Toniolo and Linder, Equation (10+)

Average Accuracy: 49.6% → 83.4%

Time: 46.2s

Precision: binary64

Cost: 21396

Math

\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

↓

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ t_2 := k \cdot \sin k\\ t_3 := {\sin k}^{2}\\ \mathbf{if}\;k \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_2}}{t_2 \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{\frac{2}{\sin k}}{t_1}}{\frac{t}{\frac{\frac{\ell}{\tan k}}{t}}}\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_3}{\ell}\right)}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 5.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{\ell}{t}}} \cdot \frac{\frac{\frac{2}{\tan k}}{\sin k \cdot t_1}}{\frac{t}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_3}\right)\\ \end{array} \]

FPCore

(FPCore (t l k)
 :precision binary64
 (/
  2.0
  (*
   (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
   (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))

↓

(FPCore (t l k)
 :precision binary64
 (let* ((t_1 (+ 2.0 (pow (/ k t) 2.0)))
        (t_2 (* k (sin k)))
        (t_3 (pow (sin k) 2.0)))
   (if (<= k -2.3e+24)
     (* 2.0 (/ (/ l t_2) (* t_2 (/ t (* l (cos k))))))
     (if (<= k -2.4e-70)
       (/ (* (/ l t) (/ (/ 2.0 (sin k)) t_1)) (/ t (/ (/ l (tan k)) t)))
       (if (<= k -1.35e-99)
         (/ 2.0 (* (/ (* k k) (cos k)) (* (/ t l) (/ t_3 l))))
         (if (<= k 6e-101)
           (* (/ (* (/ l t) (* (/ l t) (/ 1.0 (tan k)))) t) (/ 1.0 (sin k)))
           (if (<= k 5.4e+83)
             (*
              (/ 1.0 (/ t (/ l t)))
              (/ (/ (/ 2.0 (tan k)) (* (sin k) t_1)) (/ t l)))
             (* 2.0 (* (* (/ l k) (/ l k)) (/ (cos k) (* t t_3)))))))))))

C

double code(double t, double l, double k) {
	return 2.0 / ((((pow(t, 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + pow((k / t), 2.0)) + 1.0));
}

↓

double code(double t, double l, double k) {
	double t_1 = 2.0 + pow((k / t), 2.0);
	double t_2 = k * sin(k);
	double t_3 = pow(sin(k), 2.0);
	double tmp;
	if (k <= -2.3e+24) {
		tmp = 2.0 * ((l / t_2) / (t_2 * (t / (l * cos(k)))));
	} else if (k <= -2.4e-70) {
		tmp = ((l / t) * ((2.0 / sin(k)) / t_1)) / (t / ((l / tan(k)) / t));
	} else if (k <= -1.35e-99) {
		tmp = 2.0 / (((k * k) / cos(k)) * ((t / l) * (t_3 / l)));
	} else if (k <= 6e-101) {
		tmp = (((l / t) * ((l / t) * (1.0 / tan(k)))) / t) * (1.0 / sin(k));
	} else if (k <= 5.4e+83) {
		tmp = (1.0 / (t / (l / t))) * (((2.0 / tan(k)) / (sin(k) * t_1)) / (t / l));
	} else {
		tmp = 2.0 * (((l / k) * (l / k)) * (cos(k) / (t * t_3)));
	}
	return tmp;
}

Fortran

real(8) function code(t, l, k)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = 2.0d0 / (((((t ** 3.0d0) / (l * l)) * sin(k)) * tan(k)) * ((1.0d0 + ((k / t) ** 2.0d0)) + 1.0d0))
end function

↓

real(8) function code(t, l, k)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 + ((k / t) ** 2.0d0)
    t_2 = k * sin(k)
    t_3 = sin(k) ** 2.0d0
    if (k <= (-2.3d+24)) then
        tmp = 2.0d0 * ((l / t_2) / (t_2 * (t / (l * cos(k)))))
    else if (k <= (-2.4d-70)) then
        tmp = ((l / t) * ((2.0d0 / sin(k)) / t_1)) / (t / ((l / tan(k)) / t))
    else if (k <= (-1.35d-99)) then
        tmp = 2.0d0 / (((k * k) / cos(k)) * ((t / l) * (t_3 / l)))
    else if (k <= 6d-101) then
        tmp = (((l / t) * ((l / t) * (1.0d0 / tan(k)))) / t) * (1.0d0 / sin(k))
    else if (k <= 5.4d+83) then
        tmp = (1.0d0 / (t / (l / t))) * (((2.0d0 / tan(k)) / (sin(k) * t_1)) / (t / l))
    else
        tmp = 2.0d0 * (((l / k) * (l / k)) * (cos(k) / (t * t_3)))
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double k) {
	return 2.0 / ((((Math.pow(t, 3.0) / (l * l)) * Math.sin(k)) * Math.tan(k)) * ((1.0 + Math.pow((k / t), 2.0)) + 1.0));
}

↓

public static double code(double t, double l, double k) {
	double t_1 = 2.0 + Math.pow((k / t), 2.0);
	double t_2 = k * Math.sin(k);
	double t_3 = Math.pow(Math.sin(k), 2.0);
	double tmp;
	if (k <= -2.3e+24) {
		tmp = 2.0 * ((l / t_2) / (t_2 * (t / (l * Math.cos(k)))));
	} else if (k <= -2.4e-70) {
		tmp = ((l / t) * ((2.0 / Math.sin(k)) / t_1)) / (t / ((l / Math.tan(k)) / t));
	} else if (k <= -1.35e-99) {
		tmp = 2.0 / (((k * k) / Math.cos(k)) * ((t / l) * (t_3 / l)));
	} else if (k <= 6e-101) {
		tmp = (((l / t) * ((l / t) * (1.0 / Math.tan(k)))) / t) * (1.0 / Math.sin(k));
	} else if (k <= 5.4e+83) {
		tmp = (1.0 / (t / (l / t))) * (((2.0 / Math.tan(k)) / (Math.sin(k) * t_1)) / (t / l));
	} else {
		tmp = 2.0 * (((l / k) * (l / k)) * (Math.cos(k) / (t * t_3)));
	}
	return tmp;
}

Python

def code(t, l, k):
	return 2.0 / ((((math.pow(t, 3.0) / (l * l)) * math.sin(k)) * math.tan(k)) * ((1.0 + math.pow((k / t), 2.0)) + 1.0))

↓

def code(t, l, k):
	t_1 = 2.0 + math.pow((k / t), 2.0)
	t_2 = k * math.sin(k)
	t_3 = math.pow(math.sin(k), 2.0)
	tmp = 0
	if k <= -2.3e+24:
		tmp = 2.0 * ((l / t_2) / (t_2 * (t / (l * math.cos(k)))))
	elif k <= -2.4e-70:
		tmp = ((l / t) * ((2.0 / math.sin(k)) / t_1)) / (t / ((l / math.tan(k)) / t))
	elif k <= -1.35e-99:
		tmp = 2.0 / (((k * k) / math.cos(k)) * ((t / l) * (t_3 / l)))
	elif k <= 6e-101:
		tmp = (((l / t) * ((l / t) * (1.0 / math.tan(k)))) / t) * (1.0 / math.sin(k))
	elif k <= 5.4e+83:
		tmp = (1.0 / (t / (l / t))) * (((2.0 / math.tan(k)) / (math.sin(k) * t_1)) / (t / l))
	else:
		tmp = 2.0 * (((l / k) * (l / k)) * (math.cos(k) / (t * t_3)))
	return tmp

Julia

function code(t, l, k)
	return Float64(2.0 / Float64(Float64(Float64(Float64((t ^ 3.0) / Float64(l * l)) * sin(k)) * tan(k)) * Float64(Float64(1.0 + (Float64(k / t) ^ 2.0)) + 1.0)))
end

↓

function code(t, l, k)
	t_1 = Float64(2.0 + (Float64(k / t) ^ 2.0))
	t_2 = Float64(k * sin(k))
	t_3 = sin(k) ^ 2.0
	tmp = 0.0
	if (k <= -2.3e+24)
		tmp = Float64(2.0 * Float64(Float64(l / t_2) / Float64(t_2 * Float64(t / Float64(l * cos(k))))));
	elseif (k <= -2.4e-70)
		tmp = Float64(Float64(Float64(l / t) * Float64(Float64(2.0 / sin(k)) / t_1)) / Float64(t / Float64(Float64(l / tan(k)) / t)));
	elseif (k <= -1.35e-99)
		tmp = Float64(2.0 / Float64(Float64(Float64(k * k) / cos(k)) * Float64(Float64(t / l) * Float64(t_3 / l))));
	elseif (k <= 6e-101)
		tmp = Float64(Float64(Float64(Float64(l / t) * Float64(Float64(l / t) * Float64(1.0 / tan(k)))) / t) * Float64(1.0 / sin(k)));
	elseif (k <= 5.4e+83)
		tmp = Float64(Float64(1.0 / Float64(t / Float64(l / t))) * Float64(Float64(Float64(2.0 / tan(k)) / Float64(sin(k) * t_1)) / Float64(t / l)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(l / k) * Float64(l / k)) * Float64(cos(k) / Float64(t * t_3))));
	end
	return tmp
end

MATLAB

function tmp = code(t, l, k)
	tmp = 2.0 / (((((t ^ 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + ((k / t) ^ 2.0)) + 1.0));
end

↓

function tmp_2 = code(t, l, k)
	t_1 = 2.0 + ((k / t) ^ 2.0);
	t_2 = k * sin(k);
	t_3 = sin(k) ^ 2.0;
	tmp = 0.0;
	if (k <= -2.3e+24)
		tmp = 2.0 * ((l / t_2) / (t_2 * (t / (l * cos(k)))));
	elseif (k <= -2.4e-70)
		tmp = ((l / t) * ((2.0 / sin(k)) / t_1)) / (t / ((l / tan(k)) / t));
	elseif (k <= -1.35e-99)
		tmp = 2.0 / (((k * k) / cos(k)) * ((t / l) * (t_3 / l)));
	elseif (k <= 6e-101)
		tmp = (((l / t) * ((l / t) * (1.0 / tan(k)))) / t) * (1.0 / sin(k));
	elseif (k <= 5.4e+83)
		tmp = (1.0 / (t / (l / t))) * (((2.0 / tan(k)) / (sin(k) * t_1)) / (t / l));
	else
		tmp = 2.0 * (((l / k) * (l / k)) * (cos(k) / (t * t_3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, k_] := N[(2.0 / N[(N[(N[(N[(N[Power[t, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[t_, l_, k_] := Block[{t$95$1 = N[(2.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[Sin[k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[k, -2.3e+24], N[(2.0 * N[(N[(l / t$95$2), $MachinePrecision] / N[(t$95$2 * N[(t / N[(l * N[Cos[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.4e-70], N[(N[(N[(l / t), $MachinePrecision] * N[(N[(2.0 / N[Sin[k], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t / N[(N[(l / N[Tan[k], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.35e-99], N[(2.0 / N[(N[(N[(k * k), $MachinePrecision] / N[Cos[k], $MachinePrecision]), $MachinePrecision] * N[(N[(t / l), $MachinePrecision] * N[(t$95$3 / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6e-101], N[(N[(N[(N[(l / t), $MachinePrecision] * N[(N[(l / t), $MachinePrecision] * N[(1.0 / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] * N[(1.0 / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.4e+83], N[(N[(1.0 / N[(t / N[(l / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 / N[Tan[k], $MachinePrecision]), $MachinePrecision] / N[(N[Sin[k], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(l / k), $MachinePrecision] * N[(l / k), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -2.2999999999999999e24

   1. Initial program 49.1%

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

   2. Simplified 49.1%

      \[\leadsto \color{blue}{\frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      Proof

      [Start] 49.1	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 49.1	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      +-commutative [=>] 49.1	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\right)} \]

   3. Taylor expanded in t around 0 67.9%

      \[\leadsto \color{blue}{2 \cdot \frac{\cos k \cdot {\ell}^{2}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}} \]

   4. Simplified 67.9%

      \[\leadsto \color{blue}{2 \cdot \frac{\left(\ell \cdot \ell\right) \cdot \cos k}{\left(\left(k \cdot k\right) \cdot {\sin k}^{2}\right) \cdot t}} \]
      Proof

      [Start] 67.9	\[ 2 \cdot \frac{\cos k \cdot {\ell}^{2}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      *-commutative [=>] 67.9	\[ 2 \cdot \frac{\color{blue}{{\ell}^{2} \cdot \cos k}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      unpow2 [=>] 67.9	\[ 2 \cdot \frac{\color{blue}{\left(\ell \cdot \ell\right)} \cdot \cos k}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      associate-*r* [=>] 67.9	\[ 2 \cdot \frac{\left(\ell \cdot \ell\right) \cdot \cos k}{\color{blue}{\left({k}^{2} \cdot {\sin k}^{2}\right) \cdot t}} \]
      unpow2 [=>] 67.9	\[ 2 \cdot \frac{\left(\ell \cdot \ell\right) \cdot \cos k}{\left(\color{blue}{\left(k \cdot k\right)} \cdot {\sin k}^{2}\right) \cdot t} \]

   5. Applied egg-rr 69.7%

      \[\leadsto 2 \cdot \color{blue}{\left(\frac{\ell}{{\left(k \cdot \sin k\right)}^{2}} \cdot \frac{\ell \cdot \cos k}{t}\right)} \]
      Proof

      [Start] 67.9	\[ 2 \cdot \frac{\left(\ell \cdot \ell\right) \cdot \cos k}{\left(\left(k \cdot k\right) \cdot {\sin k}^{2}\right) \cdot t} \]
      associate-*l* [=>] 67.9	\[ 2 \cdot \frac{\color{blue}{\ell \cdot \left(\ell \cdot \cos k\right)}}{\left(\left(k \cdot k\right) \cdot {\sin k}^{2}\right) \cdot t} \]
      times-frac [=>] 69.6	\[ 2 \cdot \color{blue}{\left(\frac{\ell}{\left(k \cdot k\right) \cdot {\sin k}^{2}} \cdot \frac{\ell \cdot \cos k}{t}\right)} \]
      pow2 [=>] 69.6	\[ 2 \cdot \left(\frac{\ell}{\color{blue}{{k}^{2}} \cdot {\sin k}^{2}} \cdot \frac{\ell \cdot \cos k}{t}\right) \]
      pow-prod-down [=>] 69.7	\[ 2 \cdot \left(\frac{\ell}{\color{blue}{{\left(k \cdot \sin k\right)}^{2}}} \cdot \frac{\ell \cdot \cos k}{t}\right) \]

   6. Applied egg-rr 83.7%

      \[\leadsto 2 \cdot \color{blue}{\frac{\frac{\ell}{k \cdot \sin k}}{\frac{t}{\ell \cdot \cos k} \cdot \left(k \cdot \sin k\right)}} \]
      Proof

      [Start] 69.7	\[ 2 \cdot \left(\frac{\ell}{{\left(k \cdot \sin k\right)}^{2}} \cdot \frac{\ell \cdot \cos k}{t}\right) \]
      associate-*r/ [=>] 69.0	\[ 2 \cdot \color{blue}{\frac{\frac{\ell}{{\left(k \cdot \sin k\right)}^{2}} \cdot \left(\ell \cdot \cos k\right)}{t}} \]
      associate-/l* [=>] 70.0	\[ 2 \cdot \color{blue}{\frac{\frac{\ell}{{\left(k \cdot \sin k\right)}^{2}}}{\frac{t}{\ell \cdot \cos k}}} \]
      unpow2 [=>] 70.0	\[ 2 \cdot \frac{\frac{\ell}{\color{blue}{\left(k \cdot \sin k\right) \cdot \left(k \cdot \sin k\right)}}}{\frac{t}{\ell \cdot \cos k}} \]
      associate-/r* [=>] 77.2	\[ 2 \cdot \frac{\color{blue}{\frac{\frac{\ell}{k \cdot \sin k}}{k \cdot \sin k}}}{\frac{t}{\ell \cdot \cos k}} \]
      associate-/l/ [=>] 83.7	\[ 2 \cdot \color{blue}{\frac{\frac{\ell}{k \cdot \sin k}}{\frac{t}{\ell \cdot \cos k} \cdot \left(k \cdot \sin k\right)}} \]

   if -2.2999999999999999e24 < k < -2.4000000000000001e-70

   1. Initial program 54.3%

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

   2. Simplified 54.4%

      \[\leadsto \color{blue}{\frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      Proof

      [Start] 54.3	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 54.3	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      distribute-rgt1-in [<=] 54.3	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      *-commutative [=>] 54.3	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      associate-*l* [=>] 54.3	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-*l* [=>] 54.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      distribute-lft-in [=>] 54.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \color{blue}{\left(\tan k \cdot 1 + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)}\right)} \]
      *-rgt-identity [=>] 54.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\color{blue}{\tan k} + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)} \]
      distribute-lft-in [=>] 54.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \color{blue}{\left(\sin k \cdot \tan k + \sin k \cdot \left(\tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]

   3. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}} \]
      Proof

      [Start] 54.4	\[ \frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-commutative [=>] 54.4	\[ \frac{2}{\color{blue}{\left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}}} \]
      associate-/r* [=>] 54.4	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\frac{{t}^{3}}{\ell \cdot \ell}}} \]
      cube-mult [=>] 54.4	\[ \frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\frac{\color{blue}{t \cdot \left(t \cdot t\right)}}{\ell \cdot \ell}} \]
      associate-/l* [=>] 60.0	\[ \frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\color{blue}{\frac{t}{\frac{\ell \cdot \ell}{t \cdot t}}}} \]
      associate-/r/ [=>] 62.3	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}} \]
      *-commutative [=>] 62.3	\[ \frac{\frac{2}{\color{blue}{\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \sin k}}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]
      associate-*l* [=>] 62.3	\[ \frac{\frac{2}{\color{blue}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]

   4. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}\right)} - 1} \]
      Proof

      [Start] 62.3	\[ \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]
      expm1-log1p-u [=>] 56.8	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}\right)\right)} \]
      expm1-udef [=>] 45.6	\[ \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}\right)} - 1} \]

   5. Simplified 79.2%

      \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      Proof

      [Start] 51.3	\[ e^{\mathsf{log1p}\left(\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}\right)} - 1 \]
      expm1-def [=>] 71.6	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}\right)\right)} \]
      expm1-log1p [=>] 80.0	\[ \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}} \]
      associate-/l* [=>] 82.3	\[ \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{\frac{t}{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}}} \]
      associate-/r/ [=>] 79.2	\[ \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}} \]
      *-commutative [=>] 79.2	\[ \frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\color{blue}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]

   6. Applied egg-rr 80.0%

      \[\leadsto \frac{\color{blue}{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      Proof

      [Start] 79.2	\[ \frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      div-inv [=>] 79.2	\[ \frac{\color{blue}{{\left(\frac{\ell}{t}\right)}^{2} \cdot \frac{1}{\tan k}}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      unpow2 [=>] 79.2	\[ \frac{\color{blue}{\left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)} \cdot \frac{1}{\tan k}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      associate-*l* [=>] 80.0	\[ \frac{\color{blue}{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]

   7. Applied egg-rr 84.2%

      \[\leadsto \color{blue}{\frac{\frac{\frac{2}{\sin k}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\ell}{t}}{\frac{t}{\frac{\frac{\ell}{\tan k}}{t}}}} \]
      Proof

      [Start] 80.0	\[ \frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      *-commutative [=>] 80.0	\[ \color{blue}{\frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t}} \]
      associate-/l* [=>] 81.4	\[ \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \color{blue}{\frac{\frac{\ell}{t}}{\frac{t}{\frac{\ell}{t} \cdot \frac{1}{\tan k}}}} \]
      associate-*r/ [=>] 85.3	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\ell}{t}}{\frac{t}{\frac{\ell}{t} \cdot \frac{1}{\tan k}}}} \]
      associate-/r* [=>] 85.3	\[ \frac{\color{blue}{\frac{\frac{2}{\sin k}}{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \frac{\ell}{t}}{\frac{t}{\frac{\ell}{t} \cdot \frac{1}{\tan k}}} \]
      associate-*l/ [=>] 84.2	\[ \frac{\frac{\frac{2}{\sin k}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\ell}{t}}{\frac{t}{\color{blue}{\frac{\ell \cdot \frac{1}{\tan k}}{t}}}} \]
      un-div-inv [=>] 84.2	\[ \frac{\frac{\frac{2}{\sin k}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\ell}{t}}{\frac{t}{\frac{\color{blue}{\frac{\ell}{\tan k}}}{t}}} \]

   if -2.4000000000000001e-70 < k < -1.35e-99

   1. Initial program 56.6%

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

   2. Simplified 51.0%

      \[\leadsto \color{blue}{\frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      Proof

      [Start] 56.6	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 56.6	\[ \frac{2}{\color{blue}{\left(\tan k \cdot \left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right)\right)} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-/r/ [<=] 53.6	\[ \frac{2}{\left(\tan k \cdot \color{blue}{\frac{{t}^{3}}{\frac{\ell \cdot \ell}{\sin k}}}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*r/ [=>] 51.0	\[ \frac{2}{\color{blue}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell \cdot \ell}{\sin k}}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-/l* [=>] 51.0	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\color{blue}{\frac{\ell}{\frac{\sin k}{\ell}}}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      +-commutative [=>] 51.0	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-+r+ [=>] 51.0	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \color{blue}{\left(\left(1 + 1\right) + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      metadata-eval [=>] 51.0	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \left(\color{blue}{2} + {\left(\frac{k}{t}\right)}^{2}\right)} \]

   3. Taylor expanded in k around inf 15.8%

      \[\leadsto \frac{2}{\color{blue}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}}} \]

   4. Simplified 45.2%

      \[\leadsto \frac{2}{\color{blue}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}} \]
      Proof

      [Start] 15.8	\[ \frac{2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}} \]
      times-frac [=>] 28.7	\[ \frac{2}{\color{blue}{\frac{{k}^{2}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}}} \]
      unpow2 [=>] 28.7	\[ \frac{2}{\frac{\color{blue}{k \cdot k}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}} \]
      *-commutative [=>] 28.7	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{\color{blue}{t \cdot {\sin k}^{2}}}{{\ell}^{2}}} \]
      unpow2 [=>] 28.7	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{t \cdot {\sin k}^{2}}{\color{blue}{\ell \cdot \ell}}} \]
      times-frac [=>] 45.2	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \color{blue}{\left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}} \]

   if -1.35e-99 < k < 6.0000000000000006e-101

   1. Initial program 43.5%

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

   2. Simplified 18.7%

      \[\leadsto \color{blue}{\frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      Proof

      [Start] 43.5	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 43.5	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      distribute-rgt1-in [<=] 43.5	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      *-commutative [=>] 43.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      associate-*l* [=>] 43.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-*l* [=>] 19.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      distribute-lft-in [=>] 19.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \color{blue}{\left(\tan k \cdot 1 + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)}\right)} \]
      *-rgt-identity [=>] 19.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\color{blue}{\tan k} + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)} \]
      distribute-lft-in [=>] 19.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \color{blue}{\left(\sin k \cdot \tan k + \sin k \cdot \left(\tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]

   3. Applied egg-rr 17.8%

      \[\leadsto \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}} \]
      Proof

      [Start] 18.7	\[ \frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-commutative [=>] 18.7	\[ \frac{2}{\color{blue}{\left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}}} \]
      associate-/r* [=>] 16.8	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\frac{{t}^{3}}{\ell \cdot \ell}}} \]
      cube-mult [=>] 16.8	\[ \frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\frac{\color{blue}{t \cdot \left(t \cdot t\right)}}{\ell \cdot \ell}} \]
      associate-/l* [=>] 17.7	\[ \frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\color{blue}{\frac{t}{\frac{\ell \cdot \ell}{t \cdot t}}}} \]
      associate-/r/ [=>] 17.8	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}} \]
      *-commutative [=>] 17.8	\[ \frac{\frac{2}{\color{blue}{\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \sin k}}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]
      associate-*l* [=>] 17.8	\[ \frac{\frac{2}{\color{blue}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]

   4. Applied egg-rr 43.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}\right)} - 1} \]
      Proof

      [Start] 17.8	\[ \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]
      expm1-log1p-u [=>] 15.5	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}\right)\right)} \]
      expm1-udef [=>] 14.4	\[ \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}\right)} - 1} \]

   5. Simplified 69.6%

      \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      Proof

      [Start] 43.5	\[ e^{\mathsf{log1p}\left(\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}\right)} - 1 \]
      expm1-def [=>] 51.5	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}\right)\right)} \]
      expm1-log1p [=>] 61.6	\[ \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{t}} \]
      associate-/l* [=>] 71.9	\[ \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{\frac{t}{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}}} \]
      associate-/r/ [=>] 69.6	\[ \color{blue}{\frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}} \]
      *-commutative [=>] 69.6	\[ \frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\color{blue}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]

   6. Applied egg-rr 81.7%

      \[\leadsto \frac{\color{blue}{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      Proof

      [Start] 69.6	\[ \frac{\frac{{\left(\frac{\ell}{t}\right)}^{2}}{\tan k}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      div-inv [=>] 69.6	\[ \frac{\color{blue}{{\left(\frac{\ell}{t}\right)}^{2} \cdot \frac{1}{\tan k}}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      unpow2 [=>] 69.6	\[ \frac{\color{blue}{\left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)} \cdot \frac{1}{\tan k}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]
      associate-*l* [=>] 81.7	\[ \frac{\color{blue}{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}}{t} \cdot \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \]

   7. Taylor expanded in t around inf 80.0%

      \[\leadsto \frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \color{blue}{\frac{1}{\sin k}} \]

   if 6.0000000000000006e-101 < k < 5.40000000000000014e83

   1. Initial program 56.3%

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

   2. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      Proof

      [Start] 56.3	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 56.3	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      distribute-rgt1-in [<=] 56.3	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      *-commutative [=>] 56.3	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      associate-*l* [=>] 56.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-*l* [=>] 56.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      distribute-lft-in [=>] 56.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \color{blue}{\left(\tan k \cdot 1 + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)}\right)} \]
      *-rgt-identity [=>] 56.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\color{blue}{\tan k} + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)} \]
      distribute-lft-in [=>] 56.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \color{blue}{\left(\sin k \cdot \tan k + \sin k \cdot \left(\tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]

   3. Applied egg-rr 62.5%

      \[\leadsto \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}} \]
      Proof

      [Start] 56.4	\[ \frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-commutative [=>] 56.4	\[ \frac{2}{\color{blue}{\left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}}} \]
      associate-/r* [=>] 56.6	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\frac{{t}^{3}}{\ell \cdot \ell}}} \]
      cube-mult [=>] 56.6	\[ \frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\frac{\color{blue}{t \cdot \left(t \cdot t\right)}}{\ell \cdot \ell}} \]
      associate-/l* [=>] 60.8	\[ \frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{\color{blue}{\frac{t}{\frac{\ell \cdot \ell}{t \cdot t}}}} \]
      associate-/r/ [=>] 62.5	\[ \color{blue}{\frac{\frac{2}{\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t}} \]
      *-commutative [=>] 62.5	\[ \frac{\frac{2}{\color{blue}{\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \sin k}}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]
      associate-*l* [=>] 62.5	\[ \frac{\frac{2}{\color{blue}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]

   4. Applied egg-rr 79.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)}} \]
      Proof

      [Start] 62.5	\[ \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \frac{\ell \cdot \ell}{t \cdot t} \]
      clear-num [=>] 62.3	\[ \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t} \cdot \color{blue}{\frac{1}{\frac{t \cdot t}{\ell \cdot \ell}}} \]
      frac-times [=>] 60.8	\[ \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)} \cdot 1}{t \cdot \frac{t \cdot t}{\ell \cdot \ell}}} \]
      *-commutative [<=] 60.8	\[ \frac{\color{blue}{1 \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}}{t \cdot \frac{t \cdot t}{\ell \cdot \ell}} \]
      *-un-lft-identity [<=] 60.8	\[ \frac{\color{blue}{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}}{t \cdot \frac{t \cdot t}{\ell \cdot \ell}} \]
      times-frac [=>] 79.0	\[ \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t \cdot \color{blue}{\left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)}} \]

   5. Applied egg-rr 84.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{\frac{\ell}{t}}} \cdot \frac{\frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}{\frac{t}{\ell}}} \]
      Proof

      [Start] 79.0	\[ \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{t \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)} \]
      *-un-lft-identity [=>] 79.0	\[ \frac{\color{blue}{1 \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}}{t \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)} \]
      associate-*r* [=>] 80.0	\[ \frac{1 \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{\color{blue}{\left(t \cdot \frac{t}{\ell}\right) \cdot \frac{t}{\ell}}} \]
      times-frac [=>] 84.7	\[ \color{blue}{\frac{1}{t \cdot \frac{t}{\ell}} \cdot \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{\frac{t}{\ell}}} \]
      clear-num [=>] 84.7	\[ \frac{1}{t \cdot \color{blue}{\frac{1}{\frac{\ell}{t}}}} \cdot \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{\frac{t}{\ell}} \]
      un-div-inv [=>] 84.8	\[ \frac{1}{\color{blue}{\frac{t}{\frac{\ell}{t}}}} \cdot \frac{\frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k\right)}}{\frac{t}{\ell}} \]
      associate-/r* [=>] 84.7	\[ \frac{1}{\frac{t}{\frac{\ell}{t}}} \cdot \frac{\color{blue}{\frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}}}{\frac{t}{\ell}} \]

   if 5.40000000000000014e83 < k

   1. Initial program 49.2%

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

   2. Simplified 49.2%

      \[\leadsto \color{blue}{\frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      Proof

      [Start] 49.2	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 49.2	\[ \frac{2}{\color{blue}{\left(\tan k \cdot \left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right)\right)} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-/r/ [<=] 49.2	\[ \frac{2}{\left(\tan k \cdot \color{blue}{\frac{{t}^{3}}{\frac{\ell \cdot \ell}{\sin k}}}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*r/ [=>] 49.2	\[ \frac{2}{\color{blue}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell \cdot \ell}{\sin k}}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-/l* [=>] 49.2	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\color{blue}{\frac{\ell}{\frac{\sin k}{\ell}}}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      +-commutative [=>] 49.2	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-+r+ [=>] 49.2	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \color{blue}{\left(\left(1 + 1\right) + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      metadata-eval [=>] 49.2	\[ \frac{2}{\frac{\tan k \cdot {t}^{3}}{\frac{\ell}{\frac{\sin k}{\ell}}} \cdot \left(\color{blue}{2} + {\left(\frac{k}{t}\right)}^{2}\right)} \]

   3. Taylor expanded in k around inf 68.3%

      \[\leadsto \color{blue}{2 \cdot \frac{\cos k \cdot {\ell}^{2}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}} \]

   4. Simplified 88.1%

      \[\leadsto \color{blue}{2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot {\sin k}^{2}}\right)} \]
      Proof

      [Start] 68.3	\[ 2 \cdot \frac{\cos k \cdot {\ell}^{2}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      *-commutative [=>] 68.3	\[ 2 \cdot \frac{\color{blue}{{\ell}^{2} \cdot \cos k}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      times-frac [=>] 66.1	\[ 2 \cdot \color{blue}{\left(\frac{{\ell}^{2}}{{k}^{2}} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right)} \]
      unpow2 [=>] 66.1	\[ 2 \cdot \left(\frac{\color{blue}{\ell \cdot \ell}}{{k}^{2}} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right) \]
      unpow2 [=>] 66.1	\[ 2 \cdot \left(\frac{\ell \cdot \ell}{\color{blue}{k \cdot k}} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right) \]
      times-frac [=>] 88.1	\[ 2 \cdot \left(\color{blue}{\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right)} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right) \]
      *-commutative [=>] 88.1	\[ 2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{\color{blue}{t \cdot {\sin k}^{2}}}\right) \]

3. Recombined 6 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{k \cdot \sin k}}{\left(k \cdot \sin k\right) \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{\frac{2}{\sin k}}{2 + {\left(\frac{k}{t}\right)}^{2}}}{\frac{t}{\frac{\frac{\ell}{\tan k}}{t}}}\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 5.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{\ell}{t}}} \cdot \frac{\frac{\frac{2}{\tan k}}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}}{\frac{t}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot {\sin k}^{2}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	82.0%
Cost	21268

\[\begin{array}{l} t_1 := \frac{\frac{2}{\tan k \cdot \left(\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)\\ t_2 := {\sin k}^{2}\\ t_3 := k \cdot \sin k\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_3}}{t_3 \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_2}{\ell}\right)}\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 0.058:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_2}\right)\\ \end{array} \]

Alternative 2
Accuracy	81.6%
Cost	21268

\[\begin{array}{l} t_1 := \tan k \cdot \left(\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ t_2 := {\sin k}^{2}\\ t_3 := k \cdot \sin k\\ \mathbf{if}\;k \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_3}}{t_3 \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{2}{t_1}}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_2}{\ell}\right)}\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 0.058:\\ \;\;\;\;\frac{\ell \cdot 2}{\left(t \cdot \frac{t}{\ell}\right) \cdot \left(t \cdot t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_2}\right)\\ \end{array} \]

Alternative 3
Accuracy	83.1%
Cost	21268

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t} \cdot \frac{\frac{2}{\sin k}}{2 + {\left(\frac{k}{t}\right)}^{2}}}{\frac{t}{\frac{\frac{\ell}{\tan k}}{t}}}\\ t_2 := k \cdot \sin k\\ t_3 := {\sin k}^{2}\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_2}}{t_2 \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_3}{\ell}\right)}\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_3}\right)\\ \end{array} \]

Alternative 4
Accuracy	81.8%
Cost	21016

\[\begin{array}{l} t_1 := \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ t_2 := {\sin k}^{2}\\ t_3 := 2 \cdot \frac{\frac{\ell}{\frac{t}{\ell \cdot \cos k} \cdot \left(k \cdot k\right)}}{t_2}\\ t_4 := 2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_2}\right)\\ \mathbf{if}\;k \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -1.42 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 0.04:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Accuracy	81.8%
Cost	21016

\[\begin{array}{l} t_1 := \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ t_2 := {\sin k}^{2}\\ t_3 := 2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_2}\right)\\ \mathbf{if}\;k \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -1.15 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{\frac{t}{\ell \cdot \cos k} \cdot \left(k \cdot k\right)}}{t_2}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_2}{\ell}\right)}\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 0.027:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	87.9%
Cost	21005

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ t_2 := k \cdot \sin k\\ \mathbf{if}\;t \leq -2 \cdot 10^{+163}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{1}{\frac{t \cdot \tan k}{\ell}}}{t} \cdot \frac{2}{\sin k \cdot t_1}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-110} \lor \neg \left(t \leq 7.4 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{\frac{2}{\sin k}}{t_1}}{\frac{t}{\frac{\frac{\ell}{\tan k}}{t}}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_2}}{t_2 \cdot \frac{t}{\ell \cdot \cos k}}\\ \end{array} \]

Alternative 7
Accuracy	88.0%
Cost	21005

\[\begin{array}{l} t_1 := k \cdot \sin k\\ t_2 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+155}:\\ \;\;\;\;\frac{2}{\sin k \cdot t_2} \cdot \frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-100} \lor \neg \left(t \leq 1.9 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{\frac{2}{\sin k}}{t_2}}{\frac{t}{\frac{\frac{\ell}{\tan k}}{t}}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_1}}{t_1 \cdot \frac{t}{\ell \cdot \cos k}}\\ \end{array} \]

Alternative 8
Accuracy	80.8%
Cost	20884

\[\begin{array}{l} t_1 := \frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ t_2 := {\sin k}^{2}\\ t_3 := k \cdot \sin k\\ \mathbf{if}\;k \leq -2.15 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_3}}{t_3 \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_2}{\ell}\right)}\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-268}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 0.0255:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_2}\right)\\ \end{array} \]

Alternative 9
Accuracy	80.4%
Cost	20884

\[\begin{array}{l} t_1 := \sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\\ t_2 := k \cdot \sin k\\ t_3 := {\sin k}^{2}\\ \mathbf{if}\;k \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t_2}}{t_2 \cdot \frac{t}{\ell \cdot \cos k}}\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{2}{t}}{\tan k \cdot t_1} \cdot \frac{\ell}{\frac{t \cdot t}{\ell}}\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{t_3}{\ell}\right)}\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;k \leq 0.057:\\ \;\;\;\;\frac{2}{t_1} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot t_3}\right)\\ \end{array} \]

Alternative 10
Accuracy	82.9%
Cost	20620

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t \cdot {\sin k}^{2}}\right)\\ \mathbf{if}\;k \leq -9 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(\left(\ell \cdot \cos k\right) \cdot \frac{\ell}{t \cdot {\left(k \cdot \sin k\right)}^{2}}\right)\\ \mathbf{elif}\;k \leq 0.058:\\ \;\;\;\;\frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	75.9%
Cost	20361

\[\begin{array}{l} \mathbf{if}\;k \leq -2.15 \cdot 10^{-8} \lor \neg \left(k \leq 0.00345\right):\\ \;\;\;\;2 \cdot \left(\left(\ell \cdot \cos k\right) \cdot \frac{\ell}{t \cdot {\left(k \cdot \sin k\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ \end{array} \]

Alternative 12
Accuracy	73.4%
Cost	14473

\[\begin{array}{l} \mathbf{if}\;k \leq -2.35 \cdot 10^{-8} \lor \neg \left(k \leq 0.0195\right):\\ \;\;\;\;2 \cdot \left(\frac{\frac{\ell}{k \cdot k}}{\frac{1 - \cos \left(k + k\right)}{2}} \cdot \frac{\ell \cdot \cos k}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{\frac{\ell}{t} \cdot \frac{\ell}{t \cdot k}}{t}\\ \end{array} \]

Alternative 13
Accuracy	71.7%
Cost	14409

\[\begin{array}{l} \mathbf{if}\;k \leq -1.75 \cdot 10^{+24} \lor \neg \left(k \leq 0.047\right):\\ \;\;\;\;2 \cdot \left(\frac{\frac{\ell}{k \cdot k}}{\frac{1 - \cos \left(k + k\right)}{2}} \cdot \frac{\ell \cdot \cos k}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \end{array} \]

Alternative 14
Accuracy	69.7%
Cost	14280

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-105}:\\ \;\;\;\;\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \frac{{t}^{3}}{\frac{\ell}{k} \cdot \frac{\ell}{k}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell \cdot \frac{1}{t}}{k \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 15
Accuracy	69.6%
Cost	14020

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{1}{\tan k}\right)}{t} \cdot \frac{1}{\sin k}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{t \cdot t}}{k}}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell \cdot \frac{1}{t}}{k \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 16
Accuracy	68.4%
Cost	7692

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\frac{1}{k} \cdot \left(\frac{\frac{\ell}{t}}{t} \cdot \frac{\frac{\ell}{t}}{\tan k}\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{k \cdot \left(t \cdot t\right)}{\frac{\ell}{k}}}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-100}:\\ \;\;\;\;\frac{2}{2 \cdot \frac{{t}^{3}}{\frac{\ell}{k} \cdot \frac{\ell}{k}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell \cdot \frac{1}{t}}{k \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 17
Accuracy	68.2%
Cost	7492

\[\begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+156}:\\ \;\;\;\;\frac{1}{k} \cdot \frac{\frac{\frac{\ell \cdot \frac{\ell}{t}}{t}}{\tan k}}{t}\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{k \cdot \left(t \cdot t\right)}{\frac{\ell}{k}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell \cdot \frac{1}{t}}{k \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 18
Accuracy	68.6%
Cost	7492

\[\begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{\frac{\frac{\ell}{t}}{\frac{t}{\ell}}}{\tan k}}{t} \cdot \frac{1}{k}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{k \cdot \left(t \cdot t\right)}{\frac{\ell}{k}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell \cdot \frac{1}{t}}{k \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 19
Accuracy	68.5%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-26} \lor \neg \left(t \leq 1.02 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell \cdot \frac{1}{t}}{k \cdot k}\right)\\ \end{array} \]

Alternative 20
Accuracy	67.0%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;t \leq -7.3 \cdot 10^{-26} \lor \neg \left(t \leq 1.02 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\ell}{t \cdot \left(k \cdot k\right)}\right)\\ \end{array} \]

Alternative 21
Accuracy	68.1%
Cost	1225

\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot k}\\ \mathbf{if}\;t \leq -7.3 \cdot 10^{-26} \lor \neg \left(t \leq 1.02 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{t_1 \cdot t_1}{t}\\ \end{array} \]

Alternative 22
Accuracy	53.7%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-26} \lor \neg \left(t \leq 9.4 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{t \cdot \left(k \cdot \left(t \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{\frac{\ell}{t}}{\left(k \cdot k\right) \cdot \left(t \cdot t\right)}\\ \end{array} \]

Alternative 23
Accuracy	53.8%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-135} \lor \neg \left(t \leq 6.4 \cdot 10^{-119}\right):\\ \;\;\;\;\ell \cdot \frac{\frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}}{t}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{\frac{\ell}{t}}{\left(k \cdot k\right) \cdot \left(t \cdot t\right)}\\ \end{array} \]

Alternative 24
Accuracy	63.3%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq 1.55 \cdot 10^{-162} \lor \neg \left(t \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot \frac{k}{\frac{\ell}{k}}}\\ \end{array} \]

Alternative 25
Accuracy	63.4%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-151} \lor \neg \left(t \leq 10^{-55}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot t}}{t \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 26
Accuracy	63.6%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq 1.55 \cdot 10^{-162} \lor \neg \left(t \leq 10^{-52}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k}}{t \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot \left(k \cdot \frac{k}{\ell}\right)}}{t \cdot t}\\ \end{array} \]

Alternative 27
Accuracy	54.1%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-137}:\\ \;\;\;\;\ell \cdot \frac{\frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-120}:\\ \;\;\;\;\ell \cdot \frac{\frac{\ell}{t}}{\left(k \cdot k\right) \cdot \left(t \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{t \cdot t}}{k}}{t \cdot k}\\ \end{array} \]

Alternative 28
Accuracy	55.3%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\ell \cdot \frac{\frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{t \cdot t}}{k}}{t}\\ \end{array} \]

Alternative 29
Accuracy	55.1%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -130000000:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{t \cdot \left(k \cdot \left(t \cdot t\right)\right)}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot \frac{k}{\frac{\ell}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{t \cdot t}}{k}}{t}\\ \end{array} \]

Alternative 30
Accuracy	55.2%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -500000000:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{k \cdot \left(t \cdot t\right)}{\frac{\ell}{k}}}\\ \mathbf{elif}\;t \leq 10^{-54}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot \frac{k}{\frac{\ell}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{t \cdot t}}{k}}{t}\\ \end{array} \]

Alternative 31
Accuracy	54.4%
Cost	964

\[\begin{array}{l} \mathbf{if}\;\ell \leq 9 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{t \cdot t}}{k}}{t}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{\frac{\ell}{t}}{\left(k \cdot k\right) \cdot \left(t \cdot t\right)}\\ \end{array} \]

Alternative 32
Accuracy	53.2%
Cost	832

\[\frac{\ell}{k} \cdot \frac{\ell}{t \cdot \left(k \cdot \left(t \cdot t\right)\right)} \]

Reproduce

herbie shell --seed 2023135 
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  :precision binary64
  (/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))