Henrywood and Agarwal, Equation (12)

Average Accuracy: 58.8% → 73.0%

Time: 55.2s

Precision: binary64

Cost: 33672

\[ \begin{array}{c}[M, D] = \mathsf{sort}([M, D])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt{d \cdot \frac{\frac{d}{h}}{\ell}}\\ \mathbf{if}\;d \leq -2.8 \cdot 10^{-146}:\\ \;\;\;\;\left(\frac{\sqrt{-d}}{\sqrt{-h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right)\\ \mathbf{elif}\;d \leq -3.8 \cdot 10^{-219}:\\ \;\;\;\;0.125 \cdot \left(\frac{{D}^{2} \cdot {M}^{2}}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{1}{h \cdot \ell}}\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{-220}:\\ \;\;\;\;t_0 + \left(-0.125 \cdot {\left(D \cdot \frac{M}{d}\right)}^{2}\right) \cdot \left(\frac{h}{\ell} \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

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 (sqrt (* d (/ (/ d h) l)))))
   (if (<= d -2.8e-146)
     (*
      (* (/ (sqrt (- d)) (sqrt (- h))) (sqrt (/ d l)))
      (+ 1.0 (* (* h (/ (pow (* 0.5 (/ (* M D) d)) 2.0) l)) -0.5)))
     (if (<= d -3.8e-219)
       (-
        (*
         0.125
         (* (/ (* (pow D 2.0) (pow M 2.0)) d) (sqrt (/ h (pow l 3.0)))))
        (* d (sqrt (/ 1.0 (* h l)))))
       (if (<= d 1.15e-220)
         (+ t_0 (* (* -0.125 (pow (* D (/ M d)) 2.0)) (* (/ h l) t_0)))
         (*
          (/ d (* (sqrt h) (sqrt l)))
          (+ 1.0 (* -0.5 (* h (* (/ (pow (/ D (/ d M)) 2.0) l) 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 = sqrt((d * ((d / h) / l)));
	double tmp;
	if (d <= -2.8e-146) {
		tmp = ((sqrt(-d) / sqrt(-h)) * sqrt((d / l))) * (1.0 + ((h * (pow((0.5 * ((M * D) / d)), 2.0) / l)) * -0.5));
	} else if (d <= -3.8e-219) {
		tmp = (0.125 * (((pow(D, 2.0) * pow(M, 2.0)) / d) * sqrt((h / pow(l, 3.0))))) - (d * sqrt((1.0 / (h * l))));
	} else if (d <= 1.15e-220) {
		tmp = t_0 + ((-0.125 * pow((D * (M / d)), 2.0)) * ((h / l) * t_0));
	} else {
		tmp = (d / (sqrt(h) * sqrt(l))) * (1.0 + (-0.5 * (h * ((pow((D / (d / M)), 2.0) / l) * 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) :: tmp
    t_0 = sqrt((d * ((d / h) / l)))
    if (d <= (-2.8d-146)) then
        tmp = ((sqrt(-d) / sqrt(-h)) * sqrt((d / l))) * (1.0d0 + ((h * (((0.5d0 * ((m * d_1) / d)) ** 2.0d0) / l)) * (-0.5d0)))
    else if (d <= (-3.8d-219)) then
        tmp = (0.125d0 * ((((d_1 ** 2.0d0) * (m ** 2.0d0)) / d) * sqrt((h / (l ** 3.0d0))))) - (d * sqrt((1.0d0 / (h * l))))
    else if (d <= 1.15d-220) then
        tmp = t_0 + (((-0.125d0) * ((d_1 * (m / d)) ** 2.0d0)) * ((h / l) * t_0))
    else
        tmp = (d / (sqrt(h) * sqrt(l))) * (1.0d0 + ((-0.5d0) * (h * ((((d_1 / (d / m)) ** 2.0d0) / l) * 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 = Math.sqrt((d * ((d / h) / l)));
	double tmp;
	if (d <= -2.8e-146) {
		tmp = ((Math.sqrt(-d) / Math.sqrt(-h)) * Math.sqrt((d / l))) * (1.0 + ((h * (Math.pow((0.5 * ((M * D) / d)), 2.0) / l)) * -0.5));
	} else if (d <= -3.8e-219) {
		tmp = (0.125 * (((Math.pow(D, 2.0) * Math.pow(M, 2.0)) / d) * Math.sqrt((h / Math.pow(l, 3.0))))) - (d * Math.sqrt((1.0 / (h * l))));
	} else if (d <= 1.15e-220) {
		tmp = t_0 + ((-0.125 * Math.pow((D * (M / d)), 2.0)) * ((h / l) * t_0));
	} else {
		tmp = (d / (Math.sqrt(h) * Math.sqrt(l))) * (1.0 + (-0.5 * (h * ((Math.pow((D / (d / M)), 2.0) / l) * 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 = math.sqrt((d * ((d / h) / l)))
	tmp = 0
	if d <= -2.8e-146:
		tmp = ((math.sqrt(-d) / math.sqrt(-h)) * math.sqrt((d / l))) * (1.0 + ((h * (math.pow((0.5 * ((M * D) / d)), 2.0) / l)) * -0.5))
	elif d <= -3.8e-219:
		tmp = (0.125 * (((math.pow(D, 2.0) * math.pow(M, 2.0)) / d) * math.sqrt((h / math.pow(l, 3.0))))) - (d * math.sqrt((1.0 / (h * l))))
	elif d <= 1.15e-220:
		tmp = t_0 + ((-0.125 * math.pow((D * (M / d)), 2.0)) * ((h / l) * t_0))
	else:
		tmp = (d / (math.sqrt(h) * math.sqrt(l))) * (1.0 + (-0.5 * (h * ((math.pow((D / (d / M)), 2.0) / l) * 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 = sqrt(Float64(d * Float64(Float64(d / h) / l)))
	tmp = 0.0
	if (d <= -2.8e-146)
		tmp = Float64(Float64(Float64(sqrt(Float64(-d)) / sqrt(Float64(-h))) * sqrt(Float64(d / l))) * Float64(1.0 + Float64(Float64(h * Float64((Float64(0.5 * Float64(Float64(M * D) / d)) ^ 2.0) / l)) * -0.5)));
	elseif (d <= -3.8e-219)
		tmp = Float64(Float64(0.125 * Float64(Float64(Float64((D ^ 2.0) * (M ^ 2.0)) / d) * sqrt(Float64(h / (l ^ 3.0))))) - Float64(d * sqrt(Float64(1.0 / Float64(h * l)))));
	elseif (d <= 1.15e-220)
		tmp = Float64(t_0 + Float64(Float64(-0.125 * (Float64(D * Float64(M / d)) ^ 2.0)) * Float64(Float64(h / l) * t_0)));
	else
		tmp = Float64(Float64(d / Float64(sqrt(h) * sqrt(l))) * Float64(1.0 + Float64(-0.5 * Float64(h * Float64(Float64((Float64(D / Float64(d / M)) ^ 2.0) / l) * 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 = sqrt((d * ((d / h) / l)));
	tmp = 0.0;
	if (d <= -2.8e-146)
		tmp = ((sqrt(-d) / sqrt(-h)) * sqrt((d / l))) * (1.0 + ((h * (((0.5 * ((M * D) / d)) ^ 2.0) / l)) * -0.5));
	elseif (d <= -3.8e-219)
		tmp = (0.125 * ((((D ^ 2.0) * (M ^ 2.0)) / d) * sqrt((h / (l ^ 3.0))))) - (d * sqrt((1.0 / (h * l))));
	elseif (d <= 1.15e-220)
		tmp = t_0 + ((-0.125 * ((D * (M / d)) ^ 2.0)) * ((h / l) * t_0));
	else
		tmp = (d / (sqrt(h) * sqrt(l))) * (1.0 + (-0.5 * (h * ((((D / (d / M)) ^ 2.0) / l) * 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[Sqrt[N[(d * N[(N[(d / h), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[d, -2.8e-146], N[(N[(N[(N[Sqrt[(-d)], $MachinePrecision] / N[Sqrt[(-h)], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(d / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(h * N[(N[Power[N[(0.5 * N[(N[(M * D), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -3.8e-219], N[(N[(0.125 * N[(N[(N[(N[Power[D, 2.0], $MachinePrecision] * N[Power[M, 2.0], $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] * N[Sqrt[N[(h / N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(d * N[Sqrt[N[(1.0 / N[(h * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.15e-220], N[(t$95$0 + N[(N[(-0.125 * N[Power[N[(D * N[(M / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(h / l), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(d / N[(N[Sqrt[h], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(-0.5 * N[(h * N[(N[(N[Power[N[(D / N[(d / M), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -2.80000000000000003e-146

   1. Initial program 63.9%

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

   2. Simplified 63.7%

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

      [Start] 63.9	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 63.9	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 63.9	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 63.9	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 63.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 63.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 63.9	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 63.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Applied egg-rr 63.1%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)} - 1\right)}\right) \]

   4. Simplified 66.7%

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

      [Start] 63.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(e^{\mathsf{log1p}\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)} - 1\right)\right) \]
      expm1-def [=>] 63.1	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)\right)}\right) \]
      expm1-log1p [=>] 63.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      associate-*r/ [=>] 65.6	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\frac{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot h}{\ell}}\right) \]
      associate-*l/ [<=] 66.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(\frac{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}}{\ell} \cdot h\right)}\right) \]
      *-commutative [=>] 66.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(h \cdot \frac{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}}{\ell}\right)}\right) \]
      *-commutative [=>] 66.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(h \cdot \frac{{\left(M \cdot \color{blue}{\left(\frac{D}{d} \cdot 0.5\right)}\right)}^{2}}{\ell}\right)\right) \]
      associate-*r* [=>] 66.7	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(h \cdot \frac{{\color{blue}{\left(\left(M \cdot \frac{D}{d}\right) \cdot 0.5\right)}}^{2}}{\ell}\right)\right) \]

   5. Applied egg-rr 66.8%

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

   6. Applied egg-rr 78.5%

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

   if -2.80000000000000003e-146 < d < -3.80000000000000025e-219

   1. Initial program 43.6%

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

   2. Applied egg-rr 35.3%

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

   3. Taylor expanded in d around -inf 41.3%

      \[\leadsto {\color{blue}{\left(0.125 \cdot \left(\frac{{D}^{2} \cdot {M}^{2}}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) + -1 \cdot \left(d \cdot \sqrt{\frac{1}{\ell \cdot h}}\right)\right)}}^{1} \]

   if -3.80000000000000025e-219 < d < 1.1499999999999999e-220

   1. Initial program 34.5%

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

   2. Applied egg-rr 27.0%

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

   3. Applied egg-rr 27.1%

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

   if 1.1499999999999999e-220 < d

   1. Initial program 63.0%

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

   2. Simplified 62.5%

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

      [Start] 63.0	\[ \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 63.0	\[ \left({\left(\frac{d}{h}\right)}^{\color{blue}{0.5}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 63.0	\[ \left(\color{blue}{\sqrt{\frac{d}{h}}} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      metadata-eval [=>] 63.0	\[ \left(\sqrt{\frac{d}{h}} \cdot {\left(\frac{d}{\ell}\right)}^{\color{blue}{0.5}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      unpow1/2 [=>] 63.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \color{blue}{\sqrt{\frac{d}{\ell}}}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right) \]
      associate-*l* [=>] 63.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{\frac{1}{2} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      metadata-eval [=>] 63.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \color{blue}{0.5} \cdot \left({\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\right)\right) \]
      times-frac [=>] 62.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left({\color{blue}{\left(\frac{M}{2} \cdot \frac{D}{d}\right)}}^{2} \cdot \frac{h}{\ell}\right)\right) \]

   3. Applied egg-rr 61.8%

      \[\leadsto \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)} - 1\right)}\right) \]

   4. Simplified 65.0%

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

      [Start] 61.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(e^{\mathsf{log1p}\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)} - 1\right)\right) \]
      expm1-def [=>] 61.8	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)\right)}\right) \]
      expm1-log1p [=>] 62.5	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left({\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot \frac{h}{\ell}\right)}\right) \]
      associate-*r/ [=>] 64.2	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\frac{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2} \cdot h}{\ell}}\right) \]
      associate-*l/ [<=] 65.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(\frac{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}}{\ell} \cdot h\right)}\right) \]
      *-commutative [=>] 65.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \color{blue}{\left(h \cdot \frac{{\left(M \cdot \left(0.5 \cdot \frac{D}{d}\right)\right)}^{2}}{\ell}\right)}\right) \]
      *-commutative [=>] 65.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(h \cdot \frac{{\left(M \cdot \color{blue}{\left(\frac{D}{d} \cdot 0.5\right)}\right)}^{2}}{\ell}\right)\right) \]
      associate-*r* [=>] 65.0	\[ \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.5 \cdot \left(h \cdot \frac{{\color{blue}{\left(\left(M \cdot \frac{D}{d}\right) \cdot 0.5\right)}}^{2}}{\ell}\right)\right) \]

   5. Applied egg-rr 84.8%

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

   6. Simplified 84.7%

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

      [Start] 84.8	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} + \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(\left(-0.5 \cdot h\right) \cdot \frac{{\left(\frac{M}{\frac{d}{D}}\right)}^{2}}{\frac{\ell}{0.25}}\right) \]
      *-lft-identity [<=] 84.8	\[ \color{blue}{1 \cdot \frac{d}{\sqrt{h} \cdot \sqrt{\ell}}} + \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(\left(-0.5 \cdot h\right) \cdot \frac{{\left(\frac{M}{\frac{d}{D}}\right)}^{2}}{\frac{\ell}{0.25}}\right) \]
      *-commutative [<=] 84.8	\[ 1 \cdot \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} + \color{blue}{\left(\left(-0.5 \cdot h\right) \cdot \frac{{\left(\frac{M}{\frac{d}{D}}\right)}^{2}}{\frac{\ell}{0.25}}\right) \cdot \frac{d}{\sqrt{h} \cdot \sqrt{\ell}}} \]
      distribute-rgt-in [<=] 84.8	\[ \color{blue}{\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + \left(-0.5 \cdot h\right) \cdot \frac{{\left(\frac{M}{\frac{d}{D}}\right)}^{2}}{\frac{\ell}{0.25}}\right)} \]
      associate-*l* [=>] 84.8	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + \color{blue}{-0.5 \cdot \left(h \cdot \frac{{\left(\frac{M}{\frac{d}{D}}\right)}^{2}}{\frac{\ell}{0.25}}\right)}\right) \]
      associate-/r/ [=>] 84.8	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \color{blue}{\left(\frac{{\left(\frac{M}{\frac{d}{D}}\right)}^{2}}{\ell} \cdot 0.25\right)}\right)\right) \]
      associate-/l* [<=] 85.1	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\color{blue}{\left(\frac{M \cdot D}{d}\right)}}^{2}}{\ell} \cdot 0.25\right)\right)\right) \]
      *-commutative [<=] 85.1	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{\color{blue}{D \cdot M}}{d}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right) \]
      associate-/l* [=>] 84.7	\[ \frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\color{blue}{\left(\frac{D}{\frac{d}{M}}\right)}}^{2}}{\ell} \cdot 0.25\right)\right)\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -2.8 \cdot 10^{-146}:\\ \;\;\;\;\left(\frac{\sqrt{-d}}{\sqrt{-h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right)\\ \mathbf{elif}\;d \leq -3.8 \cdot 10^{-219}:\\ \;\;\;\;0.125 \cdot \left(\frac{{D}^{2} \cdot {M}^{2}}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{1}{h \cdot \ell}}\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{-220}:\\ \;\;\;\;\sqrt{d \cdot \frac{\frac{d}{h}}{\ell}} + \left(-0.125 \cdot {\left(D \cdot \frac{M}{d}\right)}^{2}\right) \cdot \left(\frac{h}{\ell} \cdot \sqrt{d \cdot \frac{\frac{d}{h}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	72.3%
Cost	27536

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}}\\ \mathbf{if}\;d \leq -5.2 \cdot 10^{+101}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -1.14 \cdot 10^{-144}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right) \cdot \left(t_0 \cdot t_1\right)\\ \mathbf{elif}\;d \leq -3 \cdot 10^{-219}:\\ \;\;\;\;\left(\left(M \cdot M\right) \cdot \left(D \cdot \frac{D}{d}\right)\right) \cdot \left(0.125 \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;t_1 \cdot \left(t_0 \cdot \mathsf{fma}\left({\left(D \cdot \frac{\frac{M}{d}}{2}\right)}^{2}, \frac{-0.5}{\frac{\ell}{h}}, 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	72.2%
Cost	27536

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ t_1 := \sqrt{\frac{d}{h}}\\ \mathbf{if}\;d \leq -1.7 \cdot 10^{+101}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -2.5 \cdot 10^{-145}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right) \cdot \left(t_0 \cdot t_1\right)\\ \mathbf{elif}\;d \leq -5 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(\sqrt{\frac{h}{{\ell}^{3}}} \cdot \left(\frac{D \cdot D}{d} \cdot \left(M \cdot M\right)\right), 0.125, d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;t_1 \cdot \left(t_0 \cdot \mathsf{fma}\left({\left(D \cdot \frac{\frac{M}{d}}{2}\right)}^{2}, \frac{-0.5}{\frac{\ell}{h}}, 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	74.2%
Cost	27404

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ \mathbf{if}\;d \leq -4.2 \cdot 10^{-146}:\\ \;\;\;\;\left(\frac{\sqrt{-d}}{\sqrt{-h}} \cdot t_0\right) \cdot \left(1 + -0.5 \cdot \left(h \cdot \frac{{\left(0.5 \cdot \left(M \cdot \frac{D}{d}\right)\right)}^{2}}{\ell}\right)\right)\\ \mathbf{elif}\;d \leq -6.5 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{fma}\left(\sqrt{\frac{h}{{\ell}^{3}}} \cdot \left(\frac{D \cdot D}{d} \cdot \left(M \cdot M\right)\right), 0.125, d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\right)\\ \mathbf{elif}\;d \leq 2.05 \cdot 10^{-276}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(t_0 \cdot \mathsf{fma}\left({\left(D \cdot \frac{\frac{M}{d}}{2}\right)}^{2}, \frac{-0.5}{\frac{\ell}{h}}, 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	74.1%
Cost	27404

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ \mathbf{if}\;d \leq -2.8 \cdot 10^{-146}:\\ \;\;\;\;\left(\frac{\sqrt{-d}}{\sqrt{-h}} \cdot t_0\right) \cdot \left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right)\\ \mathbf{elif}\;d \leq -1.9 \cdot 10^{-218}:\\ \;\;\;\;\mathsf{fma}\left(\sqrt{\frac{h}{{\ell}^{3}}} \cdot \left(\frac{D \cdot D}{d} \cdot \left(M \cdot M\right)\right), 0.125, d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(t_0 \cdot \mathsf{fma}\left({\left(D \cdot \frac{\frac{M}{d}}{2}\right)}^{2}, \frac{-0.5}{\frac{\ell}{h}}, 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	72.3%
Cost	27396

\[\begin{array}{l} \mathbf{if}\;\ell \leq -9.5 \cdot 10^{+36}:\\ \;\;\;\;\left(\sqrt{\frac{d}{h}} \cdot \frac{\sqrt{-d}}{\sqrt{-\ell}}\right) \cdot \left(1 + -0.5 \cdot \left(\frac{h}{\ell} \cdot {\left(\frac{D}{d} \cdot \frac{M}{2}\right)}^{2}\right)\right)\\ \mathbf{elif}\;\ell \leq -0.0035:\\ \;\;\;\;\left(\left(M \cdot M\right) \cdot \left(D \cdot \frac{D}{d}\right)\right) \cdot \left(0.125 \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \mathbf{elif}\;\ell \leq 4.1 \cdot 10^{-298}:\\ \;\;\;\;\left({\left(\frac{d}{h}\right)}^{0.5} \cdot {\left(\frac{d}{\ell}\right)}^{0.5}\right) \cdot \left(1 + \frac{-0.5 \cdot \left(h \cdot {\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}\right)}{\ell}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	72.7%
Cost	27396

\[\begin{array}{l} t_0 := \sqrt{d \cdot \frac{\frac{d}{h}}{\ell}}\\ \mathbf{if}\;d \leq -1.5 \cdot 10^{-145}:\\ \;\;\;\;\left(\frac{\sqrt{-d}}{\sqrt{-h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(\sqrt{\frac{h}{{\ell}^{3}}} \cdot \left(\frac{D \cdot D}{d} \cdot \left(M \cdot M\right)\right), 0.125, d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\right)\\ \mathbf{elif}\;d \leq 1.2 \cdot 10^{-220}:\\ \;\;\;\;t_0 + \left(-0.125 \cdot {\left(D \cdot \frac{M}{d}\right)}^{2}\right) \cdot \left(\frac{h}{\ell} \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	72.3%
Cost	21328

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}}\\ \mathbf{if}\;d \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -2.8 \cdot 10^{-143}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right) \cdot \left(t_0 \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \leq -1.35 \cdot 10^{-219}:\\ \;\;\;\;\left(\left(M \cdot M\right) \cdot \left(D \cdot \frac{D}{d}\right)\right) \cdot \left(0.125 \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \mathbf{elif}\;d \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;\left(t_0 \cdot {\left(\frac{d}{h}\right)}^{0.5}\right) \cdot \left(1 + \frac{h}{\ell} \cdot \left(-0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	71.2%
Cost	21136

\[\begin{array}{l} \mathbf{if}\;d \leq -4.3 \cdot 10^{+88}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-123}:\\ \;\;\;\;\left({\left(\frac{d}{h}\right)}^{0.5} \cdot {\left(\frac{d}{\ell}\right)}^{0.5}\right) \cdot \left(1 + \frac{D \cdot \left(\frac{M}{\frac{d}{D}} \cdot \frac{M}{\frac{\ell}{h \cdot 0.125}}\right)}{-d}\right)\\ \mathbf{elif}\;d \leq -1 \cdot 10^{-219}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	71.0%
Cost	21136

\[\begin{array}{l} \mathbf{if}\;d \leq -3.85 \cdot 10^{+90}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -1.55 \cdot 10^{-124}:\\ \;\;\;\;\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 - {\left(\frac{D}{d} \cdot \frac{M}{2}\right)}^{2} \cdot \left(h \cdot \frac{0.5}{\ell}\right)\right)\right)\\ \mathbf{elif}\;d \leq -3.1 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	71.9%
Cost	21136

\[\begin{array}{l} \mathbf{if}\;d \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -1.3 \cdot 10^{-124}:\\ \;\;\;\;\left(1 + -0.5 \cdot \left(h \cdot \frac{{\left(0.5 \cdot \left(M \cdot \frac{D}{d}\right)\right)}^{2}}{\ell}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.05 \cdot 10^{-276}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	72.1%
Cost	21136

\[\begin{array}{l} \mathbf{if}\;d \leq -1.25 \cdot 10^{+102}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -9.5 \cdot 10^{-124}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \leq -4.8 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	71.8%
Cost	21136

\[\begin{array}{l} \mathbf{if}\;d \leq -1.65 \cdot 10^{+102}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -4.6 \cdot 10^{-144}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{{\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}}{\ell}\right) \cdot -0.5\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \leq -3.45 \cdot 10^{-220}:\\ \;\;\;\;\left(\left(M \cdot M\right) \cdot \left(D \cdot \frac{D}{d}\right)\right) \cdot \left(0.125 \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	71.8%
Cost	21136

\[\begin{array}{l} t_0 := {\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}\\ \mathbf{if}\;d \leq -2.05 \cdot 10^{+102}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -4.2 \cdot 10^{-141}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{t_0}{\ell}\right) \cdot -0.5\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \leq -4.5 \cdot 10^{-220}:\\ \;\;\;\;\left(\left(M \cdot M\right) \cdot \left(D \cdot \frac{D}{d}\right)\right) \cdot \left(0.125 \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \mathbf{elif}\;d \leq 3 \cdot 10^{-277}:\\ \;\;\;\;\left(1 - 0.5 \cdot \left(\frac{h}{\ell} \cdot t_0\right)\right) \cdot {\left(d \cdot \frac{\frac{d}{h}}{\ell}\right)}^{0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	71.7%
Cost	21136

\[\begin{array}{l} t_0 := {\left(0.5 \cdot \frac{M \cdot D}{d}\right)}^{2}\\ \mathbf{if}\;d \leq -2.3 \cdot 10^{+102}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -4.6 \cdot 10^{-146}:\\ \;\;\;\;\left(1 + \left(h \cdot \frac{t_0}{\ell}\right) \cdot -0.5\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-219}:\\ \;\;\;\;\left(\left(M \cdot M\right) \cdot \left(D \cdot \frac{D}{d}\right)\right) \cdot \left(0.125 \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right) - d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \mathbf{elif}\;d \leq 1.4 \cdot 10^{-274}:\\ \;\;\;\;\frac{1}{\sqrt{\frac{h \cdot \frac{\ell}{d}}{d}}} \cdot \left(1 - 0.5 \cdot \left(\frac{h}{\ell} \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}} \cdot \left(1 + -0.5 \cdot \left(h \cdot \left(\frac{{\left(\frac{D}{\frac{d}{M}}\right)}^{2}}{\ell} \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	65.7%
Cost	15444

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\\ \mathbf{if}\;d \leq -1.15 \cdot 10^{+101}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-123}:\\ \;\;\;\;t_0 \cdot \left(1 - -0.5 \cdot \left(\frac{\frac{\left(M \cdot D\right) \cdot \left(h \cdot D\right)}{d \cdot d}}{\frac{\ell}{M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -4.8 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 7.6 \cdot 10^{-156}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{elif}\;d \leq 8.6 \cdot 10^{+73}:\\ \;\;\;\;t_0 \cdot \left(1 + 0.5 \cdot \left(0.25 \cdot \frac{\left(D \cdot \left(h \cdot \left(M \cdot D\right)\right)\right) \cdot \frac{\frac{-1}{d}}{d}}{\frac{\ell}{M}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 16
Accuracy	67.3%
Cost	15444

\[\begin{array}{l} t_0 := \left({\left(\frac{d}{h}\right)}^{0.5} \cdot {\left(\frac{d}{\ell}\right)}^{0.5}\right) \cdot \left(1 + \frac{D \cdot \left(\frac{M}{\frac{d}{D}} \cdot \frac{M}{\frac{\ell}{h \cdot 0.125}}\right)}{-d}\right)\\ \mathbf{if}\;d \leq -9.5 \cdot 10^{+86}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -1.2 \cdot 10^{-218}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 8.8 \cdot 10^{+73}:\\ \;\;\;\;\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 + 0.5 \cdot \left(0.25 \cdot \frac{\left(D \cdot \left(h \cdot \left(M \cdot D\right)\right)\right) \cdot \frac{\frac{-1}{d}}{d}}{\frac{\ell}{M}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 17
Accuracy	65.1%
Cost	14920

\[\begin{array}{l} \mathbf{if}\;d \leq -4 \cdot 10^{+80}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -8 \cdot 10^{-132}:\\ \;\;\;\;\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 + 0.5 \cdot \left(\frac{D \cdot \left(M \cdot D\right)}{\frac{\ell}{M} \cdot \frac{d}{\frac{h}{d}}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 18
Accuracy	66.1%
Cost	14920

\[\begin{array}{l} \mathbf{if}\;d \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -1.15 \cdot 10^{-122}:\\ \;\;\;\;\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - -0.5 \cdot \left(\frac{\frac{\left(M \cdot D\right) \cdot \left(h \cdot D\right)}{d \cdot d}}{\frac{\ell}{M}} \cdot -0.25\right)\right)\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 19
Accuracy	64.1%
Cost	14864

\[\begin{array}{l} \mathbf{if}\;d \leq -5.5 \cdot 10^{+82}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -4.9 \cdot 10^{-141}:\\ \;\;\;\;\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\\ \mathbf{elif}\;d \leq -2.65 \cdot 10^{-219}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq -1.4 \cdot 10^{-289}:\\ \;\;\;\;\sqrt{d \cdot \frac{\frac{d}{\ell}}{h}} \cdot \left(1 + {\left(0.5 \cdot \left(M \cdot \frac{D}{d}\right)\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 20
Accuracy	64.1%
Cost	14864

\[\begin{array}{l} \mathbf{if}\;d \leq -5.1 \cdot 10^{+82}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -9.4 \cdot 10^{-141}:\\ \;\;\;\;\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-220}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq -1.4 \cdot 10^{-289}:\\ \;\;\;\;\sqrt{\frac{d}{h \cdot \frac{\ell}{d}}} \cdot \left(1 + -0.5 \cdot \left(\frac{h}{\ell} \cdot {\left(0.5 \cdot \frac{M}{\frac{d}{D}}\right)}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 21
Accuracy	64.1%
Cost	14864

\[\begin{array}{l} \mathbf{if}\;d \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -1.92 \cdot 10^{-143}:\\ \;\;\;\;\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\\ \mathbf{elif}\;d \leq -4.8 \cdot 10^{-219}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + {\left(\left(M \cdot D\right) \cdot \frac{0.5}{d}\right)}^{2} \cdot \left(\frac{h}{\ell} \cdot -0.5\right)\right) \cdot \sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 22
Accuracy	64.3%
Cost	13776

\[\begin{array}{l} t_0 := \sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\\ \mathbf{if}\;d \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{elif}\;d \leq -2.06 \cdot 10^{-140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -1.6 \cdot 10^{-211}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{\frac{1}{h}}{\ell}}\right)\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{-277}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 23
Accuracy	64.1%
Cost	13252

\[\begin{array}{l} \mathbf{if}\;d \leq -4 \cdot 10^{-310}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 24
Accuracy	57.6%
Cost	7044

\[\begin{array}{l} \mathbf{if}\;\ell \leq 4.1 \cdot 10^{-298}:\\ \;\;\;\;d \cdot \left(-\sqrt{\frac{1}{h \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \end{array} \]

Alternative 25
Accuracy	48.4%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;\ell \leq 8 \cdot 10^{-300}:\\ \;\;\;\;\sqrt{\frac{d}{\ell} \cdot \frac{d}{h}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h \cdot \ell}}\\ \end{array} \]

Alternative 26
Accuracy	48.2%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;\ell \leq 10^{-302}:\\ \;\;\;\;\sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{\sqrt{h \cdot \ell}}\\ \end{array} \]

Alternative 27
Accuracy	48.3%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;\ell \leq 10^{-302}:\\ \;\;\;\;\sqrt{\frac{d}{h \cdot \frac{\ell}{d}}}\\ \mathbf{else}:\\ \;\;\;\;d \cdot \sqrt{\frac{\frac{1}{\ell}}{h}}\\ \end{array} \]

Alternative 28
Accuracy	31.2%
Cost	6720

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

Reproduce

herbie shell --seed 2023122 
(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)))))