Henrywood and Agarwal, Equation (12)

Average Accuracy: 58.2% → 71.8%

Time: 50.4s

Precision: binary64

Cost: 40528

Math

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

↓

\[\begin{array}{l} t_0 := 1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\\ t_1 := \sqrt{\frac{d}{\ell}}\\ t_2 := \sqrt{\frac{d}{h}}\\ t_3 := \sqrt{-d}\\ \mathbf{if}\;h \leq -1.65 \cdot 10^{+61}:\\ \;\;\;\;\left(t_2 \cdot \frac{t_3}{\sqrt{-\ell}}\right) \cdot t_0\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(\frac{t_3}{\sqrt{-h}} \cdot t_1\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;h \leq 1.95 \cdot 10^{-153}:\\ \;\;\;\;\frac{\left(t_1 \cdot \sqrt{d}\right) \cdot \left(1 + -0.125 \cdot \frac{D \cdot \frac{h}{\frac{d}{M}}}{\frac{d}{M} \cdot \frac{\ell}{D}}\right)}{\sqrt{h}}\\ \mathbf{elif}\;h \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;\left({\left(\frac{d}{h}\right)}^{0.5} \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right) \cdot \left(1 - {\left(\frac{\sqrt{0.5} \cdot \left(M \cdot \left(0.5 \cdot D\right)\right)}{d} \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right)\\ \mathbf{elif}\;h \leq 7.6 \cdot 10^{+150}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{elif}\;h \leq 1.85 \cdot 10^{+264}:\\ \;\;\;\;t_0 \cdot \left(t_2 \cdot \frac{1}{\frac{\sqrt{\ell}}{\sqrt{d}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 \cdot t_1\right) \cdot \left(1 + 0.5 \cdot \left({\left(\left(M \cdot \frac{D}{\sqrt{\ell}}\right) \cdot \frac{\sqrt{h}}{d}\right)}^{2} \cdot -0.25\right)\right)\\ \end{array} \]

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)))))

↓

(FPCore (d h l M D)
 :precision binary64
 (let* ((t_0
         (+ 1.0 (* 0.5 (* (/ (* D M) (* (* d (/ d h)) (/ l (* D M)))) -0.25))))
        (t_1 (sqrt (/ d l)))
        (t_2 (sqrt (/ d h)))
        (t_3 (sqrt (- d))))
   (if (<= h -1.65e+61)
     (* (* t_2 (/ t_3 (sqrt (- l)))) t_0)
     (if (<= h -5e-310)
       (*
        (* (/ t_3 (sqrt (- h))) t_1)
        (+ 1.0 (* 0.5 (* (/ (* D (* M (/ h d))) (* (/ d D) (/ l M))) -0.25))))
       (if (<= h 1.95e-153)
         (/
          (*
           (* t_1 (sqrt d))
           (+ 1.0 (* -0.125 (/ (* D (/ h (/ d M))) (* (/ d M) (/ l D))))))
          (sqrt h))
         (if (<= h 1.15e+61)
           (*
            (* (pow (/ d h) 0.5) (/ (sqrt d) (sqrt l)))
            (-
             1.0
             (pow
              (* (/ (* (sqrt 0.5) (* M (* 0.5 D))) d) (sqrt (/ h l)))
              2.0)))
           (if (<= h 7.6e+150)
             (*
              (/ d (* (sqrt h) (sqrt l)))
              (+ 1.0 (* (pow (* M (* 0.5 (/ D d))) 2.0) (* (/ h l) -0.5))))
             (if (<= h 1.85e+264)
               (* t_0 (* t_2 (/ 1.0 (/ (sqrt l) (sqrt d)))))
               (*
                (* t_2 t_1)
                (+
                 1.0
                 (*
                  0.5
                  (*
                   (pow (* (* M (/ D (sqrt l))) (/ (sqrt h) d)) 2.0)
                   -0.25))))))))))))

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)));
}

↓

double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 + (0.5 * (((D * M) / ((d * (d / h)) * (l / (D * M)))) * -0.25));
	double t_1 = sqrt((d / l));
	double t_2 = sqrt((d / h));
	double t_3 = sqrt(-d);
	double tmp;
	if (h <= -1.65e+61) {
		tmp = (t_2 * (t_3 / sqrt(-l))) * t_0;
	} else if (h <= -5e-310) {
		tmp = ((t_3 / sqrt(-h)) * t_1) * (1.0 + (0.5 * (((D * (M * (h / d))) / ((d / D) * (l / M))) * -0.25)));
	} else if (h <= 1.95e-153) {
		tmp = ((t_1 * sqrt(d)) * (1.0 + (-0.125 * ((D * (h / (d / M))) / ((d / M) * (l / D)))))) / sqrt(h);
	} else if (h <= 1.15e+61) {
		tmp = (pow((d / h), 0.5) * (sqrt(d) / sqrt(l))) * (1.0 - pow((((sqrt(0.5) * (M * (0.5 * D))) / d) * sqrt((h / l))), 2.0));
	} else if (h <= 7.6e+150) {
		tmp = (d / (sqrt(h) * sqrt(l))) * (1.0 + (pow((M * (0.5 * (D / d))), 2.0) * ((h / l) * -0.5)));
	} else if (h <= 1.85e+264) {
		tmp = t_0 * (t_2 * (1.0 / (sqrt(l) / sqrt(d))));
	} else {
		tmp = (t_2 * t_1) * (1.0 + (0.5 * (pow(((M * (D / sqrt(l))) * (sqrt(h) / d)), 2.0) * -0.25)));
	}
	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
    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

↓

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) :: t_3
    real(8) :: tmp
    t_0 = 1.0d0 + (0.5d0 * (((d_1 * m) / ((d * (d / h)) * (l / (d_1 * m)))) * (-0.25d0)))
    t_1 = sqrt((d / l))
    t_2 = sqrt((d / h))
    t_3 = sqrt(-d)
    if (h <= (-1.65d+61)) then
        tmp = (t_2 * (t_3 / sqrt(-l))) * t_0
    else if (h <= (-5d-310)) then
        tmp = ((t_3 / sqrt(-h)) * t_1) * (1.0d0 + (0.5d0 * (((d_1 * (m * (h / d))) / ((d / d_1) * (l / m))) * (-0.25d0))))
    else if (h <= 1.95d-153) then
        tmp = ((t_1 * sqrt(d)) * (1.0d0 + ((-0.125d0) * ((d_1 * (h / (d / m))) / ((d / m) * (l / d_1)))))) / sqrt(h)
    else if (h <= 1.15d+61) then
        tmp = (((d / h) ** 0.5d0) * (sqrt(d) / sqrt(l))) * (1.0d0 - ((((sqrt(0.5d0) * (m * (0.5d0 * d_1))) / d) * sqrt((h / l))) ** 2.0d0))
    else if (h <= 7.6d+150) then
        tmp = (d / (sqrt(h) * sqrt(l))) * (1.0d0 + (((m * (0.5d0 * (d_1 / d))) ** 2.0d0) * ((h / l) * (-0.5d0))))
    else if (h <= 1.85d+264) then
        tmp = t_0 * (t_2 * (1.0d0 / (sqrt(l) / sqrt(d))))
    else
        tmp = (t_2 * t_1) * (1.0d0 + (0.5d0 * ((((m * (d_1 / sqrt(l))) * (sqrt(h) / d)) ** 2.0d0) * (-0.25d0))))
    end if
    code = tmp
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)));
}

↓

public static double code(double d, double h, double l, double M, double D) {
	double t_0 = 1.0 + (0.5 * (((D * M) / ((d * (d / h)) * (l / (D * M)))) * -0.25));
	double t_1 = Math.sqrt((d / l));
	double t_2 = Math.sqrt((d / h));
	double t_3 = Math.sqrt(-d);
	double tmp;
	if (h <= -1.65e+61) {
		tmp = (t_2 * (t_3 / Math.sqrt(-l))) * t_0;
	} else if (h <= -5e-310) {
		tmp = ((t_3 / Math.sqrt(-h)) * t_1) * (1.0 + (0.5 * (((D * (M * (h / d))) / ((d / D) * (l / M))) * -0.25)));
	} else if (h <= 1.95e-153) {
		tmp = ((t_1 * Math.sqrt(d)) * (1.0 + (-0.125 * ((D * (h / (d / M))) / ((d / M) * (l / D)))))) / Math.sqrt(h);
	} else if (h <= 1.15e+61) {
		tmp = (Math.pow((d / h), 0.5) * (Math.sqrt(d) / Math.sqrt(l))) * (1.0 - Math.pow((((Math.sqrt(0.5) * (M * (0.5 * D))) / d) * Math.sqrt((h / l))), 2.0));
	} else if (h <= 7.6e+150) {
		tmp = (d / (Math.sqrt(h) * Math.sqrt(l))) * (1.0 + (Math.pow((M * (0.5 * (D / d))), 2.0) * ((h / l) * -0.5)));
	} else if (h <= 1.85e+264) {
		tmp = t_0 * (t_2 * (1.0 / (Math.sqrt(l) / Math.sqrt(d))));
	} else {
		tmp = (t_2 * t_1) * (1.0 + (0.5 * (Math.pow(((M * (D / Math.sqrt(l))) * (Math.sqrt(h) / d)), 2.0) * -0.25)));
	}
	return tmp;
}

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)))

↓

def code(d, h, l, M, D):
	t_0 = 1.0 + (0.5 * (((D * M) / ((d * (d / h)) * (l / (D * M)))) * -0.25))
	t_1 = math.sqrt((d / l))
	t_2 = math.sqrt((d / h))
	t_3 = math.sqrt(-d)
	tmp = 0
	if h <= -1.65e+61:
		tmp = (t_2 * (t_3 / math.sqrt(-l))) * t_0
	elif h <= -5e-310:
		tmp = ((t_3 / math.sqrt(-h)) * t_1) * (1.0 + (0.5 * (((D * (M * (h / d))) / ((d / D) * (l / M))) * -0.25)))
	elif h <= 1.95e-153:
		tmp = ((t_1 * math.sqrt(d)) * (1.0 + (-0.125 * ((D * (h / (d / M))) / ((d / M) * (l / D)))))) / math.sqrt(h)
	elif h <= 1.15e+61:
		tmp = (math.pow((d / h), 0.5) * (math.sqrt(d) / math.sqrt(l))) * (1.0 - math.pow((((math.sqrt(0.5) * (M * (0.5 * D))) / d) * math.sqrt((h / l))), 2.0))
	elif h <= 7.6e+150:
		tmp = (d / (math.sqrt(h) * math.sqrt(l))) * (1.0 + (math.pow((M * (0.5 * (D / d))), 2.0) * ((h / l) * -0.5)))
	elif h <= 1.85e+264:
		tmp = t_0 * (t_2 * (1.0 / (math.sqrt(l) / math.sqrt(d))))
	else:
		tmp = (t_2 * t_1) * (1.0 + (0.5 * (math.pow(((M * (D / math.sqrt(l))) * (math.sqrt(h) / d)), 2.0) * -0.25)))
	return tmp

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

↓

function code(d, h, l, M, D)
	t_0 = Float64(1.0 + Float64(0.5 * Float64(Float64(Float64(D * M) / Float64(Float64(d * Float64(d / h)) * Float64(l / Float64(D * M)))) * -0.25)))
	t_1 = sqrt(Float64(d / l))
	t_2 = sqrt(Float64(d / h))
	t_3 = sqrt(Float64(-d))
	tmp = 0.0
	if (h <= -1.65e+61)
		tmp = Float64(Float64(t_2 * Float64(t_3 / sqrt(Float64(-l)))) * t_0);
	elseif (h <= -5e-310)
		tmp = Float64(Float64(Float64(t_3 / sqrt(Float64(-h))) * t_1) * Float64(1.0 + Float64(0.5 * Float64(Float64(Float64(D * Float64(M * Float64(h / d))) / Float64(Float64(d / D) * Float64(l / M))) * -0.25))));
	elseif (h <= 1.95e-153)
		tmp = Float64(Float64(Float64(t_1 * sqrt(d)) * Float64(1.0 + Float64(-0.125 * Float64(Float64(D * Float64(h / Float64(d / M))) / Float64(Float64(d / M) * Float64(l / D)))))) / sqrt(h));
	elseif (h <= 1.15e+61)
		tmp = Float64(Float64((Float64(d / h) ^ 0.5) * Float64(sqrt(d) / sqrt(l))) * Float64(1.0 - (Float64(Float64(Float64(sqrt(0.5) * Float64(M * Float64(0.5 * D))) / d) * sqrt(Float64(h / l))) ^ 2.0)));
	elseif (h <= 7.6e+150)
		tmp = Float64(Float64(d / Float64(sqrt(h) * sqrt(l))) * Float64(1.0 + Float64((Float64(M * Float64(0.5 * Float64(D / d))) ^ 2.0) * Float64(Float64(h / l) * -0.5))));
	elseif (h <= 1.85e+264)
		tmp = Float64(t_0 * Float64(t_2 * Float64(1.0 / Float64(sqrt(l) / sqrt(d)))));
	else
		tmp = Float64(Float64(t_2 * t_1) * Float64(1.0 + Float64(0.5 * Float64((Float64(Float64(M * Float64(D / sqrt(l))) * Float64(sqrt(h) / d)) ^ 2.0) * -0.25))));
	end
	return tmp
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

↓

function tmp_2 = code(d, h, l, M, D)
	t_0 = 1.0 + (0.5 * (((D * M) / ((d * (d / h)) * (l / (D * M)))) * -0.25));
	t_1 = sqrt((d / l));
	t_2 = sqrt((d / h));
	t_3 = sqrt(-d);
	tmp = 0.0;
	if (h <= -1.65e+61)
		tmp = (t_2 * (t_3 / sqrt(-l))) * t_0;
	elseif (h <= -5e-310)
		tmp = ((t_3 / sqrt(-h)) * t_1) * (1.0 + (0.5 * (((D * (M * (h / d))) / ((d / D) * (l / M))) * -0.25)));
	elseif (h <= 1.95e-153)
		tmp = ((t_1 * sqrt(d)) * (1.0 + (-0.125 * ((D * (h / (d / M))) / ((d / M) * (l / D)))))) / sqrt(h);
	elseif (h <= 1.15e+61)
		tmp = (((d / h) ^ 0.5) * (sqrt(d) / sqrt(l))) * (1.0 - ((((sqrt(0.5) * (M * (0.5 * D))) / d) * sqrt((h / l))) ^ 2.0));
	elseif (h <= 7.6e+150)
		tmp = (d / (sqrt(h) * sqrt(l))) * (1.0 + (((M * (0.5 * (D / d))) ^ 2.0) * ((h / l) * -0.5)));
	elseif (h <= 1.85e+264)
		tmp = t_0 * (t_2 * (1.0 / (sqrt(l) / sqrt(d))));
	else
		tmp = (t_2 * t_1) * (1.0 + (0.5 * ((((M * (D / sqrt(l))) * (sqrt(h) / d)) ^ 2.0) * -0.25)));
	end
	tmp_2 = tmp;
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]

↓

code[d_, h_, l_, M_, D_] := Block[{t$95$0 = N[(1.0 + N[(0.5 * N[(N[(N[(D * M), $MachinePrecision] / N[(N[(d * N[(d / h), $MachinePrecision]), $MachinePrecision] * N[(l / N[(D * M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(d / h), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[(-d)], $MachinePrecision]}, If[LessEqual[h, -1.65e+61], N[(N[(t$95$2 * N[(t$95$3 / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[h, -5e-310], N[(N[(N[(t$95$3 / N[Sqrt[(-h)], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(N[(N[(D * N[(M * N[(h / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(d / D), $MachinePrecision] * N[(l / M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[h, 1.95e-153], N[(N[(N[(t$95$1 * N[Sqrt[d], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(-0.125 * N[(N[(D * N[(h / N[(d / M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(d / M), $MachinePrecision] * N[(l / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[h], $MachinePrecision]), $MachinePrecision], If[LessEqual[h, 1.15e+61], N[(N[(N[Power[N[(d / h), $MachinePrecision], 0.5], $MachinePrecision] * N[(N[Sqrt[d], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[Power[N[(N[(N[(N[Sqrt[0.5], $MachinePrecision] * N[(M * N[(0.5 * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] * N[Sqrt[N[(h / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[h, 7.6e+150], N[(N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[Power[N[(M * N[(0.5 * N[(D / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(N[(h / l), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[h, 1.85e+264], N[(t$95$0 * N[(t$95$2 * N[(1.0 / N[(N[Sqrt[l], $MachinePrecision] / N[Sqrt[d], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 * t$95$1), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(N[Power[N[(N[(M * N[(D / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[h], $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if h < -1.6499999999999999e61

   1. Initial program 58.4%

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

   2. Simplified 58.3%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\left(\frac{M}{2} \cdot \frac{D}{d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right)} \]
      Proof

      [Start] 58.4	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 58.4	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 58.4	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 58.4	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 58.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 58.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 58.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 58.3	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Taylor expanded in M around 0 32.8%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)}\right) \]

   4. Simplified 41.9%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{\frac{h}{d}}{d}\right)\right)}\right) \]
      Proof

      [Start] 32.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)\right) \]
      associate-/r* [=>] 34.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell}}{{d}^{2}}}\right)\right) \]
      associate-/l/ [=>] 32.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2} \cdot \ell}}\right)\right) \]
      associate-*r* [=>] 37.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\color{blue}{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}}{{d}^{2} \cdot \ell}\right)\right) \]
      *-commutative [<=] 37.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{\color{blue}{\ell \cdot {d}^{2}}}\right)\right) \]
      times-frac [=>] 36.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\left(\frac{{D}^{2} \cdot {M}^{2}}{\ell} \cdot \frac{h}{{d}^{2}}\right)}\right)\right) \]
      unpow2 [=>] 36.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{{D}^{2} \cdot \color{blue}{\left(M \cdot M\right)}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      associate-*r* [=>] 41.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\color{blue}{\left({D}^{2} \cdot M\right) \cdot M}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 41.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\color{blue}{\left(D \cdot D\right)} \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 41.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{\color{blue}{d \cdot d}}\right)\right)\right) \]
      associate-/r* [=>] 41.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \color{blue}{\frac{\frac{h}{d}}{d}}\right)\right)\right) \]

   5. Applied egg-rr 53.9%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}}}\right)\right) \]

   6. Applied egg-rr 63.7%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\frac{\sqrt{-d}}{\sqrt{-\ell}}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}}\right)\right) \]

   if -1.6499999999999999e61 < h < -4.999999999999985e-310

   1. Initial program 58.7%

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

   2. Simplified 57.9%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\left(\frac{M}{2} \cdot \frac{D}{d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right)} \]
      Proof

      [Start] 58.7	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 58.7	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 58.7	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 58.7	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 58.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 58.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 58.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 57.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Taylor expanded in M around 0 33.4%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)}\right) \]

   4. Simplified 44.5%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{\frac{h}{d}}{d}\right)\right)}\right) \]
      Proof

      [Start] 33.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)\right) \]
      associate-/r* [=>] 36.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell}}{{d}^{2}}}\right)\right) \]
      associate-/l/ [=>] 33.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2} \cdot \ell}}\right)\right) \]
      associate-*r* [=>] 33.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\color{blue}{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}}{{d}^{2} \cdot \ell}\right)\right) \]
      *-commutative [<=] 33.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{\color{blue}{\ell \cdot {d}^{2}}}\right)\right) \]
      times-frac [=>] 35.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\left(\frac{{D}^{2} \cdot {M}^{2}}{\ell} \cdot \frac{h}{{d}^{2}}\right)}\right)\right) \]
      unpow2 [=>] 35.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{{D}^{2} \cdot \color{blue}{\left(M \cdot M\right)}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      associate-*r* [=>] 40.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\color{blue}{\left({D}^{2} \cdot M\right) \cdot M}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 40.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\color{blue}{\left(D \cdot D\right)} \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 40.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{\color{blue}{d \cdot d}}\right)\right)\right) \]
      associate-/r* [=>] 44.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \color{blue}{\frac{\frac{h}{d}}{d}}\right)\right)\right) \]

   5. Applied egg-rr 49.0%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{\left(D \cdot \left(D \cdot M\right)\right) \cdot \left(-h\right)}{d \cdot \left(\frac{\ell}{M} \cdot \left(-d\right)\right)}}\right)\right) \]

   6. Simplified 57.5%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\left(\frac{D \cdot M}{\frac{d}{D}} \cdot \frac{1 \cdot \frac{h}{d}}{\frac{\ell}{M}}\right)}\right)\right) \]
      Proof

      [Start] 49.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\left(D \cdot \left(D \cdot M\right)\right) \cdot \left(-h\right)}{d \cdot \left(\frac{\ell}{M} \cdot \left(-d\right)\right)}\right)\right) \]
      times-frac [=>] 53.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\left(\frac{D \cdot \left(D \cdot M\right)}{d} \cdot \frac{-h}{\frac{\ell}{M} \cdot \left(-d\right)}\right)}\right)\right) \]
      *-commutative [=>] 53.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\color{blue}{\left(D \cdot M\right) \cdot D}}{d} \cdot \frac{-h}{\frac{\ell}{M} \cdot \left(-d\right)}\right)\right)\right) \]
      associate-/l* [=>] 55.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\color{blue}{\frac{D \cdot M}{\frac{d}{D}}} \cdot \frac{-h}{\frac{\ell}{M} \cdot \left(-d\right)}\right)\right)\right) \]
      *-commutative [<=] 55.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{D \cdot M}{\frac{d}{D}} \cdot \frac{-h}{\color{blue}{\left(-d\right) \cdot \frac{\ell}{M}}}\right)\right)\right) \]
      associate-/r* [=>] 57.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{D \cdot M}{\frac{d}{D}} \cdot \color{blue}{\frac{\frac{-h}{-d}}{\frac{\ell}{M}}}\right)\right)\right) \]
      neg-mul-1 [=>] 57.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{D \cdot M}{\frac{d}{D}} \cdot \frac{\frac{\color{blue}{-1 \cdot h}}{-d}}{\frac{\ell}{M}}\right)\right)\right) \]
      neg-mul-1 [=>] 57.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{D \cdot M}{\frac{d}{D}} \cdot \frac{\frac{-1 \cdot h}{\color{blue}{-1 \cdot d}}}{\frac{\ell}{M}}\right)\right)\right) \]
      times-frac [=>] 57.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{D \cdot M}{\frac{d}{D}} \cdot \frac{\color{blue}{\frac{-1}{-1} \cdot \frac{h}{d}}}{\frac{\ell}{M}}\right)\right)\right) \]
      metadata-eval [=>] 57.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{D \cdot M}{\frac{d}{D}} \cdot \frac{\color{blue}{1} \cdot \frac{h}{d}}{\frac{\ell}{M}}\right)\right)\right) \]

   7. Applied egg-rr 60.7%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}}}\right)\right) \]

   8. Applied egg-rr 73.8%

      \[\leadsto \left(\color{blue}{\frac{\sqrt{-d}}{\sqrt{-h}}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}}\right)\right) \]

   if -4.999999999999985e-310 < h < 1.9500000000000001e-153

   1. Initial program 46.1%

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

   2. Simplified 44.2%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\left(\frac{M}{2} \cdot \frac{D}{d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right)} \]
      Proof

      [Start] 46.1	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 46.1	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 46.1	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 46.1	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 46.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 46.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 46.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 44.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Applied egg-rr 68.9%

      \[\leadsto \color{blue}{\frac{\sqrt{d} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right)\right)}{\sqrt{h}}} \]

   4. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)}{\sqrt{h}}} \]
      Proof

      [Start] 68.9	\[ \frac{\sqrt{d} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 + \left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right)\right)}{\sqrt{h}} \]
      associate-*r* [=>] 68.9	\[ \frac{\color{blue}{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right)}}{\sqrt{h}} \]
      *-commutative [=>] 68.9	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \color{blue}{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(-0.5 \cdot \frac{h}{\ell}\right)}\right)}{\sqrt{h}} \]
      *-commutative [=>] 68.9	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \color{blue}{\left(\frac{h}{\ell} \cdot -0.5\right)}\right)}{\sqrt{h}} \]

   5. Taylor expanded in M around 0 41.6%

      \[\leadsto \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \color{blue}{-0.125 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}}\right)}{\sqrt{h}} \]

   6. Simplified 57.2%

      \[\leadsto \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \color{blue}{-0.125 \cdot \left(\frac{D}{\frac{\ell}{D}} \cdot \left(\frac{h}{d} \cdot \frac{M \cdot M}{d}\right)\right)}\right)}{\sqrt{h}} \]
      Proof

      [Start] 41.6	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)}{\sqrt{h}} \]
      associate-/r* [=>] 45.5	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \color{blue}{\frac{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell}}{{d}^{2}}}\right)}{\sqrt{h}} \]
      *-commutative [<=] 45.5	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \frac{\frac{{D}^{2} \cdot \color{blue}{\left(h \cdot {M}^{2}\right)}}{\ell}}{{d}^{2}}\right)}{\sqrt{h}} \]
      associate-/r* [<=] 41.6	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \color{blue}{\frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{\ell \cdot {d}^{2}}}\right)}{\sqrt{h}} \]
      times-frac [=>] 44.7	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \color{blue}{\left(\frac{{D}^{2}}{\ell} \cdot \frac{h \cdot {M}^{2}}{{d}^{2}}\right)}\right)}{\sqrt{h}} \]
      unpow2 [=>] 44.7	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \left(\frac{\color{blue}{D \cdot D}}{\ell} \cdot \frac{h \cdot {M}^{2}}{{d}^{2}}\right)\right)}{\sqrt{h}} \]
      associate-/l* [=>] 49.9	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \left(\color{blue}{\frac{D}{\frac{\ell}{D}}} \cdot \frac{h \cdot {M}^{2}}{{d}^{2}}\right)\right)}{\sqrt{h}} \]
      unpow2 [=>] 49.9	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \left(\frac{D}{\frac{\ell}{D}} \cdot \frac{h \cdot {M}^{2}}{\color{blue}{d \cdot d}}\right)\right)}{\sqrt{h}} \]
      times-frac [=>] 57.2	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \left(\frac{D}{\frac{\ell}{D}} \cdot \color{blue}{\left(\frac{h}{d} \cdot \frac{{M}^{2}}{d}\right)}\right)\right)}{\sqrt{h}} \]
      unpow2 [=>] 57.2	\[ \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \left(\frac{D}{\frac{\ell}{D}} \cdot \left(\frac{h}{d} \cdot \frac{\color{blue}{M \cdot M}}{d}\right)\right)\right)}{\sqrt{h}} \]

   7. Applied egg-rr 66.5%

      \[\leadsto \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \left(\frac{D}{\frac{\ell}{D}} \cdot \color{blue}{\frac{\frac{h \cdot M}{d} \cdot M}{d}}\right)\right)}{\sqrt{h}} \]

   8. Applied egg-rr 76.2%

      \[\leadsto \frac{\left(\sqrt{d} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + -0.125 \cdot \color{blue}{\frac{\frac{h}{\frac{d}{M}} \cdot D}{\frac{d}{M} \cdot \frac{\ell}{D}}}\right)}{\sqrt{h}} \]

   if 1.9500000000000001e-153 < h < 1.15e61

   1. Initial program 67.5%

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

   2. Applied egg-rr 69.8%

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{{\left(\left(\left(M \cdot \left(D \cdot \frac{0.5}{d}\right)\right) \cdot \sqrt{0.5}\right) \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}}\right) \]

   3. Simplified 70.7%

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{{\left(\frac{\sqrt{0.5} \cdot \left(M \cdot \left(D \cdot 0.5\right)\right)}{d} \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}}\right) \]
      Proof

      [Start] 69.8	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - {\left(\left(\left(M \cdot \left(D \cdot \frac{0.5}{d}\right)\right) \cdot \sqrt{0.5}\right) \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right) \]
      *-commutative [=>] 69.8	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - {\left(\color{blue}{\left(\sqrt{0.5} \cdot \left(M \cdot \left(D \cdot \frac{0.5}{d}\right)\right)\right)} \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right) \]
      associate-*r/ [=>] 69.8	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - {\left(\left(\sqrt{0.5} \cdot \left(M \cdot \color{blue}{\frac{D \cdot 0.5}{d}}\right)\right) \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right) \]
      associate-*r/ [=>] 70.7	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - {\left(\left(\sqrt{0.5} \cdot \color{blue}{\frac{M \cdot \left(D \cdot 0.5\right)}{d}}\right) \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right) \]
      associate-*r/ [=>] 70.7	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - {\left(\color{blue}{\frac{\sqrt{0.5} \cdot \left(M \cdot \left(D \cdot 0.5\right)\right)}{d}} \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right) \]

   4. Applied egg-rr 82.2%

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot \color{blue}{\frac{\sqrt{d}}{\sqrt{\ell}}}\right) \cdot \left(1 - {\left(\frac{\sqrt{0.5} \cdot \left(M \cdot \left(D \cdot 0.5\right)\right)}{d} \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right) \]

   if 1.15e61 < h < 7.59999999999999978e150

   1. Initial program 65.3%

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

   2. Simplified 65.5%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\left(\frac{M}{2} \cdot \frac{D}{d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right)} \]
      Proof

      [Start] 65.3	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 65.3	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 65.3	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 65.3	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 65.3	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 65.3	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 65.3	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 65.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} + \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(\left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right)} \]

   4. Simplified 74.6%

      \[\leadsto \color{blue}{\frac{d}{\sqrt{\ell} \cdot \sqrt{h}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)} \]
      Proof

      [Start] 74.6	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} + \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(\left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right) \]
      *-lft-identity [<=] 74.6	\[ \color{blue}{1 \cdot \frac{d}{\sqrt{h} \cdot \sqrt{\ell}}} + \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(\left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right) \]
      *-commutative [<=] 74.6	\[ 1 \cdot \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} + \color{blue}{\left(\left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right) \cdot \frac{d}{\sqrt{h} \cdot \sqrt{\ell}}} \]
      distribute-rgt-in [<=] 74.6	\[ \color{blue}{\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + \left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right)} \]
      *-commutative [=>] 74.6	\[ \frac{d}{\color{blue}{\sqrt{\ell} \cdot \sqrt{h}}} \cdot \left(1 + \left(-0.5 \cdot \frac{h}{\ell}\right) \cdot {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\right) \]
      *-commutative [=>] 74.6	\[ \frac{d}{\sqrt{\ell} \cdot \sqrt{h}} \cdot \left(1 + \color{blue}{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(-0.5 \cdot \frac{h}{\ell}\right)}\right) \]
      *-commutative [=>] 74.6	\[ \frac{d}{\sqrt{\ell} \cdot \sqrt{h}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \color{blue}{\left(\frac{h}{\ell} \cdot -0.5\right)}\right) \]

   if 7.59999999999999978e150 < h < 1.85e264

   1. Initial program 55.2%

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

   2. Simplified 54.8%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\left(\frac{M}{2} \cdot \frac{D}{d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right)} \]
      Proof

      [Start] 55.2	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 55.2	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 55.2	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 55.2	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 55.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 55.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 55.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 54.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Taylor expanded in M around 0 31.9%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)}\right) \]

   4. Simplified 38.8%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{\frac{h}{d}}{d}\right)\right)}\right) \]
      Proof

      [Start] 31.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)\right) \]
      associate-/r* [=>] 32.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell}}{{d}^{2}}}\right)\right) \]
      associate-/l/ [=>] 31.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2} \cdot \ell}}\right)\right) \]
      associate-*r* [=>] 36.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\color{blue}{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}}{{d}^{2} \cdot \ell}\right)\right) \]
      *-commutative [<=] 36.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{\color{blue}{\ell \cdot {d}^{2}}}\right)\right) \]
      times-frac [=>] 34.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\left(\frac{{D}^{2} \cdot {M}^{2}}{\ell} \cdot \frac{h}{{d}^{2}}\right)}\right)\right) \]
      unpow2 [=>] 34.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{{D}^{2} \cdot \color{blue}{\left(M \cdot M\right)}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      associate-*r* [=>] 38.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\color{blue}{\left({D}^{2} \cdot M\right) \cdot M}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 38.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\color{blue}{\left(D \cdot D\right)} \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 38.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{\color{blue}{d \cdot d}}\right)\right)\right) \]
      associate-/r* [=>] 38.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \color{blue}{\frac{\frac{h}{d}}{d}}\right)\right)\right) \]

   5. Applied egg-rr 50.6%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}}}\right)\right) \]

   6. Applied egg-rr 61.0%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\frac{1}{\frac{\sqrt{\ell}}{\sqrt{d}}}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}}\right)\right) \]

   if 1.85e264 < h

   1. Initial program 40.7%

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

   2. Simplified 41.8%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\left(\frac{M}{2} \cdot \frac{D}{d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right)} \]
      Proof

      [Start] 40.7	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 40.7	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 40.7	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 40.7	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 40.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 40.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 40.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 41.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Taylor expanded in M around 0 28.1%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)}\right) \]

   4. Simplified 36.0%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{\frac{h}{d}}{d}\right)\right)}\right) \]
      Proof

      [Start] 28.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell \cdot {d}^{2}}\right)\right) \]
      associate-/r* [=>] 28.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{\ell}}{{d}^{2}}}\right)\right) \]
      associate-/l/ [=>] 28.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2} \cdot \ell}}\right)\right) \]
      associate-*r* [=>] 31.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\color{blue}{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}}{{d}^{2} \cdot \ell}\right)\right) \]
      *-commutative [<=] 31.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{\color{blue}{\ell \cdot {d}^{2}}}\right)\right) \]
      times-frac [=>] 31.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{\left(\frac{{D}^{2} \cdot {M}^{2}}{\ell} \cdot \frac{h}{{d}^{2}}\right)}\right)\right) \]
      unpow2 [=>] 31.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{{D}^{2} \cdot \color{blue}{\left(M \cdot M\right)}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      associate-*r* [=>] 34.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\color{blue}{\left({D}^{2} \cdot M\right) \cdot M}}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 34.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\color{blue}{\left(D \cdot D\right)} \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{{d}^{2}}\right)\right)\right) \]
      unpow2 [=>] 34.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \frac{h}{\color{blue}{d \cdot d}}\right)\right)\right) \]
      associate-/r* [=>] 36.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \left(\frac{\left(\left(D \cdot D\right) \cdot M\right) \cdot M}{\ell} \cdot \color{blue}{\frac{\frac{h}{d}}{d}}\right)\right)\right) \]

   5. Applied egg-rr 51.4%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{{\left(\frac{D \cdot M}{\sqrt{\ell}} \cdot \frac{\sqrt{h}}{d}\right)}^{2}}\right)\right) \]

   6. Simplified 52.9%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot \color{blue}{{\left(\left(\frac{D}{\sqrt{\ell}} \cdot M\right) \cdot \frac{\sqrt{h}}{d}\right)}^{2}}\right)\right) \]
      Proof

      [Start] 51.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot {\left(\frac{D \cdot M}{\sqrt{\ell}} \cdot \frac{\sqrt{h}}{d}\right)}^{2}\right)\right) \]
      associate-/l* [=>] 52.4	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot {\left(\color{blue}{\frac{D}{\frac{\sqrt{\ell}}{M}}} \cdot \frac{\sqrt{h}}{d}\right)}^{2}\right)\right) \]
      associate-/r/ [=>] 52.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(0.25 \cdot {\left(\color{blue}{\left(\frac{D}{\sqrt{\ell}} \cdot M\right)} \cdot \frac{\sqrt{h}}{d}\right)}^{2}\right)\right) \]

3. Recombined 7 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;h \leq -1.65 \cdot 10^{+61}:\\ \;\;\;\;\left(\sqrt{\frac{d}{h}} \cdot \frac{\sqrt{-d}}{\sqrt{-\ell}}\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(\frac{\sqrt{-d}}{\sqrt{-h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;h \leq 1.95 \cdot 10^{-153}:\\ \;\;\;\;\frac{\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{d}\right) \cdot \left(1 + -0.125 \cdot \frac{D \cdot \frac{h}{\frac{d}{M}}}{\frac{d}{M} \cdot \frac{\ell}{D}}\right)}{\sqrt{h}}\\ \mathbf{elif}\;h \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;\left({\left(\frac{d}{h}\right)}^{0.5} \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right) \cdot \left(1 - {\left(\frac{\sqrt{0.5} \cdot \left(M \cdot \left(0.5 \cdot D\right)\right)}{d} \cdot \sqrt{\frac{h}{\ell}}\right)}^{2}\right)\\ \mathbf{elif}\;h \leq 7.6 \cdot 10^{+150}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{elif}\;h \leq 1.85 \cdot 10^{+264}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \frac{1}{\frac{\sqrt{\ell}}{\sqrt{d}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + 0.5 \cdot \left({\left(\left(M \cdot \frac{D}{\sqrt{\ell}}\right) \cdot \frac{\sqrt{h}}{d}\right)}^{2} \cdot -0.25\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	71.9%
Cost	34064

\[\begin{array}{l} t_0 := 1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\\ t_1 := \sqrt{\frac{d}{\ell}}\\ t_2 := \sqrt{\frac{d}{h}}\\ t_3 := \sqrt{-d}\\ \mathbf{if}\;h \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;\left(t_2 \cdot \frac{t_3}{\sqrt{-\ell}}\right) \cdot t_0\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(\frac{t_3}{\sqrt{-h}} \cdot t_1\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;h \leq 3.7 \cdot 10^{+150}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{elif}\;h \leq 7.2 \cdot 10^{+264}:\\ \;\;\;\;t_0 \cdot \left(t_2 \cdot \frac{1}{\frac{\sqrt{\ell}}{\sqrt{d}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 \cdot t_1\right) \cdot \left(1 + 0.5 \cdot \left({\left(\left(M \cdot \frac{D}{\sqrt{\ell}}\right) \cdot \frac{\sqrt{h}}{d}\right)}^{2} \cdot -0.25\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	67.8%
Cost	22116

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}} \cdot t_0\\ t_2 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ t_3 := \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ t_4 := \left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right) \cdot t_1\\ \mathbf{if}\;d \leq -5.6 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -3.2 \cdot 10^{+124}:\\ \;\;\;\;\left(t_0 \cdot \frac{1}{\sqrt{\frac{h}{d}}}\right) \cdot \left(1 + 0.5 \cdot \left(\left(\frac{M \cdot \left(M \cdot \left(D \cdot D\right)\right)}{\ell} \cdot \frac{\frac{h}{d}}{d}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -1.38 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -6.1 \cdot 10^{-103}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;d \leq -5.5 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-285}:\\ \;\;\;\;t_1 \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{\frac{D \cdot M}{\ell}}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;d \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{+145}:\\ \;\;\;\;\frac{\left(t_0 \cdot \sqrt{d}\right) \cdot \left(1 + -0.125 \cdot \frac{D \cdot \frac{h}{\frac{d}{M}}}{\frac{d}{M} \cdot \frac{\ell}{D}}\right)}{\sqrt{h}}\\ \mathbf{elif}\;d \leq 3.7 \cdot 10^{+247}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 3
Accuracy	69.6%
Cost	21844

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\\ t_2 := 1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\\ t_3 := \sqrt{\frac{d}{h}}\\ t_4 := \left(t_3 \cdot \frac{\sqrt{-d}}{\sqrt{-\ell}}\right) \cdot t_2\\ \mathbf{if}\;h \leq -1.18 \cdot 10^{+61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;h \leq -7.4 \cdot 10^{-159}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right) \cdot \left(t_0 \cdot \frac{1}{\sqrt{\frac{h}{d}}}\right)\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;h \leq 8.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + t_1 \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{elif}\;h \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t_2 \cdot \left(t_3 \cdot \frac{1}{\frac{\sqrt{\ell}}{\sqrt{d}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_3 \cdot t_0\right) \cdot \left(1 + -0.5 \cdot \frac{h \cdot t_1}{\ell}\right)\\ \end{array} \]

Alternative 4
Accuracy	69.0%
Cost	21844

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := 1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\\ t_2 := \sqrt{\frac{d}{h}}\\ t_3 := \sqrt{-d}\\ t_4 := {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}\\ \mathbf{if}\;h \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;\left(t_2 \cdot \frac{t_3}{\sqrt{-\ell}}\right) \cdot t_1\\ \mathbf{elif}\;h \leq -9.5 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right) \cdot \left(t_0 \cdot \frac{1}{\sqrt{\frac{h}{d}}}\right)\\ \mathbf{elif}\;h \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(\frac{t_3}{\sqrt{-h}} \cdot t_0\right) \cdot \left(1 + 0.5 \cdot \left(\left(\frac{M \cdot \left(M \cdot \left(D \cdot D\right)\right)}{\ell} \cdot \frac{\frac{h}{d}}{d}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;h \leq 1.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + t_4 \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{elif}\;h \leq 1.15 \cdot 10^{+264}:\\ \;\;\;\;t_1 \cdot \left(t_2 \cdot \frac{1}{\frac{\sqrt{\ell}}{\sqrt{d}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 \cdot t_0\right) \cdot \left(1 + -0.5 \cdot \frac{h \cdot t_4}{\ell}\right)\\ \end{array} \]

Alternative 5
Accuracy	66.6%
Cost	21532

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}} \cdot t_0\\ t_2 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ t_3 := \frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ t_4 := t_0 \cdot \frac{1}{\sqrt{\frac{h}{d}}}\\ t_5 := D \cdot \left(M \cdot \frac{h}{d}\right)\\ \mathbf{if}\;d \leq -6.5 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -1.3 \cdot 10^{+124}:\\ \;\;\;\;t_4 \cdot \left(1 + 0.5 \cdot \left(\left(\frac{M \cdot \left(M \cdot \left(D \cdot D\right)\right)}{\ell} \cdot \frac{\frac{h}{d}}{d}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -8.5 \cdot 10^{-98}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right) \cdot t_1\\ \mathbf{elif}\;d \leq -5.8 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-285}:\\ \;\;\;\;t_1 \cdot \left(1 + 0.5 \cdot \left(\frac{t_5}{\frac{d}{\frac{D \cdot M}{\ell}}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq 1.55 \cdot 10^{-95}:\\ \;\;\;\;t_3 \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{elif}\;d \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{t_5}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right) \cdot t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	72.5%
Cost	21448

\[\begin{array}{l} t_0 := \sqrt{-d}\\ \mathbf{if}\;\ell \leq -1.8 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t_0}{\sqrt{-h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{D} \cdot \frac{\ell}{M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;\ell \leq -4.6 \cdot 10^{-305}:\\ \;\;\;\;\left(\sqrt{\frac{d}{h}} \cdot \frac{t_0}{\sqrt{-\ell}}\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;\ell \leq 8.6 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{h}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{+248}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + {\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{1}{\frac{\sqrt{\ell}}{{h}^{-0.5}}}\\ \end{array} \]

Alternative 7
Accuracy	64.2%
Cost	15580

\[\begin{array}{l} t_0 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ t_1 := \sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ t_2 := t_1 \cdot \left(1 + 0.5 \cdot \left(\left(\left(D \cdot M\right) \cdot \frac{\frac{D}{d} \cdot \frac{M}{\ell}}{\frac{d}{h}}\right) \cdot -0.25\right)\right)\\ \mathbf{if}\;\ell \leq -2.4 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq -5.5 \cdot 10^{+120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -2.8 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq -4.4 \cdot 10^{-268}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -1 \cdot 10^{-310}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 7.5 \cdot 10^{-99}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \leq 7.4 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 8
Accuracy	65.7%
Cost	15448

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ t_1 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ t_2 := \frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \mathbf{if}\;d \leq -5.6 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -1.5 \cdot 10^{+124}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot \frac{M \cdot \left(D \cdot \left(D \cdot M\right)\right)}{\ell}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -9.2 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-285}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(\left(\left(D \cdot M\right) \cdot \frac{\frac{D}{d} \cdot \frac{M}{\ell}}{\frac{d}{h}}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq 1.85 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq 3.4 \cdot 10^{+33}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(\frac{D}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{M \cdot \left(D \cdot M\right)}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq 1.2 \cdot 10^{+163}:\\ \;\;\;\;\frac{\frac{d}{\sqrt{\ell}}}{\sqrt{h}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	64.9%
Cost	15448

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ t_1 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{if}\;d \leq -9.2 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -1.3 \cdot 10^{+124}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot \frac{M \cdot \left(D \cdot \left(D \cdot M\right)\right)}{\ell}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -1.38 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -2.22 \cdot 10^{-103}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right) \cdot t_0\\ \mathbf{elif}\;d \leq -1.9 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq 7 \cdot 10^{-190}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{\frac{D \cdot M}{\ell}}} \cdot -0.25\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 10
Accuracy	64.7%
Cost	15448

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}} \cdot t_0\\ t_2 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{if}\;d \leq -6.2 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -3.2 \cdot 10^{+124}:\\ \;\;\;\;\left(t_0 \cdot \frac{1}{\sqrt{\frac{h}{d}}}\right) \cdot \left(1 + 0.5 \cdot \left(\left(\frac{M \cdot \left(M \cdot \left(D \cdot D\right)\right)}{\ell} \cdot \frac{\frac{h}{d}}{d}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -1.02 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq -2.3 \cdot 10^{-99}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right) \cdot t_1\\ \mathbf{elif}\;d \leq -8 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d \leq 1.25 \cdot 10^{-188}:\\ \;\;\;\;t_1 \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot \frac{h}{d}\right)}{\frac{d}{\frac{D \cdot M}{\ell}}} \cdot -0.25\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 11
Accuracy	65.8%
Cost	15184

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ t_1 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{if}\;d \leq -5.6 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot \frac{M \cdot \left(D \cdot \left(D \cdot M\right)\right)}{\ell}\right) \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -1.26 \cdot 10^{-100}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(\frac{D \cdot M}{\left(d \cdot \frac{d}{h}\right) \cdot \frac{\ell}{D \cdot M}} \cdot -0.25\right)\right) \cdot t_0\\ \mathbf{elif}\;d \leq -1.4 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq 1.35 \cdot 10^{-248}:\\ \;\;\;\;\left(1 + -0.5 \cdot \left(\frac{h}{\ell} \cdot {\left(M \cdot \left(D \cdot \frac{0.5}{d}\right)\right)}^{2}\right)\right) \cdot \sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 12
Accuracy	63.6%
Cost	13580

\[\begin{array}{l} t_0 := d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{if}\;d \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -8 \cdot 10^{-68}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\\ \mathbf{elif}\;d \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;d \cdot \frac{{h}^{-0.5}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 13
Accuracy	62.4%
Cost	13316

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

Alternative 14
Accuracy	62.5%
Cost	13252

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

Alternative 15
Accuracy	46.7%
Cost	7508

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{if}\;d \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -4.9 \cdot 10^{+55}:\\ \;\;\;\;\sqrt{d \cdot \frac{d}{h \cdot \ell}}\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 3.5 \cdot 10^{+77}:\\ \;\;\;\;d \cdot {\left(h \cdot \ell\right)}^{-0.5}\\ \mathbf{elif}\;d \leq 4.1 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h \cdot \ell}}\\ \end{array} \]

Alternative 16
Accuracy	46.7%
Cost	7508

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{if}\;d \leq -3.6 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;\sqrt{\frac{d \cdot d}{h \cdot \ell}}\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;d \cdot {\left(h \cdot \ell\right)}^{-0.5}\\ \mathbf{elif}\;d \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h \cdot \ell}}\\ \end{array} \]

Alternative 17
Accuracy	46.6%
Cost	7508

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{if}\;d \leq -1.9 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -9.2 \cdot 10^{+55}:\\ \;\;\;\;\sqrt{\frac{d \cdot d}{h \cdot \ell}}\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 3.5 \cdot 10^{+77}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{h}}{\ell}}\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h \cdot \ell}}\\ \end{array} \]

Alternative 18
Accuracy	46.7%
Cost	7508

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{if}\;d \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -1.1 \cdot 10^{+56}:\\ \;\;\;\;\sqrt{\frac{d \cdot d}{h \cdot \ell}}\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 2.05 \cdot 10^{-27}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{h}}{\ell}}\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{+107}:\\ \;\;\;\;\sqrt{\frac{\frac{d \cdot d}{\ell}}{h}}\\ \mathbf{else}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \end{array} \]

Alternative 19
Accuracy	54.5%
Cost	7376

\[\begin{array}{l} \mathbf{if}\;d \leq -2 \cdot 10^{-258}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq 2.2 \cdot 10^{-224}:\\ \;\;\;\;\sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{elif}\;d \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{h}}{\ell}}\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{+107}:\\ \;\;\;\;\sqrt{\frac{\frac{d \cdot d}{\ell}}{h}}\\ \mathbf{else}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \end{array} \]

Alternative 20
Accuracy	46.9%
Cost	7244

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{h} \cdot \frac{d}{\ell}}\\ \mathbf{if}\;d \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 3.5 \cdot 10^{+77}:\\ \;\;\;\;d \cdot {\left(h \cdot \ell\right)}^{-0.5}\\ \mathbf{elif}\;d \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h \cdot \ell}}\\ \end{array} \]

Alternative 21
Accuracy	31.5%
Cost	6784

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

Alternative 22
Accuracy	31.6%
Cost	6720

\[\frac{d}{\sqrt{h \cdot \ell}} \]

Reproduce

herbie shell --seed 2023125 
(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)))))