (pow (/ d h) 0.5) (pow (/ d l) 0.5))
       (- 1.0 (* (/ h l) (* 0.5 (pow (/ (* M_m D) (* d 2.0)) 2.0)))))
      INFINITY)
   (*
    (* (sqrt (/ d l)) (sqrt (/ d h)))
    (- 1.0 (* 0.5 (pow (* D (* (* M_m (/ 0.5 d)) (sqrt (/ h l)))) 2.0))))
   (* -0.125 (* (/ (pow (* M_m D) 2.0) d) (sqrt (/ h (pow l 3.0)))))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (((pow((d / h), 0.5) * pow((d / l), 0.5)) * (1.0 - ((h / l) * (0.5 * pow(((M_m * D) / (d * 2.0)), 2.0))))) <= ((double) INFINITY)) {
		tmp = (sqrt((d / l)) * sqrt((d / h))) * (1.0 - (0.5 * pow((D * ((M_m * (0.5 / d)) * sqrt((h / l)))), 2.0)));
	} else {
		tmp = -0.125 * ((pow((M_m * D), 2.0) / d) * sqrt((h / pow(l, 3.0))));
	}
	return tmp;
}

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (((Math.pow((d / h), 0.5) * Math.pow((d / l), 0.5)) * (1.0 - ((h / l) * (0.5 * Math.pow(((M_m * D) / (d * 2.0)), 2.0))))) <= Double.POSITIVE_INFINITY) {
		tmp = (Math.sqrt((d / l)) * Math.sqrt((d / h))) * (1.0 - (0.5 * Math.pow((D * ((M_m * (0.5 / d)) * Math.sqrt((h / l)))), 2.0)));
	} else {
		tmp = -0.125 * ((Math.pow((M_m * D), 2.0) / d) * Math.sqrt((h / Math.pow(l, 3.0))));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if ((math.pow((d / h), 0.5) * math.pow((d / l), 0.5)) * (1.0 - ((h / l) * (0.5 * math.pow(((M_m * D) / (d * 2.0)), 2.0))))) <= math.inf:
		tmp = (math.sqrt((d / l)) * math.sqrt((d / h))) * (1.0 - (0.5 * math.pow((D * ((M_m * (0.5 / d)) * math.sqrt((h / l)))), 2.0)))
	else:
		tmp = -0.125 * ((math.pow((M_m * D), 2.0) / d) * math.sqrt((h / math.pow(l, 3.0))))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (Float64(Float64((Float64(d / h) ^ 0.5) * (Float64(d / l) ^ 0.5)) * Float64(1.0 - Float64(Float64(h / l) * Float64(0.5 * (Float64(Float64(M_m * D) / Float64(d * 2.0)) ^ 2.0))))) <= Inf)
		tmp = Float64(Float64(sqrt(Float64(d / l)) * sqrt(Float64(d / h))) * Float64(1.0 - Float64(0.5 * (Float64(D * Float64(Float64(M_m * Float64(0.5 / d)) * sqrt(Float64(h / l)))) ^ 2.0))));
	else
		tmp = Float64(-0.125 * Float64(Float64((Float64(M_m * D) ^ 2.0) / d) * sqrt(Float64(h / (l ^ 3.0)))));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (((((d / h) ^ 0.5) * ((d / l) ^ 0.5)) * (1.0 - ((h / l) * (0.5 * (((M_m * D) / (d * 2.0)) ^ 2.0))))) <= Inf)
		tmp = (sqrt((d / l)) * sqrt((d / h))) * (1.0 - (0.5 * ((D * ((M_m * (0.5 / d)) * sqrt((h / l)))) ^ 2.0)));
	else
		tmp = -0.125 * ((((M_m * D) ^ 2.0) / d) * sqrt((h / (l ^ 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[N[(N[(N[Power[N[(d / h), $MachinePrecision], 0.5], $MachinePrecision] * N[Power[N[(d / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(N[(h / l), $MachinePrecision] * N[(0.5 * N[Power[N[(N[(M$95$m * D), $MachinePrecision] / N[(d * 2.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(0.5 * N[Power[N[(D * N[(N[(M$95$m * N[(0.5 / d), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(h / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.125 * N[(N[(N[Power[N[(M$95$m * D), $MachinePrecision], 2.0], $MachinePrecision] / d), $MachinePrecision] * N[Sqrt[N[(h / N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 70.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}}\\ \mathbf{if}\;\ell \leq 2.8 \cdot 10^{-308}:\\ \;\;\;\;\left(t_0 \cdot t_1\right) \cdot \left(1 + 0.5 \cdot \frac{h \cdot {\left(\frac{M_m}{d \cdot \frac{2}{D}}\right)}^{2}}{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 4.7 \cdot 10^{+176}:\\ \;\;\;\;\left(t_0 \cdot \left(1 + \frac{h}{\ell} \cdot \left({\left(\frac{M_m}{2} \cdot \frac{D}{d}\right)}^{2} \cdot -0.5\right)\right)\right) \cdot \frac{\sqrt{d}}{\sqrt{h}}\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(\frac{h}{\ell} \cdot {\left(\frac{D}{2} \cdot \frac{M_m}{d}\right)}^{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (let* ((t_0 (sqrt (/ d l))) (t_1 (sqrt (/ d h))))
   (if (<= l 2.8e-308)
     (*
      (* t_0 t_1)
      (+ 1.0 (* 0.5 (/ (* h (pow (/ M_m (* d (/ 2.0 D))) 2.0)) (- l)))))
     (if (<= l 4.7e+176)
       (*
        (* t_0 (+ 1.0 (* (/ h l) (* (pow (* (/ M_m 2.0) (/ D d)) 2.0) -0.5))))
        (/ (sqrt d) (sqrt h)))
       (*
        (* t_1 (/ (sqrt d) (sqrt l)))
        (- 1.0 (* 0.5 (* (/ h l) (pow (* (/ D 2.0) (/ M_m d)) 2.0)))))))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double t_0 = sqrt((d / l));
	double t_1 = sqrt((d / h));
	double tmp;
	if (l <= 2.8e-308) {
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * pow((M_m / (d * (2.0 / D))), 2.0)) / -l)));
	} else if (l <= 4.7e+176) {
		tmp = (t_0 * (1.0 + ((h / l) * (pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5)))) * (sqrt(d) / sqrt(h));
	} else {
		tmp = (t_1 * (sqrt(d) / sqrt(l))) * (1.0 - (0.5 * ((h / l) * pow(((D / 2.0) * (M_m / d)), 2.0))));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt((d / l))
    t_1 = sqrt((d / h))
    if (l <= 2.8d-308) then
        tmp = (t_0 * t_1) * (1.0d0 + (0.5d0 * ((h * ((m_m / (d * (2.0d0 / d_1))) ** 2.0d0)) / -l)))
    else if (l <= 4.7d+176) then
        tmp = (t_0 * (1.0d0 + ((h / l) * ((((m_m / 2.0d0) * (d_1 / d)) ** 2.0d0) * (-0.5d0))))) * (sqrt(d) / sqrt(h))
    else
        tmp = (t_1 * (sqrt(d) / sqrt(l))) * (1.0d0 - (0.5d0 * ((h / l) * (((d_1 / 2.0d0) * (m_m / d)) ** 2.0d0))))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double t_0 = Math.sqrt((d / l));
	double t_1 = Math.sqrt((d / h));
	double tmp;
	if (l <= 2.8e-308) {
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * Math.pow((M_m / (d * (2.0 / D))), 2.0)) / -l)));
	} else if (l <= 4.7e+176) {
		tmp = (t_0 * (1.0 + ((h / l) * (Math.pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5)))) * (Math.sqrt(d) / Math.sqrt(h));
	} else {
		tmp = (t_1 * (Math.sqrt(d) / Math.sqrt(l))) * (1.0 - (0.5 * ((h / l) * Math.pow(((D / 2.0) * (M_m / d)), 2.0))));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	t_0 = math.sqrt((d / l))
	t_1 = math.sqrt((d / h))
	tmp = 0
	if l <= 2.8e-308:
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * math.pow((M_m / (d * (2.0 / D))), 2.0)) / -l)))
	elif l <= 4.7e+176:
		tmp = (t_0 * (1.0 + ((h / l) * (math.pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5)))) * (math.sqrt(d) / math.sqrt(h))
	else:
		tmp = (t_1 * (math.sqrt(d) / math.sqrt(l))) * (1.0 - (0.5 * ((h / l) * math.pow(((D / 2.0) * (M_m / d)), 2.0))))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	t_0 = sqrt(Float64(d / l))
	t_1 = sqrt(Float64(d / h))
	tmp = 0.0
	if (l <= 2.8e-308)
		tmp = Float64(Float64(t_0 * t_1) * Float64(1.0 + Float64(0.5 * Float64(Float64(h * (Float64(M_m / Float64(d * Float64(2.0 / D))) ^ 2.0)) / Float64(-l)))));
	elseif (l <= 4.7e+176)
		tmp = Float64(Float64(t_0 * Float64(1.0 + Float64(Float64(h / l) * Float64((Float64(Float64(M_m / 2.0) * Float64(D / d)) ^ 2.0) * -0.5)))) * Float64(sqrt(d) / sqrt(h)));
	else
		tmp = Float64(Float64(t_1 * Float64(sqrt(d) / sqrt(l))) * Float64(1.0 - Float64(0.5 * Float64(Float64(h / l) * (Float64(Float64(D / 2.0) * Float64(M_m / d)) ^ 2.0)))));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	t_0 = sqrt((d / l));
	t_1 = sqrt((d / h));
	tmp = 0.0;
	if (l <= 2.8e-308)
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * ((M_m / (d * (2.0 / D))) ^ 2.0)) / -l)));
	elseif (l <= 4.7e+176)
		tmp = (t_0 * (1.0 + ((h / l) * ((((M_m / 2.0) * (D / d)) ^ 2.0) * -0.5)))) * (sqrt(d) / sqrt(h));
	else
		tmp = (t_1 * (sqrt(d) / sqrt(l))) * (1.0 - (0.5 * ((h / l) * (((D / 2.0) * (M_m / d)) ^ 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := Block[{t$95$0 = N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[l, 2.8e-308], N[(N[(t$95$0 * t$95$1), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(N[(h * N[Power[N[(M$95$m / N[(d * N[(2.0 / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / (-l)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 4.7e+176], N[(N[(t$95$0 * N[(1.0 + N[(N[(h / l), $MachinePrecision] * N[(N[Power[N[(N[(M$95$m / 2.0), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(0.5 * N[(N[(h / l), $MachinePrecision] * N[Power[N[(N[(D / 2.0), $MachinePrecision] * N[(M$95$m / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 4: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}}\\ \mathbf{if}\;\ell \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\left(t_0 \cdot t_1\right) \cdot \left(1 + 0.5 \cdot \frac{h \cdot {\left(\frac{M_m}{d \cdot \frac{2}{D}}\right)}^{2}}{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 6.2 \cdot 10^{+178}:\\ \;\;\;\;\frac{\sqrt{d}}{\sqrt{h}} \cdot \left(t_0 \cdot \left(1 + \frac{h \cdot \left(-0.5 \cdot {\left(\frac{D}{d} \cdot \left(M_m \cdot 0.5\right)\right)}^{2}\right)}{\ell}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(\frac{h}{\ell} \cdot {\left(\frac{D}{2} \cdot \frac{M_m}{d}\right)}^{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (let* ((t_0 (sqrt (/ d l))) (t_1 (sqrt (/ d h))))
   (if (<= l -5e-311)
     (*
      (* t_0 t_1)
      (+ 1.0 (* 0.5 (/ (* h (pow (/ M_m (* d (/ 2.0 D))) 2.0)) (- l)))))
     (if (<= l 6.2e+178)
       (*
        (/ (sqrt d) (sqrt h))
        (* t_0 (+ 1.0 (/ (* h (* -0.5 (pow (* (/ D d) (* M_m 0.5)) 2.0))) l))))
       (*
        (* t_1 (/ (sqrt d) (sqrt l)))
        (- 1.0 (* 0.5 (* (/ h l) (pow (* (/ D 2.0) (/ M_m d)) 2.0)))))))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double t_0 = sqrt((d / l));
	double t_1 = sqrt((d / h));
	double tmp;
	if (l <= -5e-311) {
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * pow((M_m / (d * (2.0 / D))), 2.0)) / -l)));
	} else if (l <= 6.2e+178) {
		tmp = (sqrt(d) / sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * pow(((D / d) * (M_m * 0.5)), 2.0))) / l)));
	} else {
		tmp = (t_1 * (sqrt(d) / sqrt(l))) * (1.0 - (0.5 * ((h / l) * pow(((D / 2.0) * (M_m / d)), 2.0))));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt((d / l))
    t_1 = sqrt((d / h))
    if (l <= (-5d-311)) then
        tmp = (t_0 * t_1) * (1.0d0 + (0.5d0 * ((h * ((m_m / (d * (2.0d0 / d_1))) ** 2.0d0)) / -l)))
    else if (l <= 6.2d+178) then
        tmp = (sqrt(d) / sqrt(h)) * (t_0 * (1.0d0 + ((h * ((-0.5d0) * (((d_1 / d) * (m_m * 0.5d0)) ** 2.0d0))) / l)))
    else
        tmp = (t_1 * (sqrt(d) / sqrt(l))) * (1.0d0 - (0.5d0 * ((h / l) * (((d_1 / 2.0d0) * (m_m / d)) ** 2.0d0))))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double t_0 = Math.sqrt((d / l));
	double t_1 = Math.sqrt((d / h));
	double tmp;
	if (l <= -5e-311) {
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * Math.pow((M_m / (d * (2.0 / D))), 2.0)) / -l)));
	} else if (l <= 6.2e+178) {
		tmp = (Math.sqrt(d) / Math.sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * Math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)));
	} else {
		tmp = (t_1 * (Math.sqrt(d) / Math.sqrt(l))) * (1.0 - (0.5 * ((h / l) * Math.pow(((D / 2.0) * (M_m / d)), 2.0))));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	t_0 = math.sqrt((d / l))
	t_1 = math.sqrt((d / h))
	tmp = 0
	if l <= -5e-311:
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * math.pow((M_m / (d * (2.0 / D))), 2.0)) / -l)))
	elif l <= 6.2e+178:
		tmp = (math.sqrt(d) / math.sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)))
	else:
		tmp = (t_1 * (math.sqrt(d) / math.sqrt(l))) * (1.0 - (0.5 * ((h / l) * math.pow(((D / 2.0) * (M_m / d)), 2.0))))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	t_0 = sqrt(Float64(d / l))
	t_1 = sqrt(Float64(d / h))
	tmp = 0.0
	if (l <= -5e-311)
		tmp = Float64(Float64(t_0 * t_1) * Float64(1.0 + Float64(0.5 * Float64(Float64(h * (Float64(M_m / Float64(d * Float64(2.0 / D))) ^ 2.0)) / Float64(-l)))));
	elseif (l <= 6.2e+178)
		tmp = Float64(Float64(sqrt(d) / sqrt(h)) * Float64(t_0 * Float64(1.0 + Float64(Float64(h * Float64(-0.5 * (Float64(Float64(D / d) * Float64(M_m * 0.5)) ^ 2.0))) / l))));
	else
		tmp = Float64(Float64(t_1 * Float64(sqrt(d) / sqrt(l))) * Float64(1.0 - Float64(0.5 * Float64(Float64(h / l) * (Float64(Float64(D / 2.0) * Float64(M_m / d)) ^ 2.0)))));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	t_0 = sqrt((d / l));
	t_1 = sqrt((d / h));
	tmp = 0.0;
	if (l <= -5e-311)
		tmp = (t_0 * t_1) * (1.0 + (0.5 * ((h * ((M_m / (d * (2.0 / D))) ^ 2.0)) / -l)));
	elseif (l <= 6.2e+178)
		tmp = (sqrt(d) / sqrt(h)) * (t_0 * (1.0 + ((h * (-0.5 * (((D / d) * (M_m * 0.5)) ^ 2.0))) / l)));
	else
		tmp = (t_1 * (sqrt(d) / sqrt(l))) * (1.0 - (0.5 * ((h / l) * (((D / 2.0) * (M_m / d)) ^ 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := Block[{t$95$0 = N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[l, -5e-311], N[(N[(t$95$0 * t$95$1), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(N[(h * N[Power[N[(M$95$m / N[(d * N[(2.0 / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / (-l)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 6.2e+178], N[(N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(1.0 + N[(N[(h * N[(-0.5 * N[Power[N[(N[(D / d), $MachinePrecision] * N[(M$95$m * 0.5), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(0.5 * N[(N[(h / l), $MachinePrecision] * N[Power[N[(N[(D / 2.0), $MachinePrecision] * N[(M$95$m / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} t_0 := 1 + \frac{h \cdot \left(-0.5 \cdot {\left(\frac{D}{d} \cdot \left(M_m \cdot 0.5\right)\right)}^{2}\right)}{\ell}\\ \mathbf{if}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\frac{\sqrt{-d}}{\sqrt{-\ell}} \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{d}}{\sqrt{h}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot t_0\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* h (* -0.5 (pow (* (/ D d) (* M_m 0.5)) 2.0))) l))))
   (if (<= h -5e-310)
     (* (sqrt (/ d h)) (* (/ (sqrt (- d)) (sqrt (- l))) t_0))
     (* (/ (sqrt d) (sqrt h)) (* (sqrt (/ d l)) t_0)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double t_0 = 1.0 + ((h * (-0.5 * pow(((D / d) * (M_m * 0.5)), 2.0))) / l);
	double tmp;
	if (h <= -5e-310) {
		tmp = sqrt((d / h)) * ((sqrt(-d) / sqrt(-l)) * t_0);
	} else {
		tmp = (sqrt(d) / sqrt(h)) * (sqrt((d / l)) * t_0);
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((h * ((-0.5d0) * (((d_1 / d) * (m_m * 0.5d0)) ** 2.0d0))) / l)
    if (h <= (-5d-310)) then
        tmp = sqrt((d / h)) * ((sqrt(-d) / sqrt(-l)) * t_0)
    else
        tmp = (sqrt(d) / sqrt(h)) * (sqrt((d / l)) * t_0)
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double t_0 = 1.0 + ((h * (-0.5 * Math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l);
	double tmp;
	if (h <= -5e-310) {
		tmp = Math.sqrt((d / h)) * ((Math.sqrt(-d) / Math.sqrt(-l)) * t_0);
	} else {
		tmp = (Math.sqrt(d) / Math.sqrt(h)) * (Math.sqrt((d / l)) * t_0);
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	t_0 = 1.0 + ((h * (-0.5 * math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)
	tmp = 0
	if h <= -5e-310:
		tmp = math.sqrt((d / h)) * ((math.sqrt(-d) / math.sqrt(-l)) * t_0)
	else:
		tmp = (math.sqrt(d) / math.sqrt(h)) * (math.sqrt((d / l)) * t_0)
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	t_0 = Float64(1.0 + Float64(Float64(h * Float64(-0.5 * (Float64(Float64(D / d) * Float64(M_m * 0.5)) ^ 2.0))) / l))
	tmp = 0.0
	if (h <= -5e-310)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(Float64(sqrt(Float64(-d)) / sqrt(Float64(-l))) * t_0));
	else
		tmp = Float64(Float64(sqrt(d) / sqrt(h)) * Float64(sqrt(Float64(d / l)) * t_0));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	t_0 = 1.0 + ((h * (-0.5 * (((D / d) * (M_m * 0.5)) ^ 2.0))) / l);
	tmp = 0.0;
	if (h <= -5e-310)
		tmp = sqrt((d / h)) * ((sqrt(-d) / sqrt(-l)) * t_0);
	else
		tmp = (sqrt(d) / sqrt(h)) * (sqrt((d / l)) * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := Block[{t$95$0 = N[(1.0 + N[(N[(h * N[(-0.5 * N[Power[N[(N[(D / d), $MachinePrecision] * N[(M$95$m * 0.5), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[h, -5e-310], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[(N[Sqrt[(-d)], $MachinePrecision] / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 6: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq 7 \cdot 10^{+169}:\\ \;\;\;\;\left(1 + 0.5 \cdot \frac{h \cdot {\left(D \cdot \frac{M_m}{d \cdot 2}\right)}^{2}}{-\ell}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l 7e+169)
   (*
    (+ 1.0 (* 0.5 (/ (* h (pow (* D (/ M_m (* d 2.0))) 2.0)) (- l))))
    (* (sqrt (/ d l)) (sqrt (/ d h))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 7e+169) {
		tmp = (1.0 + (0.5 * ((h * pow((D * (M_m / (d * 2.0))), 2.0)) / -l))) * (sqrt((d / l)) * sqrt((d / h)));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= 7d+169) then
        tmp = (1.0d0 + (0.5d0 * ((h * ((d_1 * (m_m / (d * 2.0d0))) ** 2.0d0)) / -l))) * (sqrt((d / l)) * sqrt((d / h)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 7e+169) {
		tmp = (1.0 + (0.5 * ((h * Math.pow((D * (M_m / (d * 2.0))), 2.0)) / -l))) * (Math.sqrt((d / l)) * Math.sqrt((d / h)));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= 7e+169:
		tmp = (1.0 + (0.5 * ((h * math.pow((D * (M_m / (d * 2.0))), 2.0)) / -l))) * (math.sqrt((d / l)) * math.sqrt((d / h)))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= 7e+169)
		tmp = Float64(Float64(1.0 + Float64(0.5 * Float64(Float64(h * (Float64(D * Float64(M_m / Float64(d * 2.0))) ^ 2.0)) / Float64(-l)))) * Float64(sqrt(Float64(d / l)) * sqrt(Float64(d / h))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= 7e+169)
		tmp = (1.0 + (0.5 * ((h * ((D * (M_m / (d * 2.0))) ^ 2.0)) / -l))) * (sqrt((d / l)) * sqrt((d / h)));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, 7e+169], N[(N[(1.0 + N[(0.5 * N[(N[(h * N[Power[N[(D * N[(M$95$m / N[(d * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / (-l)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq 6.5 \cdot 10^{+169}:\\ \;\;\;\;\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 + 0.5 \cdot \frac{h \cdot {\left(\frac{M_m}{d \cdot \frac{2}{D}}\right)}^{2}}{-\ell}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l 6.5e+169)
   (*
    (* (sqrt (/ d l)) (sqrt (/ d h)))
    (+ 1.0 (* 0.5 (/ (* h (pow (/ M_m (* d (/ 2.0 D))) 2.0)) (- l)))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 6.5e+169) {
		tmp = (sqrt((d / l)) * sqrt((d / h))) * (1.0 + (0.5 * ((h * pow((M_m / (d * (2.0 / D))), 2.0)) / -l)));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= 6.5d+169) then
        tmp = (sqrt((d / l)) * sqrt((d / h))) * (1.0d0 + (0.5d0 * ((h * ((m_m / (d * (2.0d0 / d_1))) ** 2.0d0)) / -l)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 6.5e+169) {
		tmp = (Math.sqrt((d / l)) * Math.sqrt((d / h))) * (1.0 + (0.5 * ((h * Math.pow((M_m / (d * (2.0 / D))), 2.0)) / -l)));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= 6.5e+169:
		tmp = (math.sqrt((d / l)) * math.sqrt((d / h))) * (1.0 + (0.5 * ((h * math.pow((M_m / (d * (2.0 / D))), 2.0)) / -l)))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= 6.5e+169)
		tmp = Float64(Float64(sqrt(Float64(d / l)) * sqrt(Float64(d / h))) * Float64(1.0 + Float64(0.5 * Float64(Float64(h * (Float64(M_m / Float64(d * Float64(2.0 / D))) ^ 2.0)) / Float64(-l)))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= 6.5e+169)
		tmp = (sqrt((d / l)) * sqrt((d / h))) * (1.0 + (0.5 * ((h * ((M_m / (d * (2.0 / D))) ^ 2.0)) / -l)));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, 6.5e+169], N[(N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(N[(h * N[Power[N[(M$95$m / N[(d * N[(2.0 / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / (-l)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq 3.1 \cdot 10^{+168}:\\ \;\;\;\;\left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \frac{h}{\ell} \cdot \left({\left(\frac{M_m}{2} \cdot \frac{D}{d}\right)}^{2} \cdot -0.5\right)\right)\right) \cdot \sqrt{\frac{d}{h}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l 3.1e+168)
   (*
    (*
     (sqrt (/ d l))
     (+ 1.0 (* (/ h l) (* (pow (* (/ M_m 2.0) (/ D d)) 2.0) -0.5))))
    (sqrt (/ d h)))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 3.1e+168) {
		tmp = (sqrt((d / l)) * (1.0 + ((h / l) * (pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5)))) * sqrt((d / h));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= 3.1d+168) then
        tmp = (sqrt((d / l)) * (1.0d0 + ((h / l) * ((((m_m / 2.0d0) * (d_1 / d)) ** 2.0d0) * (-0.5d0))))) * sqrt((d / h))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 3.1e+168) {
		tmp = (Math.sqrt((d / l)) * (1.0 + ((h / l) * (Math.pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5)))) * Math.sqrt((d / h));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= 3.1e+168:
		tmp = (math.sqrt((d / l)) * (1.0 + ((h / l) * (math.pow(((M_m / 2.0) * (D / d)), 2.0) * -0.5)))) * math.sqrt((d / h))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= 3.1e+168)
		tmp = Float64(Float64(sqrt(Float64(d / l)) * Float64(1.0 + Float64(Float64(h / l) * Float64((Float64(Float64(M_m / 2.0) * Float64(D / d)) ^ 2.0) * -0.5)))) * sqrt(Float64(d / h)));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= 3.1e+168)
		tmp = (sqrt((d / l)) * (1.0 + ((h / l) * ((((M_m / 2.0) * (D / d)) ^ 2.0) * -0.5)))) * sqrt((d / h));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, 3.1e+168], N[(N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(N[(h / l), $MachinePrecision] * N[(N[Power[N[(N[(M$95$m / 2.0), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq 6.4 \cdot 10^{+168}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \frac{h}{\ell} \cdot \left(-0.5 \cdot {\left(\frac{M_m}{2 \cdot \frac{d}{D}}\right)}^{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l 6.4e+168)
   (*
    (sqrt (/ d h))
    (*
     (sqrt (/ d l))
     (+ 1.0 (* (/ h l) (* -0.5 (pow (/ M_m (* 2.0 (/ d D))) 2.0))))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 6.4e+168) {
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (-0.5 * pow((M_m / (2.0 * (d / D))), 2.0)))));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= 6.4d+168) then
        tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0d0 + ((h / l) * ((-0.5d0) * ((m_m / (2.0d0 * (d / d_1))) ** 2.0d0)))))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 6.4e+168) {
		tmp = Math.sqrt((d / h)) * (Math.sqrt((d / l)) * (1.0 + ((h / l) * (-0.5 * Math.pow((M_m / (2.0 * (d / D))), 2.0)))));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= 6.4e+168:
		tmp = math.sqrt((d / h)) * (math.sqrt((d / l)) * (1.0 + ((h / l) * (-0.5 * math.pow((M_m / (2.0 * (d / D))), 2.0)))))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= 6.4e+168)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(sqrt(Float64(d / l)) * Float64(1.0 + Float64(Float64(h / l) * Float64(-0.5 * (Float64(M_m / Float64(2.0 * Float64(d / D))) ^ 2.0))))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= 6.4e+168)
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (-0.5 * ((M_m / (2.0 * (d / D))) ^ 2.0)))));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, 6.4e+168], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(N[(h / l), $MachinePrecision] * N[(-0.5 * N[Power[N[(M$95$m / N[(2.0 * N[(d / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \frac{h \cdot \left(-0.5 \cdot {\left(\frac{D}{d} \cdot \left(M_m \cdot 0.5\right)\right)}^{2}\right)}{\ell}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l 3.3e+168)
   (*
    (sqrt (/ d h))
    (*
     (sqrt (/ d l))
     (+ 1.0 (/ (* h (* -0.5 (pow (* (/ D d) (* M_m 0.5)) 2.0))) l))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 3.3e+168) {
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h * (-0.5 * pow(((D / d) * (M_m * 0.5)), 2.0))) / l)));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= 3.3d+168) then
        tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0d0 + ((h * ((-0.5d0) * (((d_1 / d) * (m_m * 0.5d0)) ** 2.0d0))) / l)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= 3.3e+168) {
		tmp = Math.sqrt((d / h)) * (Math.sqrt((d / l)) * (1.0 + ((h * (-0.5 * Math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= 3.3e+168:
		tmp = math.sqrt((d / h)) * (math.sqrt((d / l)) * (1.0 + ((h * (-0.5 * math.pow(((D / d) * (M_m * 0.5)), 2.0))) / l)))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= 3.3e+168)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(sqrt(Float64(d / l)) * Float64(1.0 + Float64(Float64(h * Float64(-0.5 * (Float64(Float64(D / d) * Float64(M_m * 0.5)) ^ 2.0))) / l))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= 3.3e+168)
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h * (-0.5 * (((D / d) * (M_m * 0.5)) ^ 2.0))) / l)));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, 3.3e+168], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(N[(h * N[(-0.5 * N[Power[N[(N[(D / d), $MachinePrecision] * N[(M$95$m * 0.5), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\sqrt{-d} \cdot {\left(-\ell\right)}^{-0.5}\right)\\ \mathbf{elif}\;\ell \leq 5.8 \cdot 10^{-147} \lor \neg \left(\ell \leq 4.8 \cdot 10^{-65}\right) \land \ell \leq 10^{+36}:\\ \;\;\;\;-0.125 \cdot \left(\frac{{\left(M_m \cdot D\right)}^{2}}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l -5e-311)
   (* (sqrt (/ d h)) (* (sqrt (- d)) (pow (- l) -0.5)))
   (if (or (<= l 5.8e-147) (and (not (<= l 4.8e-65)) (<= l 1e+36)))
     (* -0.125 (* (/ (pow (* M_m D) 2.0) d) (sqrt (/ h (pow l 3.0)))))
     (/ d (* (sqrt h) (sqrt l))))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= -5e-311) {
		tmp = sqrt((d / h)) * (sqrt(-d) * pow(-l, -0.5));
	} else if ((l <= 5.8e-147) || (!(l <= 4.8e-65) && (l <= 1e+36))) {
		tmp = -0.125 * ((pow((M_m * D), 2.0) / d) * sqrt((h / pow(l, 3.0))));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= (-5d-311)) then
        tmp = sqrt((d / h)) * (sqrt(-d) * (-l ** (-0.5d0)))
    else if ((l <= 5.8d-147) .or. (.not. (l <= 4.8d-65)) .and. (l <= 1d+36)) then
        tmp = (-0.125d0) * ((((m_m * d_1) ** 2.0d0) / d) * sqrt((h / (l ** 3.0d0))))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= -5e-311) {
		tmp = Math.sqrt((d / h)) * (Math.sqrt(-d) * Math.pow(-l, -0.5));
	} else if ((l <= 5.8e-147) || (!(l <= 4.8e-65) && (l <= 1e+36))) {
		tmp = -0.125 * ((Math.pow((M_m * D), 2.0) / d) * Math.sqrt((h / Math.pow(l, 3.0))));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= -5e-311:
		tmp = math.sqrt((d / h)) * (math.sqrt(-d) * math.pow(-l, -0.5))
	elif (l <= 5.8e-147) or (not (l <= 4.8e-65) and (l <= 1e+36)):
		tmp = -0.125 * ((math.pow((M_m * D), 2.0) / d) * math.sqrt((h / math.pow(l, 3.0))))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= -5e-311)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(sqrt(Float64(-d)) * (Float64(-l) ^ -0.5)));
	elseif ((l <= 5.8e-147) || (!(l <= 4.8e-65) && (l <= 1e+36)))
		tmp = Float64(-0.125 * Float64(Float64((Float64(M_m * D) ^ 2.0) / d) * sqrt(Float64(h / (l ^ 3.0)))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= -5e-311)
		tmp = sqrt((d / h)) * (sqrt(-d) * (-l ^ -0.5));
	elseif ((l <= 5.8e-147) || (~((l <= 4.8e-65)) && (l <= 1e+36)))
		tmp = -0.125 * ((((M_m * D) ^ 2.0) / d) * sqrt((h / (l ^ 3.0))));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, -5e-311], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[(-d)], $MachinePrecision] * N[Power[(-l), -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[l, 5.8e-147], And[N[Not[LessEqual[l, 4.8e-65]], $MachinePrecision], LessEqual[l, 1e+36]]], N[(-0.125 * N[(N[(N[Power[N[(M$95$m * D), $MachinePrecision], 2.0], $MachinePrecision] / d), $MachinePrecision] * N[Sqrt[N[(h / N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 12: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\sqrt{-d} \cdot {\left(-\ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l -5e-311)
   (* (sqrt (/ d h)) (* (sqrt (- d)) (pow (- l) -0.5)))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= -5e-311) {
		tmp = sqrt((d / h)) * (sqrt(-d) * pow(-l, -0.5));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= (-5d-311)) then
        tmp = sqrt((d / h)) * (sqrt(-d) * (-l ** (-0.5d0)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= -5e-311) {
		tmp = Math.sqrt((d / h)) * (Math.sqrt(-d) * Math.pow(-l, -0.5));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= -5e-311:
		tmp = math.sqrt((d / h)) * (math.sqrt(-d) * math.pow(-l, -0.5))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= -5e-311)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(sqrt(Float64(-d)) * (Float64(-l) ^ -0.5)));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= -5e-311)
		tmp = sqrt((d / h)) * (sqrt(-d) * (-l ^ -0.5));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, -5e-311], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[(-d)], $MachinePrecision] * N[Power[(-l), -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \frac{\sqrt{-d}}{\sqrt{-\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= l -5e-311)
   (* (sqrt (/ d h)) (/ (sqrt (- d)) (sqrt (- l))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= -5e-311) {
		tmp = sqrt((d / h)) * (sqrt(-d) / sqrt(-l));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (l <= (-5d-311)) then
        tmp = sqrt((d / h)) * (sqrt(-d) / sqrt(-l))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (l <= -5e-311) {
		tmp = Math.sqrt((d / h)) * (Math.sqrt(-d) / Math.sqrt(-l));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if l <= -5e-311:
		tmp = math.sqrt((d / h)) * (math.sqrt(-d) / math.sqrt(-l))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (l <= -5e-311)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(sqrt(Float64(-d)) / sqrt(Float64(-l))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (l <= -5e-311)
		tmp = sqrt((d / h)) * (sqrt(-d) / sqrt(-l));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[l, -5e-311], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[(-d)], $MachinePrecision] / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 44.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;h \leq 1.05 \cdot 10^{-290}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \frac{1}{\sqrt{\frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= h 1.05e-290)
   (* (sqrt (/ d h)) (/ 1.0 (sqrt (/ l d))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.05e-290) {
		tmp = sqrt((d / h)) * (1.0 / sqrt((l / d)));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (h <= 1.05d-290) then
        tmp = sqrt((d / h)) * (1.0d0 / sqrt((l / d)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.05e-290) {
		tmp = Math.sqrt((d / h)) * (1.0 / Math.sqrt((l / d)));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if h <= 1.05e-290:
		tmp = math.sqrt((d / h)) * (1.0 / math.sqrt((l / d)))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (h <= 1.05e-290)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(1.0 / sqrt(Float64(l / d))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (h <= 1.05e-290)
		tmp = sqrt((d / h)) * (1.0 / sqrt((l / d)));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[h, 1.05e-290], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(1.0 / N[Sqrt[N[(l / d), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 15: 43.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;h \leq 7 \cdot 10^{-256}:\\ \;\;\;\;\sqrt{\frac{d}{\ell}} \cdot \frac{1}{\sqrt{\frac{h}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= h 7e-256)
   (* (sqrt (/ d l)) (/ 1.0 (sqrt (/ h d))))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 7e-256) {
		tmp = sqrt((d / l)) * (1.0 / sqrt((h / d)));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (h <= 7d-256) then
        tmp = sqrt((d / l)) * (1.0d0 / sqrt((h / d)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 7e-256) {
		tmp = Math.sqrt((d / l)) * (1.0 / Math.sqrt((h / d)));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if h <= 7e-256:
		tmp = math.sqrt((d / l)) * (1.0 / math.sqrt((h / d)))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (h <= 7e-256)
		tmp = Float64(sqrt(Float64(d / l)) * Float64(1.0 / sqrt(Float64(h / d))));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (h <= 7e-256)
		tmp = sqrt((d / l)) * (1.0 / sqrt((h / d)));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[h, 7e-256], N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[(1.0 / N[Sqrt[N[(h / d), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 16: 44.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;h \leq 1.05 \cdot 10^{-290}:\\ \;\;\;\;\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= h 1.05e-290)
   (* (sqrt (/ d l)) (sqrt (/ d h)))
   (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.05e-290) {
		tmp = sqrt((d / l)) * sqrt((d / h));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (h <= 1.05d-290) then
        tmp = sqrt((d / l)) * sqrt((d / h))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.05e-290) {
		tmp = Math.sqrt((d / l)) * Math.sqrt((d / h));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if h <= 1.05e-290:
		tmp = math.sqrt((d / l)) * math.sqrt((d / h))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (h <= 1.05e-290)
		tmp = Float64(sqrt(Float64(d / l)) * sqrt(Float64(d / h)));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (h <= 1.05e-290)
		tmp = sqrt((d / l)) * sqrt((d / h));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[h, 1.05e-290], N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 40.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;h \leq 1.05 \cdot 10^{-290}:\\ \;\;\;\;\sqrt{\frac{d}{\ell} \cdot \frac{d}{h}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= h 1.05e-290) (sqrt (* (/ d l) (/ d h))) (/ d (* (sqrt h) (sqrt l)))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.05e-290) {
		tmp = sqrt(((d / l) * (d / h)));
	} else {
		tmp = d / (sqrt(h) * sqrt(l));
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (h <= 1.05d-290) then
        tmp = sqrt(((d / l) * (d / h)))
    else
        tmp = d / (sqrt(h) * sqrt(l))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.05e-290) {
		tmp = Math.sqrt(((d / l) * (d / h)));
	} else {
		tmp = d / (Math.sqrt(h) * Math.sqrt(l));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if h <= 1.05e-290:
		tmp = math.sqrt(((d / l) * (d / h)))
	else:
		tmp = d / (math.sqrt(h) * math.sqrt(l))
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (h <= 1.05e-290)
		tmp = sqrt(Float64(Float64(d / l) * Float64(d / h)));
	else
		tmp = Float64(d / Float64(sqrt(h) * sqrt(l)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (h <= 1.05e-290)
		tmp = sqrt(((d / l) * (d / h)));
	else
		tmp = d / (sqrt(h) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[h, 1.05e-290], N[Sqrt[N[(N[(d / l), $MachinePrecision] * N[(d / h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 18: 36.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;h \leq 1.15 \cdot 10^{-255}:\\ \;\;\;\;\sqrt{\frac{d}{\ell} \cdot \frac{d}{h}}\\ \mathbf{else}:\\ \;\;\;\;d \cdot {\left(\frac{\frac{1}{h}}{\ell}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= h 1.15e-255)
   (sqrt (* (/ d l) (/ d h)))
   (* d (pow (/ (/ 1.0 h) l) 0.5))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.15e-255) {
		tmp = sqrt(((d / l) * (d / h)));
	} else {
		tmp = d * pow(((1.0 / h) / l), 0.5);
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (h <= 1.15d-255) then
        tmp = sqrt(((d / l) * (d / h)))
    else
        tmp = d * (((1.0d0 / h) / l) ** 0.5d0)
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 1.15e-255) {
		tmp = Math.sqrt(((d / l) * (d / h)));
	} else {
		tmp = d * Math.pow(((1.0 / h) / l), 0.5);
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if h <= 1.15e-255:
		tmp = math.sqrt(((d / l) * (d / h)))
	else:
		tmp = d * math.pow(((1.0 / h) / l), 0.5)
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (h <= 1.15e-255)
		tmp = sqrt(Float64(Float64(d / l) * Float64(d / h)));
	else
		tmp = Float64(d * (Float64(Float64(1.0 / h) / l) ^ 0.5));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (h <= 1.15e-255)
		tmp = sqrt(((d / l) * (d / h)));
	else
		tmp = d * (((1.0 / h) / l) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[h, 1.15e-255], N[Sqrt[N[(N[(d / l), $MachinePrecision] * N[(d / h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(d * N[Power[N[(N[(1.0 / h), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 19: 36.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ \begin{array}{l} \mathbf{if}\;h \leq 4.2 \cdot 10^{-256}:\\ \;\;\;\;\sqrt{\frac{d}{\ell} \cdot \frac{d}{h}}\\ \mathbf{else}:\\ \;\;\;\;d \cdot {\left(h \cdot \ell\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D)
 :precision binary64
 (if (<= h 4.2e-256) (sqrt (* (/ d l) (/ d h))) (* d (pow (* h l) -0.5))))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 4.2e-256) {
		tmp = sqrt(((d / l) * (d / h)));
	} else {
		tmp = d * pow((h * l), -0.5);
	}
	return tmp;
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (h <= 4.2d-256) then
        tmp = sqrt(((d / l) * (d / h)))
    else
        tmp = d * ((h * l) ** (-0.5d0))
    end if
    code = tmp
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	double tmp;
	if (h <= 4.2e-256) {
		tmp = Math.sqrt(((d / l) * (d / h)));
	} else {
		tmp = d * Math.pow((h * l), -0.5);
	}
	return tmp;
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	tmp = 0
	if h <= 4.2e-256:
		tmp = math.sqrt(((d / l) * (d / h)))
	else:
		tmp = d * math.pow((h * l), -0.5)
	return tmp

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	tmp = 0.0
	if (h <= 4.2e-256)
		tmp = sqrt(Float64(Float64(d / l) * Float64(d / h)));
	else
		tmp = Float64(d * (Float64(h * l) ^ -0.5));
	end
	return tmp
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp_2 = code(d, h, l, M_m, D)
	tmp = 0.0;
	if (h <= 4.2e-256)
		tmp = sqrt(((d / l) * (d / h)));
	else
		tmp = d * ((h * l) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := If[LessEqual[h, 4.2e-256], N[Sqrt[N[(N[(d / l), $MachinePrecision] * N[(d / h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(d * N[Power[N[(h * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 20: 25.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ [d, h, l, M_m, D] = \mathsf{sort}([d, h, l, M_m, D])\\ \\ d \cdot {\left(h \cdot \ell\right)}^{-0.5} \end{array} \]

FPCore

M_m = (fabs.f64 M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
(FPCore (d h l M_m D) :precision binary64 (* d (pow (* h l) -0.5)))

C

M_m = fabs(M);
assert(d < h && h < l && l < M_m && M_m < D);
double code(double d, double h, double l, double M_m, double D) {
	return d * pow((h * l), -0.5);
}

Fortran

M_m = abs(M)
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
real(8) function code(d, h, l, m_m, d_1)
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_1
    code = d * ((h * l) ** (-0.5d0))
end function

Java

M_m = Math.abs(M);
assert d < h && h < l && l < M_m && M_m < D;
public static double code(double d, double h, double l, double M_m, double D) {
	return d * Math.pow((h * l), -0.5);
}

Python

M_m = math.fabs(M)
[d, h, l, M_m, D] = sort([d, h, l, M_m, D])
def code(d, h, l, M_m, D):
	return d * math.pow((h * l), -0.5)

Julia

M_m = abs(M)
d, h, l, M_m, D = sort([d, h, l, M_m, D])
function code(d, h, l, M_m, D)
	return Float64(d * (Float64(h * l) ^ -0.5))
end

MATLAB

M_m = abs(M);
d, h, l, M_m, D = num2cell(sort([d, h, l, M_m, D])){:}
function tmp = code(d, h, l, M_m, D)
	tmp = d * ((h * l) ^ -0.5);
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
NOTE: d, h, l, M_m, and D should be sorted in increasing order before calling this function.
code[d_, h_, l_, M$95$m_, D_] := N[(d * N[Power[N[(h * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023347 
(FPCore (d h l M D)
  :name "Henrywood and Agarwal, Equation (12)"
  :precision binary64
  (* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))