Henrywood and Agarwal, Equation (12)

Percentage Accurate: 66.0% → 74.8%

Time: 25.6s

Alternatives: 19

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: 66.0% 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: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - 0.5 \cdot \frac{h \cdot {\left(\frac{\left(0.5 \cdot M\right) \cdot D}{d}\right)}^{2}}{\ell}\\ t_1 := \sqrt{\frac{d}{h}}\\ t_2 := \sqrt{-d}\\ \mathbf{if}\;h \leq -2.55 \cdot 10^{-110}:\\ \;\;\;\;\left(t_1 \cdot \frac{t_2}{\sqrt{-\ell}}\right) \cdot t_0\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{t_2}{\sqrt{-h}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \frac{h}{\ell} \cdot \left({\left(\frac{D}{\frac{d \cdot 2}{M}}\right)}^{2} \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0 (- 1.0 (* 0.5 (/ (* h (pow (/ (* (* 0.5 M) D) d) 2.0)) l))))
        (t_1 (sqrt (/ d h)))
        (t_2 (sqrt (- d))))
   (if (<= h -2.55e-110)
     (* (* t_1 (/ t_2 (sqrt (- l)))) t_0)
     (if (<= h -5e-310)
       (*
        (/ t_2 (sqrt (- h)))
        (*
         (sqrt (/ d l))
         (+ 1.0 (* (/ h l) (* (pow (/ D (/ (* d 2.0) M)) 2.0) -0.5)))))
       (* t_0 (* t_1 (/ (sqrt d) (sqrt l))))))))

C

double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 - (0.5 * ((h * pow((((0.5 * M) * D) / d), 2.0)) / l));
	double t_1 = sqrt((d / h));
	double t_2 = sqrt(-d);
	double tmp;
	if (h <= -2.55e-110) {
		tmp = (t_1 * (t_2 / sqrt(-l))) * t_0;
	} else if (h <= -5e-310) {
		tmp = (t_2 / sqrt(-h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (pow((D / ((d * 2.0) / M)), 2.0) * -0.5))));
	} else {
		tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (0.5d0 * ((h * ((((0.5d0 * m) * d_1) / d) ** 2.0d0)) / l))
    t_1 = sqrt((d / h))
    t_2 = sqrt(-d)
    if (h <= (-2.55d-110)) then
        tmp = (t_1 * (t_2 / sqrt(-l))) * t_0
    else if (h <= (-5d-310)) then
        tmp = (t_2 / sqrt(-h)) * (sqrt((d / l)) * (1.0d0 + ((h / l) * (((d_1 / ((d * 2.0d0) / m)) ** 2.0d0) * (-0.5d0)))))
    else
        tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 - (0.5 * ((h * Math.pow((((0.5 * M) * D) / d), 2.0)) / l));
	double t_1 = Math.sqrt((d / h));
	double t_2 = Math.sqrt(-d);
	double tmp;
	if (h <= -2.55e-110) {
		tmp = (t_1 * (t_2 / Math.sqrt(-l))) * t_0;
	} else if (h <= -5e-310) {
		tmp = (t_2 / Math.sqrt(-h)) * (Math.sqrt((d / l)) * (1.0 + ((h / l) * (Math.pow((D / ((d * 2.0) / M)), 2.0) * -0.5))));
	} else {
		tmp = t_0 * (t_1 * (Math.sqrt(d) / Math.sqrt(l)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	t_0 = 1.0 - (0.5 * ((h * math.pow((((0.5 * M) * D) / d), 2.0)) / l))
	t_1 = math.sqrt((d / h))
	t_2 = math.sqrt(-d)
	tmp = 0
	if h <= -2.55e-110:
		tmp = (t_1 * (t_2 / math.sqrt(-l))) * t_0
	elif h <= -5e-310:
		tmp = (t_2 / math.sqrt(-h)) * (math.sqrt((d / l)) * (1.0 + ((h / l) * (math.pow((D / ((d * 2.0) / M)), 2.0) * -0.5))))
	else:
		tmp = t_0 * (t_1 * (math.sqrt(d) / math.sqrt(l)))
	return tmp

Julia

function code(d, h, l, M, D)
	t_0 = Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(Float64(0.5 * M) * D) / d) ^ 2.0)) / l)))
	t_1 = sqrt(Float64(d / h))
	t_2 = sqrt(Float64(-d))
	tmp = 0.0
	if (h <= -2.55e-110)
		tmp = Float64(Float64(t_1 * Float64(t_2 / sqrt(Float64(-l)))) * t_0);
	elseif (h <= -5e-310)
		tmp = Float64(Float64(t_2 / sqrt(Float64(-h))) * Float64(sqrt(Float64(d / l)) * Float64(1.0 + Float64(Float64(h / l) * Float64((Float64(D / Float64(Float64(d * 2.0) / M)) ^ 2.0) * -0.5)))));
	else
		tmp = Float64(t_0 * Float64(t_1 * Float64(sqrt(d) / sqrt(l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	t_0 = 1.0 - (0.5 * ((h * ((((0.5 * M) * D) / d) ^ 2.0)) / l));
	t_1 = sqrt((d / h));
	t_2 = sqrt(-d);
	tmp = 0.0;
	if (h <= -2.55e-110)
		tmp = (t_1 * (t_2 / sqrt(-l))) * t_0;
	elseif (h <= -5e-310)
		tmp = (t_2 / sqrt(-h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (((D / ((d * 2.0) / M)) ^ 2.0) * -0.5))));
	else
		tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(N[(0.5 * M), $MachinePrecision] * D), $MachinePrecision] / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[(-d)], $MachinePrecision]}, If[LessEqual[h, -2.55e-110], N[(N[(t$95$1 * N[(t$95$2 / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[h, -5e-310], N[(N[(t$95$2 / N[Sqrt[(-h)], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(N[(h / l), $MachinePrecision] * N[(N[Power[N[(D / N[(N[(d * 2.0), $MachinePrecision] / M), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 74.0% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0 (sqrt (/ d h))))
   (if (<= d -1e-310)
     (*
      (* t_0 (/ (sqrt (- d)) (sqrt (- l))))
      (- 1.0 (* 0.5 (/ (* h (pow (* (* 0.5 M) (/ D d)) 2.0)) l))))
     (*
      (- 1.0 (* 0.5 (/ (* h (pow (/ (* (* 0.5 M) D) d) 2.0)) l)))
      (* t_0 (/ (sqrt d) (sqrt l)))))))

C

double code(double d, double h, double l, double M, double D) {
	double t_0 = sqrt((d / h));
	double tmp;
	if (d <= -1e-310) {
		tmp = (t_0 * (sqrt(-d) / sqrt(-l))) * (1.0 - (0.5 * ((h * pow(((0.5 * M) * (D / d)), 2.0)) / l)));
	} else {
		tmp = (1.0 - (0.5 * ((h * pow((((0.5 * M) * D) / d), 2.0)) / l))) * (t_0 * (sqrt(d) / sqrt(l)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt((d / h))
    if (d <= (-1d-310)) then
        tmp = (t_0 * (sqrt(-d) / sqrt(-l))) * (1.0d0 - (0.5d0 * ((h * (((0.5d0 * m) * (d_1 / d)) ** 2.0d0)) / l)))
    else
        tmp = (1.0d0 - (0.5d0 * ((h * ((((0.5d0 * m) * d_1) / d) ** 2.0d0)) / l))) * (t_0 * (sqrt(d) / sqrt(l)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = Math.sqrt((d / h));
	double tmp;
	if (d <= -1e-310) {
		tmp = (t_0 * (Math.sqrt(-d) / Math.sqrt(-l))) * (1.0 - (0.5 * ((h * Math.pow(((0.5 * M) * (D / d)), 2.0)) / l)));
	} else {
		tmp = (1.0 - (0.5 * ((h * Math.pow((((0.5 * M) * D) / d), 2.0)) / l))) * (t_0 * (Math.sqrt(d) / Math.sqrt(l)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	t_0 = math.sqrt((d / h))
	tmp = 0
	if d <= -1e-310:
		tmp = (t_0 * (math.sqrt(-d) / math.sqrt(-l))) * (1.0 - (0.5 * ((h * math.pow(((0.5 * M) * (D / d)), 2.0)) / l)))
	else:
		tmp = (1.0 - (0.5 * ((h * math.pow((((0.5 * M) * D) / d), 2.0)) / l))) * (t_0 * (math.sqrt(d) / math.sqrt(l)))
	return tmp

Julia

function code(d, h, l, M, D)
	t_0 = sqrt(Float64(d / h))
	tmp = 0.0
	if (d <= -1e-310)
		tmp = Float64(Float64(t_0 * Float64(sqrt(Float64(-d)) / sqrt(Float64(-l)))) * Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(0.5 * M) * Float64(D / d)) ^ 2.0)) / l))));
	else
		tmp = Float64(Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(Float64(0.5 * M) * D) / d) ^ 2.0)) / l))) * Float64(t_0 * Float64(sqrt(d) / sqrt(l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	t_0 = sqrt((d / h));
	tmp = 0.0;
	if (d <= -1e-310)
		tmp = (t_0 * (sqrt(-d) / sqrt(-l))) * (1.0 - (0.5 * ((h * (((0.5 * M) * (D / d)) ^ 2.0)) / l)));
	else
		tmp = (1.0 - (0.5 * ((h * ((((0.5 * M) * D) / d) ^ 2.0)) / l))) * (t_0 * (sqrt(d) / sqrt(l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[d, -1e-310], N[(N[(t$95$0 * N[(N[Sqrt[(-d)], $MachinePrecision] / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(0.5 * M), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(N[(0.5 * M), $MachinePrecision] * D), $MachinePrecision] / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - 0.5 \cdot \frac{h \cdot {\left(\frac{\left(0.5 \cdot M\right) \cdot D}{d}\right)}^{2}}{\ell}\\ t_1 := \sqrt{\frac{d}{h}}\\ \mathbf{if}\;d \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\left(t_1 \cdot \frac{\sqrt{-d}}{\sqrt{-\ell}}\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0 (- 1.0 (* 0.5 (/ (* h (pow (/ (* (* 0.5 M) D) d) 2.0)) l))))
        (t_1 (sqrt (/ d h))))
   (if (<= d -1e-310)
     (* (* t_1 (/ (sqrt (- d)) (sqrt (- l)))) t_0)
     (* t_0 (* t_1 (/ (sqrt d) (sqrt l)))))))

C

double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 - (0.5 * ((h * pow((((0.5 * M) * D) / d), 2.0)) / l));
	double t_1 = sqrt((d / h));
	double tmp;
	if (d <= -1e-310) {
		tmp = (t_1 * (sqrt(-d) / sqrt(-l))) * t_0;
	} else {
		tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (0.5d0 * ((h * ((((0.5d0 * m) * d_1) / d) ** 2.0d0)) / l))
    t_1 = sqrt((d / h))
    if (d <= (-1d-310)) then
        tmp = (t_1 * (sqrt(-d) / sqrt(-l))) * t_0
    else
        tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 - (0.5 * ((h * Math.pow((((0.5 * M) * D) / d), 2.0)) / l));
	double t_1 = Math.sqrt((d / h));
	double tmp;
	if (d <= -1e-310) {
		tmp = (t_1 * (Math.sqrt(-d) / Math.sqrt(-l))) * t_0;
	} else {
		tmp = t_0 * (t_1 * (Math.sqrt(d) / Math.sqrt(l)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	t_0 = 1.0 - (0.5 * ((h * math.pow((((0.5 * M) * D) / d), 2.0)) / l))
	t_1 = math.sqrt((d / h))
	tmp = 0
	if d <= -1e-310:
		tmp = (t_1 * (math.sqrt(-d) / math.sqrt(-l))) * t_0
	else:
		tmp = t_0 * (t_1 * (math.sqrt(d) / math.sqrt(l)))
	return tmp

Julia

function code(d, h, l, M, D)
	t_0 = Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(Float64(0.5 * M) * D) / d) ^ 2.0)) / l)))
	t_1 = sqrt(Float64(d / h))
	tmp = 0.0
	if (d <= -1e-310)
		tmp = Float64(Float64(t_1 * Float64(sqrt(Float64(-d)) / sqrt(Float64(-l)))) * t_0);
	else
		tmp = Float64(t_0 * Float64(t_1 * Float64(sqrt(d) / sqrt(l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	t_0 = 1.0 - (0.5 * ((h * ((((0.5 * M) * D) / d) ^ 2.0)) / l));
	t_1 = sqrt((d / h));
	tmp = 0.0;
	if (d <= -1e-310)
		tmp = (t_1 * (sqrt(-d) / sqrt(-l))) * t_0;
	else
		tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(N[(0.5 * M), $MachinePrecision] * D), $MachinePrecision] / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[d, -1e-310], N[(N[(t$95$1 * N[(N[Sqrt[(-d)], $MachinePrecision] / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], N[(t$95$0 * N[(t$95$1 * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 75.0% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= h -5e-310)
   (*
    (/ (sqrt (- d)) (sqrt (- h)))
    (*
     (sqrt (/ d l))
     (+ 1.0 (* (/ h l) (* -0.5 (pow (* (/ M 2.0) (/ D d)) 2.0))))))
   (*
    (- 1.0 (* 0.5 (/ (* h (pow (/ (* (* 0.5 M) D) d) 2.0)) l)))
    (* (sqrt (/ d h)) (/ (sqrt d) (sqrt l))))))

C

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

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
    real(8) :: tmp
    if (h <= (-5d-310)) then
        tmp = (sqrt(-d) / sqrt(-h)) * (sqrt((d / l)) * (1.0d0 + ((h / l) * ((-0.5d0) * (((m / 2.0d0) * (d_1 / d)) ** 2.0d0)))))
    else
        tmp = (1.0d0 - (0.5d0 * ((h * ((((0.5d0 * m) * d_1) / d) ** 2.0d0)) / l))) * (sqrt((d / h)) * (sqrt(d) / sqrt(l)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (h <= -5e-310)
		tmp = (sqrt(-d) / sqrt(-h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (-0.5 * (((M / 2.0) * (D / d)) ^ 2.0)))));
	else
		tmp = (1.0 - (0.5 * ((h * ((((0.5 * M) * D) / d) ^ 2.0)) / l))) * (sqrt((d / h)) * (sqrt(d) / sqrt(l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[h, -5e-310], N[(N[(N[Sqrt[(-d)], $MachinePrecision] / N[Sqrt[(-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[(N[(M / 2.0), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(N[(0.5 * M), $MachinePrecision] * D), $MachinePrecision] / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - 0.5 \cdot \frac{h \cdot {\left(\frac{\left(0.5 \cdot M\right) \cdot D}{d}\right)}^{2}}{\ell}\\ t_1 := \sqrt{\frac{d}{h}}\\ \mathbf{if}\;d \leq -1 \cdot 10^{-310}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot \sqrt{\frac{d}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0 (- 1.0 (* 0.5 (/ (* h (pow (/ (* (* 0.5 M) D) d) 2.0)) l))))
        (t_1 (sqrt (/ d h))))
   (if (<= d -1e-310)
     (* t_0 (* t_1 (sqrt (/ d l))))
     (* t_0 (* t_1 (/ (sqrt d) (sqrt l)))))))

C

double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 - (0.5 * ((h * pow((((0.5 * M) * D) / d), 2.0)) / l));
	double t_1 = sqrt((d / h));
	double tmp;
	if (d <= -1e-310) {
		tmp = t_0 * (t_1 * sqrt((d / l)));
	} else {
		tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (0.5d0 * ((h * ((((0.5d0 * m) * d_1) / d) ** 2.0d0)) / l))
    t_1 = sqrt((d / h))
    if (d <= (-1d-310)) then
        tmp = t_0 * (t_1 * sqrt((d / l)))
    else
        tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 - (0.5 * ((h * Math.pow((((0.5 * M) * D) / d), 2.0)) / l));
	double t_1 = Math.sqrt((d / h));
	double tmp;
	if (d <= -1e-310) {
		tmp = t_0 * (t_1 * Math.sqrt((d / l)));
	} else {
		tmp = t_0 * (t_1 * (Math.sqrt(d) / Math.sqrt(l)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	t_0 = 1.0 - (0.5 * ((h * math.pow((((0.5 * M) * D) / d), 2.0)) / l))
	t_1 = math.sqrt((d / h))
	tmp = 0
	if d <= -1e-310:
		tmp = t_0 * (t_1 * math.sqrt((d / l)))
	else:
		tmp = t_0 * (t_1 * (math.sqrt(d) / math.sqrt(l)))
	return tmp

Julia

function code(d, h, l, M, D)
	t_0 = Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(Float64(0.5 * M) * D) / d) ^ 2.0)) / l)))
	t_1 = sqrt(Float64(d / h))
	tmp = 0.0
	if (d <= -1e-310)
		tmp = Float64(t_0 * Float64(t_1 * sqrt(Float64(d / l))));
	else
		tmp = Float64(t_0 * Float64(t_1 * Float64(sqrt(d) / sqrt(l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	t_0 = 1.0 - (0.5 * ((h * ((((0.5 * M) * D) / d) ^ 2.0)) / l));
	t_1 = sqrt((d / h));
	tmp = 0.0;
	if (d <= -1e-310)
		tmp = t_0 * (t_1 * sqrt((d / l)));
	else
		tmp = t_0 * (t_1 * (sqrt(d) / sqrt(l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(N[(0.5 * M), $MachinePrecision] * D), $MachinePrecision] / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[d, -1e-310], N[(t$95$0 * N[(t$95$1 * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 6: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.9 \cdot 10^{+174}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq -6.5 \cdot 10^{-218}:\\ \;\;\;\;\sqrt{\frac{d}{h} \cdot \frac{d}{\ell}} \cdot \mathsf{fma}\left(\frac{h}{\ell}, -0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}, 1\right)\\ \mathbf{elif}\;d \leq 1.86 \cdot 10^{-298}:\\ \;\;\;\;d \cdot \log \left(e^{{\left(h \cdot \ell\right)}^{-0.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{\ell}}}{\sqrt{h}} \cdot \left(1 + \left(\frac{h}{\ell} \cdot -0.5\right) \cdot {\left(D \cdot \left(0.5 \cdot \frac{M}{d}\right)\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= d -1.9e+174)
   (* d (- (sqrt (/ (/ 1.0 h) l))))
   (if (<= d -6.5e-218)
     (*
      (sqrt (* (/ d h) (/ d l)))
      (fma (/ h l) (* -0.5 (pow (/ (* M D) (* d 2.0)) 2.0)) 1.0))
     (if (<= d 1.86e-298)
       (* d (log (exp (pow (* h l) -0.5))))
       (*
        (/ (/ d (sqrt l)) (sqrt h))
        (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0))))))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (d <= -1.9e+174) {
		tmp = d * -sqrt(((1.0 / h) / l));
	} else if (d <= -6.5e-218) {
		tmp = sqrt(((d / h) * (d / l))) * fma((h / l), (-0.5 * pow(((M * D) / (d * 2.0)), 2.0)), 1.0);
	} else if (d <= 1.86e-298) {
		tmp = d * log(exp(pow((h * l), -0.5)));
	} else {
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (d <= -1.9e+174)
		tmp = Float64(d * Float64(-sqrt(Float64(Float64(1.0 / h) / l))));
	elseif (d <= -6.5e-218)
		tmp = Float64(sqrt(Float64(Float64(d / h) * Float64(d / l))) * fma(Float64(h / l), Float64(-0.5 * (Float64(Float64(M * D) / Float64(d * 2.0)) ^ 2.0)), 1.0));
	elseif (d <= 1.86e-298)
		tmp = Float64(d * log(exp((Float64(h * l) ^ -0.5))));
	else
		tmp = Float64(Float64(Float64(d / sqrt(l)) / sqrt(h)) * Float64(1.0 + Float64(Float64(Float64(h / l) * -0.5) * (Float64(D * Float64(0.5 * Float64(M / d))) ^ 2.0))));
	end
	return tmp
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[d, -1.9e+174], N[(d * (-N[Sqrt[N[(N[(1.0 / h), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[d, -6.5e-218], N[(N[Sqrt[N[(N[(d / h), $MachinePrecision] * N[(d / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(h / l), $MachinePrecision] * N[(-0.5 * N[Power[N[(N[(M * D), $MachinePrecision] / N[(d * 2.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.86e-298], N[(d * N[Log[N[Exp[N[Power[N[(h * l), $MachinePrecision], -0.5], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;\ell \leq 1.55 \cdot 10^{-303}:\\ \;\;\;\;\left(1 - 0.5 \cdot \frac{h \cdot {\left(\left(0.5 \cdot M\right) \cdot \frac{D}{d}\right)}^{2}}{\ell}\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{\ell}}}{\sqrt{h}} \cdot \left(1 + \left(\frac{h}{\ell} \cdot -0.5\right) \cdot {\left(D \cdot \left(0.5 \cdot \frac{M}{d}\right)\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= l -3.4e+69)
   (* d (- (sqrt (/ (/ 1.0 h) l))))
   (if (<= l 1.55e-303)
     (*
      (- 1.0 (* 0.5 (/ (* h (pow (* (* 0.5 M) (/ D d)) 2.0)) l)))
      (* (sqrt (/ d h)) (sqrt (/ d l))))
     (*
      (/ (/ d (sqrt l)) (sqrt h))
      (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0)))))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (l <= -3.4e+69) {
		tmp = d * -sqrt(((1.0 / h) / l));
	} else if (l <= 1.55e-303) {
		tmp = (1.0 - (0.5 * ((h * pow(((0.5 * M) * (D / d)), 2.0)) / l))) * (sqrt((d / h)) * sqrt((d / l)));
	} else {
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (l <= (-3.4d+69)) then
        tmp = d * -sqrt(((1.0d0 / h) / l))
    else if (l <= 1.55d-303) then
        tmp = (1.0d0 - (0.5d0 * ((h * (((0.5d0 * m) * (d_1 / d)) ** 2.0d0)) / l))) * (sqrt((d / h)) * sqrt((d / l)))
    else
        tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0d0 + (((h / l) * (-0.5d0)) * ((d_1 * (0.5d0 * (m / d))) ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (l <= -3.4e+69) {
		tmp = d * -Math.sqrt(((1.0 / h) / l));
	} else if (l <= 1.55e-303) {
		tmp = (1.0 - (0.5 * ((h * Math.pow(((0.5 * M) * (D / d)), 2.0)) / l))) * (Math.sqrt((d / h)) * Math.sqrt((d / l)));
	} else {
		tmp = ((d / Math.sqrt(l)) / Math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * Math.pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if l <= -3.4e+69:
		tmp = d * -math.sqrt(((1.0 / h) / l))
	elif l <= 1.55e-303:
		tmp = (1.0 - (0.5 * ((h * math.pow(((0.5 * M) * (D / d)), 2.0)) / l))) * (math.sqrt((d / h)) * math.sqrt((d / l)))
	else:
		tmp = ((d / math.sqrt(l)) / math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * math.pow((D * (0.5 * (M / d))), 2.0)))
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (l <= -3.4e+69)
		tmp = Float64(d * Float64(-sqrt(Float64(Float64(1.0 / h) / l))));
	elseif (l <= 1.55e-303)
		tmp = Float64(Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(0.5 * M) * Float64(D / d)) ^ 2.0)) / l))) * Float64(sqrt(Float64(d / h)) * sqrt(Float64(d / l))));
	else
		tmp = Float64(Float64(Float64(d / sqrt(l)) / sqrt(h)) * Float64(1.0 + Float64(Float64(Float64(h / l) * -0.5) * (Float64(D * Float64(0.5 * Float64(M / d))) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (l <= -3.4e+69)
		tmp = d * -sqrt(((1.0 / h) / l));
	elseif (l <= 1.55e-303)
		tmp = (1.0 - (0.5 * ((h * (((0.5 * M) * (D / d)) ^ 2.0)) / l))) * (sqrt((d / h)) * sqrt((d / l)));
	else
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * ((D * (0.5 * (M / d))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[l, -3.4e+69], N[(d * (-N[Sqrt[N[(N[(1.0 / h), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[l, 1.55e-303], N[(N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(0.5 * M), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 72.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= h -5e-310)
   (*
    (sqrt (/ d h))
    (*
     (sqrt (/ d l))
     (+ 1.0 (* (/ h l) (* -0.5 (pow (* (/ M 2.0) (/ D d)) 2.0))))))
   (*
    (/ (/ d (sqrt l)) (sqrt h))
    (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0))))))

C

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

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
    real(8) :: tmp
    if (h <= (-5d-310)) then
        tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0d0 + ((h / l) * ((-0.5d0) * (((m / 2.0d0) * (d_1 / d)) ** 2.0d0)))))
    else
        tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0d0 + (((h / l) * (-0.5d0)) * ((d_1 * (0.5d0 * (m / d))) ** 2.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (h <= -5e-310)
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (-0.5 * (((M / 2.0) * (D / d)) ^ 2.0)))));
	else
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * ((D * (0.5 * (M / d))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[h, -5e-310], 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[(N[(M / 2.0), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 72.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= h -5e-310)
   (*
    (sqrt (/ d h))
    (*
     (sqrt (/ d l))
     (+ 1.0 (* (/ h l) (* (pow (/ D (/ (* d 2.0) M)) 2.0) -0.5)))))
   (*
    (/ (/ d (sqrt l)) (sqrt h))
    (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0))))))

C

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

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
    real(8) :: tmp
    if (h <= (-5d-310)) then
        tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0d0 + ((h / l) * (((d_1 / ((d * 2.0d0) / m)) ** 2.0d0) * (-0.5d0)))))
    else
        tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0d0 + (((h / l) * (-0.5d0)) * ((d_1 * (0.5d0 * (m / d))) ** 2.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (h <= -5e-310)
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h / l) * (((D / ((d * 2.0) / M)) ^ 2.0) * -0.5))));
	else
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * ((D * (0.5 * (M / d))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[h, -5e-310], 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[(N[Power[N[(D / N[(N[(d * 2.0), $MachinePrecision] / M), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;h \leq 5.4 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \frac{h \cdot \left(-0.5 \cdot {\left(\left(0.5 \cdot M\right) \cdot \frac{D}{d}\right)}^{2}\right)}{\ell}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{\ell}}}{\sqrt{h}} \cdot \left(1 + \left(\frac{h}{\ell} \cdot -0.5\right) \cdot {\left(D \cdot \left(0.5 \cdot \frac{M}{d}\right)\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= h 5.4e-240)
   (*
    (sqrt (/ d h))
    (*
     (sqrt (/ d l))
     (+ 1.0 (/ (* h (* -0.5 (pow (* (* 0.5 M) (/ D d)) 2.0))) l))))
   (*
    (/ (/ d (sqrt l)) (sqrt h))
    (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0))))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (h <= 5.4e-240) {
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h * (-0.5 * pow(((0.5 * M) * (D / d)), 2.0))) / l)));
	} else {
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (h <= 5.4d-240) then
        tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0d0 + ((h * ((-0.5d0) * (((0.5d0 * m) * (d_1 / d)) ** 2.0d0))) / l)))
    else
        tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0d0 + (((h / l) * (-0.5d0)) * ((d_1 * (0.5d0 * (m / d))) ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (h <= 5.4e-240) {
		tmp = Math.sqrt((d / h)) * (Math.sqrt((d / l)) * (1.0 + ((h * (-0.5 * Math.pow(((0.5 * M) * (D / d)), 2.0))) / l)));
	} else {
		tmp = ((d / Math.sqrt(l)) / Math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * Math.pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if h <= 5.4e-240:
		tmp = math.sqrt((d / h)) * (math.sqrt((d / l)) * (1.0 + ((h * (-0.5 * math.pow(((0.5 * M) * (D / d)), 2.0))) / l)))
	else:
		tmp = ((d / math.sqrt(l)) / math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * math.pow((D * (0.5 * (M / d))), 2.0)))
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (h <= 5.4e-240)
		tmp = Float64(sqrt(Float64(d / h)) * Float64(sqrt(Float64(d / l)) * Float64(1.0 + Float64(Float64(h * Float64(-0.5 * (Float64(Float64(0.5 * M) * Float64(D / d)) ^ 2.0))) / l))));
	else
		tmp = Float64(Float64(Float64(d / sqrt(l)) / sqrt(h)) * Float64(1.0 + Float64(Float64(Float64(h / l) * -0.5) * (Float64(D * Float64(0.5 * Float64(M / d))) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (h <= 5.4e-240)
		tmp = sqrt((d / h)) * (sqrt((d / l)) * (1.0 + ((h * (-0.5 * (((0.5 * M) * (D / d)) ^ 2.0))) / l)));
	else
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * ((D * (0.5 * (M / d))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[h, 5.4e-240], 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[(0.5 * M), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;h \leq 5.4 \cdot 10^{-240}:\\ \;\;\;\;\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \frac{h \cdot {\left(D \cdot \frac{0.5 \cdot M}{d}\right)}^{2}}{\ell}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{\ell}}}{\sqrt{h}} \cdot \left(1 + \left(\frac{h}{\ell} \cdot -0.5\right) \cdot {\left(D \cdot \left(0.5 \cdot \frac{M}{d}\right)\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= h 5.4e-240)
   (*
    (* (sqrt (/ d h)) (sqrt (/ d l)))
    (- 1.0 (* 0.5 (/ (* h (pow (* D (/ (* 0.5 M) d)) 2.0)) l))))
   (*
    (/ (/ d (sqrt l)) (sqrt h))
    (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0))))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (h <= 5.4e-240) {
		tmp = (sqrt((d / h)) * sqrt((d / l))) * (1.0 - (0.5 * ((h * pow((D * ((0.5 * M) / d)), 2.0)) / l)));
	} else {
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (h <= 5.4d-240) then
        tmp = (sqrt((d / h)) * sqrt((d / l))) * (1.0d0 - (0.5d0 * ((h * ((d_1 * ((0.5d0 * m) / d)) ** 2.0d0)) / l)))
    else
        tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0d0 + (((h / l) * (-0.5d0)) * ((d_1 * (0.5d0 * (m / d))) ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (h <= 5.4e-240) {
		tmp = (Math.sqrt((d / h)) * Math.sqrt((d / l))) * (1.0 - (0.5 * ((h * Math.pow((D * ((0.5 * M) / d)), 2.0)) / l)));
	} else {
		tmp = ((d / Math.sqrt(l)) / Math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * Math.pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if h <= 5.4e-240:
		tmp = (math.sqrt((d / h)) * math.sqrt((d / l))) * (1.0 - (0.5 * ((h * math.pow((D * ((0.5 * M) / d)), 2.0)) / l)))
	else:
		tmp = ((d / math.sqrt(l)) / math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * math.pow((D * (0.5 * (M / d))), 2.0)))
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (h <= 5.4e-240)
		tmp = Float64(Float64(sqrt(Float64(d / h)) * sqrt(Float64(d / l))) * Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(D * Float64(Float64(0.5 * M) / d)) ^ 2.0)) / l))));
	else
		tmp = Float64(Float64(Float64(d / sqrt(l)) / sqrt(h)) * Float64(1.0 + Float64(Float64(Float64(h / l) * -0.5) * (Float64(D * Float64(0.5 * Float64(M / d))) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (h <= 5.4e-240)
		tmp = (sqrt((d / h)) * sqrt((d / l))) * (1.0 - (0.5 * ((h * ((D * ((0.5 * M) / d)) ^ 2.0)) / l)));
	else
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * ((D * (0.5 * (M / d))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[h, 5.4e-240], N[(N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(D * N[(N[(0.5 * M), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;h \leq 5.8 \cdot 10^{-240}:\\ \;\;\;\;\left(1 - 0.5 \cdot \frac{h \cdot {\left(\frac{\left(0.5 \cdot M\right) \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{\ell}}}{\sqrt{h}} \cdot \left(1 + \left(\frac{h}{\ell} \cdot -0.5\right) \cdot {\left(D \cdot \left(0.5 \cdot \frac{M}{d}\right)\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= h 5.8e-240)
   (*
    (- 1.0 (* 0.5 (/ (* h (pow (/ (* (* 0.5 M) D) d) 2.0)) l)))
    (* (sqrt (/ d h)) (sqrt (/ d l))))
   (*
    (/ (/ d (sqrt l)) (sqrt h))
    (+ 1.0 (* (* (/ h l) -0.5) (pow (* D (* 0.5 (/ M d))) 2.0))))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (h <= 5.8e-240) {
		tmp = (1.0 - (0.5 * ((h * pow((((0.5 * M) * D) / d), 2.0)) / l))) * (sqrt((d / h)) * sqrt((d / l)));
	} else {
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (h <= 5.8d-240) then
        tmp = (1.0d0 - (0.5d0 * ((h * ((((0.5d0 * m) * d_1) / d) ** 2.0d0)) / l))) * (sqrt((d / h)) * sqrt((d / l)))
    else
        tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0d0 + (((h / l) * (-0.5d0)) * ((d_1 * (0.5d0 * (m / d))) ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (h <= 5.8e-240) {
		tmp = (1.0 - (0.5 * ((h * Math.pow((((0.5 * M) * D) / d), 2.0)) / l))) * (Math.sqrt((d / h)) * Math.sqrt((d / l)));
	} else {
		tmp = ((d / Math.sqrt(l)) / Math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * Math.pow((D * (0.5 * (M / d))), 2.0)));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if h <= 5.8e-240:
		tmp = (1.0 - (0.5 * ((h * math.pow((((0.5 * M) * D) / d), 2.0)) / l))) * (math.sqrt((d / h)) * math.sqrt((d / l)))
	else:
		tmp = ((d / math.sqrt(l)) / math.sqrt(h)) * (1.0 + (((h / l) * -0.5) * math.pow((D * (0.5 * (M / d))), 2.0)))
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (h <= 5.8e-240)
		tmp = Float64(Float64(1.0 - Float64(0.5 * Float64(Float64(h * (Float64(Float64(Float64(0.5 * M) * D) / d) ^ 2.0)) / l))) * Float64(sqrt(Float64(d / h)) * sqrt(Float64(d / l))));
	else
		tmp = Float64(Float64(Float64(d / sqrt(l)) / sqrt(h)) * Float64(1.0 + Float64(Float64(Float64(h / l) * -0.5) * (Float64(D * Float64(0.5 * Float64(M / d))) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (h <= 5.8e-240)
		tmp = (1.0 - (0.5 * ((h * ((((0.5 * M) * D) / d) ^ 2.0)) / l))) * (sqrt((d / h)) * sqrt((d / l)));
	else
		tmp = ((d / sqrt(l)) / sqrt(h)) * (1.0 + (((h / l) * -0.5) * ((D * (0.5 * (M / d))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[h, 5.8e-240], N[(N[(1.0 - N[(0.5 * N[(N[(h * N[Power[N[(N[(N[(0.5 * M), $MachinePrecision] * D), $MachinePrecision] / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(D * N[(0.5 * N[(M / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 45.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;D \leq 4.15 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{d}{h} \cdot \frac{d}{\ell}} \cdot \mathsf{fma}\left(\frac{h}{\ell} \cdot -0.5, {\left(\frac{M}{d} \cdot \frac{D}{2}\right)}^{2}, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= D 4.15e+96)
   (* (sqrt (/ d h)) (sqrt (/ d l)))
   (*
    (sqrt (* (/ d h) (/ d l)))
    (fma (* (/ h l) -0.5) (pow (* (/ M d) (/ D 2.0)) 2.0) 1.0))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (D <= 4.15e+96) {
		tmp = sqrt((d / h)) * sqrt((d / l));
	} else {
		tmp = sqrt(((d / h) * (d / l))) * fma(((h / l) * -0.5), pow(((M / d) * (D / 2.0)), 2.0), 1.0);
	}
	return tmp;
}

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (D <= 4.15e+96)
		tmp = Float64(sqrt(Float64(d / h)) * sqrt(Float64(d / l)));
	else
		tmp = Float64(sqrt(Float64(Float64(d / h) * Float64(d / l))) * fma(Float64(Float64(h / l) * -0.5), (Float64(Float64(M / d) * Float64(D / 2.0)) ^ 2.0), 1.0));
	end
	return tmp
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[D, 4.15e+96], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(N[(d / h), $MachinePrecision] * N[(d / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision] * N[Power[N[(N[(M / d), $MachinePrecision] * N[(D / 2.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 45.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;D \leq 3.3 \cdot 10^{+96}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{d}{h} \cdot \frac{d}{\ell}} \cdot \left(1 + -0.5 \cdot \frac{{\left(0.5 \cdot \left(M \cdot \frac{D}{d}\right)\right)}^{2}}{\frac{\ell}{h}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= D 3.3e+96)
   (* (sqrt (/ d h)) (sqrt (/ d l)))
   (*
    (sqrt (* (/ d h) (/ d l)))
    (+ 1.0 (* -0.5 (/ (pow (* 0.5 (* M (/ D d))) 2.0) (/ l h)))))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (D <= 3.3e+96) {
		tmp = sqrt((d / h)) * sqrt((d / l));
	} else {
		tmp = sqrt(((d / h) * (d / l))) * (1.0 + (-0.5 * (pow((0.5 * (M * (D / d))), 2.0) / (l / h))));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (d_1 <= 3.3d+96) then
        tmp = sqrt((d / h)) * sqrt((d / l))
    else
        tmp = sqrt(((d / h) * (d / l))) * (1.0d0 + ((-0.5d0) * (((0.5d0 * (m * (d_1 / d))) ** 2.0d0) / (l / h))))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (D <= 3.3e+96) {
		tmp = Math.sqrt((d / h)) * Math.sqrt((d / l));
	} else {
		tmp = Math.sqrt(((d / h) * (d / l))) * (1.0 + (-0.5 * (Math.pow((0.5 * (M * (D / d))), 2.0) / (l / h))));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if D <= 3.3e+96:
		tmp = math.sqrt((d / h)) * math.sqrt((d / l))
	else:
		tmp = math.sqrt(((d / h) * (d / l))) * (1.0 + (-0.5 * (math.pow((0.5 * (M * (D / d))), 2.0) / (l / h))))
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (D <= 3.3e+96)
		tmp = Float64(sqrt(Float64(d / h)) * sqrt(Float64(d / l)));
	else
		tmp = Float64(sqrt(Float64(Float64(d / h) * Float64(d / l))) * Float64(1.0 + Float64(-0.5 * Float64((Float64(0.5 * Float64(M * Float64(D / d))) ^ 2.0) / Float64(l / h)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (D <= 3.3e+96)
		tmp = sqrt((d / h)) * sqrt((d / l));
	else
		tmp = sqrt(((d / h) * (d / l))) * (1.0 + (-0.5 * (((0.5 * (M * (D / d))) ^ 2.0) / (l / h))));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[D, 3.3e+96], N[(N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(N[(d / h), $MachinePrecision] * N[(d / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(-0.5 * N[(N[Power[N[(0.5 * N[(M * N[(D / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / N[(l / h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 15: 44.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{h \cdot \ell}\\ \mathbf{if}\;\ell \leq -1.95 \cdot 10^{-78}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;\ell \leq -9 \cdot 10^{-153}:\\ \;\;\;\;d \cdot {\left({t_0}^{3}\right)}^{0.16666666666666666}\\ \mathbf{elif}\;\ell \leq 8 \cdot 10^{-216}:\\ \;\;\;\;\left(-d\right) \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0 (/ 1.0 (* h l))))
   (if (<= l -1.95e-78)
     (* d (- (sqrt (/ (/ 1.0 h) l))))
     (if (<= l -9e-153)
       (* d (pow (pow t_0 3.0) 0.16666666666666666))
       (if (<= l 8e-216)
         (* (- d) (sqrt t_0))
         (* d (/ (pow h -0.5) (sqrt l))))))))

C

double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 / (h * l);
	double tmp;
	if (l <= -1.95e-78) {
		tmp = d * -sqrt(((1.0 / h) / l));
	} else if (l <= -9e-153) {
		tmp = d * pow(pow(t_0, 3.0), 0.16666666666666666);
	} else if (l <= 8e-216) {
		tmp = -d * sqrt(t_0);
	} else {
		tmp = d * (pow(h, -0.5) / sqrt(l));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / (h * l)
    if (l <= (-1.95d-78)) then
        tmp = d * -sqrt(((1.0d0 / h) / l))
    else if (l <= (-9d-153)) then
        tmp = d * ((t_0 ** 3.0d0) ** 0.16666666666666666d0)
    else if (l <= 8d-216) then
        tmp = -d * sqrt(t_0)
    else
        tmp = d * ((h ** (-0.5d0)) / sqrt(l))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 / (h * l);
	double tmp;
	if (l <= -1.95e-78) {
		tmp = d * -Math.sqrt(((1.0 / h) / l));
	} else if (l <= -9e-153) {
		tmp = d * Math.pow(Math.pow(t_0, 3.0), 0.16666666666666666);
	} else if (l <= 8e-216) {
		tmp = -d * Math.sqrt(t_0);
	} else {
		tmp = d * (Math.pow(h, -0.5) / Math.sqrt(l));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	t_0 = 1.0 / (h * l)
	tmp = 0
	if l <= -1.95e-78:
		tmp = d * -math.sqrt(((1.0 / h) / l))
	elif l <= -9e-153:
		tmp = d * math.pow(math.pow(t_0, 3.0), 0.16666666666666666)
	elif l <= 8e-216:
		tmp = -d * math.sqrt(t_0)
	else:
		tmp = d * (math.pow(h, -0.5) / math.sqrt(l))
	return tmp

Julia

function code(d, h, l, M, D)
	t_0 = Float64(1.0 / Float64(h * l))
	tmp = 0.0
	if (l <= -1.95e-78)
		tmp = Float64(d * Float64(-sqrt(Float64(Float64(1.0 / h) / l))));
	elseif (l <= -9e-153)
		tmp = Float64(d * ((t_0 ^ 3.0) ^ 0.16666666666666666));
	elseif (l <= 8e-216)
		tmp = Float64(Float64(-d) * sqrt(t_0));
	else
		tmp = Float64(d * Float64((h ^ -0.5) / sqrt(l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	t_0 = 1.0 / (h * l);
	tmp = 0.0;
	if (l <= -1.95e-78)
		tmp = d * -sqrt(((1.0 / h) / l));
	elseif (l <= -9e-153)
		tmp = d * ((t_0 ^ 3.0) ^ 0.16666666666666666);
	elseif (l <= 8e-216)
		tmp = -d * sqrt(t_0);
	else
		tmp = d * ((h ^ -0.5) / sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[(1.0 / N[(h * l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -1.95e-78], N[(d * (-N[Sqrt[N[(N[(1.0 / h), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[l, -9e-153], N[(d * N[Power[N[Power[t$95$0, 3.0], $MachinePrecision], 0.16666666666666666], $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 8e-216], N[((-d) * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(d * N[(N[Power[h, -0.5], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 16: 45.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 5.1 \cdot 10^{-214}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= l 5.1e-214)
   (* d (- (sqrt (/ (/ 1.0 h) l))))
   (* d (/ (pow h -0.5) (sqrt l)))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (l <= 5.1e-214) {
		tmp = d * -sqrt(((1.0 / h) / l));
	} else {
		tmp = d * (pow(h, -0.5) / sqrt(l));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (l <= 5.1d-214) then
        tmp = d * -sqrt(((1.0d0 / h) / l))
    else
        tmp = d * ((h ** (-0.5d0)) / sqrt(l))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (l <= 5.1e-214) {
		tmp = d * -Math.sqrt(((1.0 / h) / l));
	} else {
		tmp = d * (Math.pow(h, -0.5) / Math.sqrt(l));
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if l <= 5.1e-214:
		tmp = d * -math.sqrt(((1.0 / h) / l))
	else:
		tmp = d * (math.pow(h, -0.5) / math.sqrt(l))
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (l <= 5.1e-214)
		tmp = Float64(d * Float64(-sqrt(Float64(Float64(1.0 / h) / l))));
	else
		tmp = Float64(d * Float64((h ^ -0.5) / sqrt(l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (l <= 5.1e-214)
		tmp = d * -sqrt(((1.0 / h) / l));
	else
		tmp = d * ((h ^ -0.5) / sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[l, 5.1e-214], N[(d * (-N[Sqrt[N[(N[(1.0 / h), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], N[(d * N[(N[Power[h, -0.5], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 42.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 2.4 \cdot 10^{-215}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;d \cdot {\left(h \cdot \ell\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (if (<= l 2.4e-215)
   (* d (- (sqrt (/ (/ 1.0 h) l))))
   (* d (pow (* h l) -0.5))))

C

double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (l <= 2.4e-215) {
		tmp = d * -sqrt(((1.0 / h) / l));
	} else {
		tmp = d * pow((h * l), -0.5);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (l <= 2.4d-215) then
        tmp = d * -sqrt(((1.0d0 / h) / l))
    else
        tmp = d * ((h * l) ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double tmp;
	if (l <= 2.4e-215) {
		tmp = d * -Math.sqrt(((1.0 / h) / l));
	} else {
		tmp = d * Math.pow((h * l), -0.5);
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	tmp = 0
	if l <= 2.4e-215:
		tmp = d * -math.sqrt(((1.0 / h) / l))
	else:
		tmp = d * math.pow((h * l), -0.5)
	return tmp

Julia

function code(d, h, l, M, D)
	tmp = 0.0
	if (l <= 2.4e-215)
		tmp = Float64(d * Float64(-sqrt(Float64(Float64(1.0 / h) / l))));
	else
		tmp = Float64(d * (Float64(h * l) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	tmp = 0.0;
	if (l <= 2.4e-215)
		tmp = d * -sqrt(((1.0 / h) / l));
	else
		tmp = d * ((h * l) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := If[LessEqual[l, 2.4e-215], N[(d * (-N[Sqrt[N[(N[(1.0 / h), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], N[(d * N[Power[N[(h * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 18: 42.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(h \cdot \ell\right)}^{-0.5}\\ \mathbf{if}\;\ell \leq 8.8 \cdot 10^{-212}:\\ \;\;\;\;\left(-d\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;d \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0 (pow (* h l) -0.5)))
   (if (<= l 8.8e-212) (* (- d) t_0) (* d t_0))))

C

double code(double d, double h, double l, double M, double D) {
	double t_0 = pow((h * l), -0.5);
	double tmp;
	if (l <= 8.8e-212) {
		tmp = -d * t_0;
	} else {
		tmp = d * t_0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (h * l) ** (-0.5d0)
    if (l <= 8.8d-212) then
        tmp = -d * t_0
    else
        tmp = d * t_0
    end if
    code = tmp
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = Math.pow((h * l), -0.5);
	double tmp;
	if (l <= 8.8e-212) {
		tmp = -d * t_0;
	} else {
		tmp = d * t_0;
	}
	return tmp;
}

Python

def code(d, h, l, M, D):
	t_0 = math.pow((h * l), -0.5)
	tmp = 0
	if l <= 8.8e-212:
		tmp = -d * t_0
	else:
		tmp = d * t_0
	return tmp

Julia

function code(d, h, l, M, D)
	t_0 = Float64(h * l) ^ -0.5
	tmp = 0.0
	if (l <= 8.8e-212)
		tmp = Float64(Float64(-d) * t_0);
	else
		tmp = Float64(d * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d, h, l, M, D)
	t_0 = (h * l) ^ -0.5;
	tmp = 0.0;
	if (l <= 8.8e-212)
		tmp = -d * t_0;
	else
		tmp = d * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[Power[N[(h * l), $MachinePrecision], -0.5], $MachinePrecision]}, If[LessEqual[l, 8.8e-212], N[((-d) * t$95$0), $MachinePrecision], N[(d * t$95$0), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 19: 26.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ d \cdot {\left(h \cdot \ell\right)}^{-0.5} \end{array} \]

FPCore

(FPCore (d h l M D) :precision binary64 (* d (pow (* h l) -0.5)))

C

double code(double d, double h, double l, double M, double D) {
	return d * pow((h * l), -0.5);
}

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 * l) ** (-0.5d0))
end function

Java

public static double code(double d, double h, double l, double M, double D) {
	return d * Math.pow((h * l), -0.5);
}

Python

def code(d, h, l, M, D):
	return d * math.pow((h * l), -0.5)

Julia

function code(d, h, l, M, D)
	return Float64(d * (Float64(h * l) ^ -0.5))
end

MATLAB

function tmp = code(d, h, l, M, D)
	tmp = d * ((h * l) ^ -0.5);
end

Wolfram

code[d_, h_, l_, M_, D_] := N[(d * N[Power[N[(h * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Reproduce

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