Toniolo and Linder, Equation (10+)

Average Accuracy: 36.0% → 61.5%

Time: 51.0s

Precision: binary64

Cost: 46480

Math

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

↓

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;k \leq -5.2 \cdot 10^{+194}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{-293}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\ell \cdot \frac{2}{\tan k}}}{t \cdot \sqrt[3]{\sin k \cdot t_1}} \cdot \sqrt[3]{\ell}\right)}^{3}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-152}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{{\left(k \cdot t\right)}^{2}}{\ell}}\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;{\left(\sqrt[3]{\frac{2}{t_1 \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

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))))
   (if (<= k -5.2e+194)
     (* 2.0 (* (* (/ l k) (/ l k)) (/ (cos k) (* (pow (sin k) 2.0) t))))
     (if (<= k 8.6e-293)
       (pow
        (*
         (/ (cbrt (* l (/ 2.0 (tan k)))) (* t (cbrt (* (sin k) t_1))))
         (cbrt l))
        3.0)
       (if (<= k 6e-152)
         (/ (/ l t) (/ (pow (* k t) 2.0) l))
         (if (<= k 5.2e+92)
           (pow
            (*
             (cbrt (/ 2.0 (* t_1 (* (sin k) (tan k)))))
             (/ (pow (cbrt l) 2.0) t))
            3.0)
           (/
            2.0
            (* t (* (/ (/ k (cos k)) l) (/ (/ k (pow (sin k) -2.0)) l))))))))))

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 tmp;
	if (k <= -5.2e+194) {
		tmp = 2.0 * (((l / k) * (l / k)) * (cos(k) / (pow(sin(k), 2.0) * t)));
	} else if (k <= 8.6e-293) {
		tmp = pow(((cbrt((l * (2.0 / tan(k)))) / (t * cbrt((sin(k) * t_1)))) * cbrt(l)), 3.0);
	} else if (k <= 6e-152) {
		tmp = (l / t) / (pow((k * t), 2.0) / l);
	} else if (k <= 5.2e+92) {
		tmp = pow((cbrt((2.0 / (t_1 * (sin(k) * tan(k))))) * (pow(cbrt(l), 2.0) / t)), 3.0);
	} else {
		tmp = 2.0 / (t * (((k / cos(k)) / l) * ((k / pow(sin(k), -2.0)) / l)));
	}
	return tmp;
}

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 tmp;
	if (k <= -5.2e+194) {
		tmp = 2.0 * (((l / k) * (l / k)) * (Math.cos(k) / (Math.pow(Math.sin(k), 2.0) * t)));
	} else if (k <= 8.6e-293) {
		tmp = Math.pow(((Math.cbrt((l * (2.0 / Math.tan(k)))) / (t * Math.cbrt((Math.sin(k) * t_1)))) * Math.cbrt(l)), 3.0);
	} else if (k <= 6e-152) {
		tmp = (l / t) / (Math.pow((k * t), 2.0) / l);
	} else if (k <= 5.2e+92) {
		tmp = Math.pow((Math.cbrt((2.0 / (t_1 * (Math.sin(k) * Math.tan(k))))) * (Math.pow(Math.cbrt(l), 2.0) / t)), 3.0);
	} else {
		tmp = 2.0 / (t * (((k / Math.cos(k)) / l) * ((k / Math.pow(Math.sin(k), -2.0)) / l)));
	}
	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))
	tmp = 0.0
	if (k <= -5.2e+194)
		tmp = Float64(2.0 * Float64(Float64(Float64(l / k) * Float64(l / k)) * Float64(cos(k) / Float64((sin(k) ^ 2.0) * t))));
	elseif (k <= 8.6e-293)
		tmp = Float64(Float64(cbrt(Float64(l * Float64(2.0 / tan(k)))) / Float64(t * cbrt(Float64(sin(k) * t_1)))) * cbrt(l)) ^ 3.0;
	elseif (k <= 6e-152)
		tmp = Float64(Float64(l / t) / Float64((Float64(k * t) ^ 2.0) / l));
	elseif (k <= 5.2e+92)
		tmp = Float64(cbrt(Float64(2.0 / Float64(t_1 * Float64(sin(k) * tan(k))))) * Float64((cbrt(l) ^ 2.0) / t)) ^ 3.0;
	else
		tmp = Float64(2.0 / Float64(t * Float64(Float64(Float64(k / cos(k)) / l) * Float64(Float64(k / (sin(k) ^ -2.0)) / l))));
	end
	return 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]}, If[LessEqual[k, -5.2e+194], N[(2.0 * N[(N[(N[(l / k), $MachinePrecision] * N[(l / k), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.6e-293], N[Power[N[(N[(N[Power[N[(l * N[(2.0 / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / N[(t * N[Power[N[(N[Sin[k], $MachinePrecision] * t$95$1), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], If[LessEqual[k, 6e-152], N[(N[(l / t), $MachinePrecision] / N[(N[Power[N[(k * t), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.2e+92], N[Power[N[(N[Power[N[(2.0 / N[(t$95$1 * N[(N[Sin[k], $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] * N[(N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], N[(2.0 / N[(t * N[(N[(N[(k / N[Cos[k], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision] * N[(N[(k / N[Power[N[Sin[k], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -5.1999999999999998e194

   1. Initial program 43.3%

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

   2. Simplified 43.6%

      \[\leadsto \color{blue}{\frac{2}{\left({t}^{3} \cdot \left(\sin k \cdot \tan k\right)\right) \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \left(\ell \cdot \ell\right)} \]
      Step-by-step derivation

      [Start] 43.3	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 43.3	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      associate-*l/ [=>] 43.3	\[ \frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\color{blue}{\frac{{t}^{3} \cdot \sin k}{\ell \cdot \ell}} \cdot \tan k\right)} \]
      associate-*l/ [=>] 43.3	\[ \frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \color{blue}{\frac{\left({t}^{3} \cdot \sin k\right) \cdot \tan k}{\ell \cdot \ell}}} \]
      associate-*r/ [=>] 43.6	\[ \frac{2}{\color{blue}{\frac{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left({t}^{3} \cdot \sin k\right) \cdot \tan k\right)}{\ell \cdot \ell}}} \]
      associate-/r/ [=>] 43.6	\[ \color{blue}{\frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left({t}^{3} \cdot \sin k\right) \cdot \tan k\right)} \cdot \left(\ell \cdot \ell\right)} \]

   3. Taylor expanded in t around 0 62.8%

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

   4. Simplified 95.2%

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

      [Start] 62.8	\[ 2 \cdot \frac{\cos k \cdot {\ell}^{2}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      *-commutative [=>] 62.8	\[ 2 \cdot \frac{\color{blue}{{\ell}^{2} \cdot \cos k}}{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)} \]
      times-frac [=>] 62.8	\[ 2 \cdot \color{blue}{\left(\frac{{\ell}^{2}}{{k}^{2}} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right)} \]
      unpow2 [=>] 62.8	\[ 2 \cdot \left(\frac{\color{blue}{\ell \cdot \ell}}{{k}^{2}} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right) \]
      unpow2 [=>] 62.8	\[ 2 \cdot \left(\frac{\ell \cdot \ell}{\color{blue}{k \cdot k}} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right) \]
      times-frac [=>] 95.2	\[ 2 \cdot \left(\color{blue}{\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right)} \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right) \]

   if -5.1999999999999998e194 < k < 8.5999999999999996e-293

   1. Initial program 40.1%

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

   2. Simplified 39.9%

      \[\leadsto \color{blue}{\left(\ell \cdot \ell\right) \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)\right)}} \]
      Step-by-step derivation

      [Start] 40.1	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-/l/ [<=] 40.1	\[ \color{blue}{\frac{\frac{2}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1}}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k}} \]
      associate-*l/ [=>] 40.9	\[ \frac{\frac{2}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1}}{\color{blue}{\frac{{t}^{3} \cdot \sin k}{\ell \cdot \ell}} \cdot \tan k} \]
      associate-*l/ [=>] 40.8	\[ \frac{\frac{2}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1}}{\color{blue}{\frac{\left({t}^{3} \cdot \sin k\right) \cdot \tan k}{\ell \cdot \ell}}} \]
      associate-/r/ [=>] 40.6	\[ \color{blue}{\frac{\frac{2}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1}}{\left({t}^{3} \cdot \sin k\right) \cdot \tan k} \cdot \left(\ell \cdot \ell\right)} \]
      *-commutative [=>] 40.6	\[ \color{blue}{\left(\ell \cdot \ell\right) \cdot \frac{\frac{2}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1}}{\left({t}^{3} \cdot \sin k\right) \cdot \tan k}} \]
      associate-/l/ [=>] 39.9	\[ \left(\ell \cdot \ell\right) \cdot \color{blue}{\frac{2}{\left(\left({t}^{3} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}} \]
      associate-*r* [<=] 39.9	\[ \left(\ell \cdot \ell\right) \cdot \frac{2}{\color{blue}{\left({t}^{3} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      *-commutative [=>] 39.9	\[ \left(\ell \cdot \ell\right) \cdot \frac{2}{\left({t}^{3} \cdot \sin k\right) \cdot \color{blue}{\left(\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \tan k\right)}} \]
      associate-*r* [=>] 39.9	\[ \left(\ell \cdot \ell\right) \cdot \frac{2}{\color{blue}{\left(\left({t}^{3} \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right) \cdot \tan k}} \]
      *-commutative [=>] 39.9	\[ \left(\ell \cdot \ell\right) \cdot \frac{2}{\color{blue}{\tan k \cdot \left(\left({t}^{3} \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]

   3. Applied egg-rr 35.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\ell \cdot \left(\ell \cdot \frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)}\right)\right)} - 1} \]
      Step-by-step derivation

      [Start] 39.9	\[ \left(\ell \cdot \ell\right) \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)\right)} \]
      expm1-log1p-u [=>] 38.8	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\ell \cdot \ell\right) \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)\right)}\right)\right)} \]
      expm1-udef [=>] 31.8	\[ \color{blue}{e^{\mathsf{log1p}\left(\left(\ell \cdot \ell\right) \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)\right)}\right)} - 1} \]
      associate-*l* [=>] 35.7	\[ e^{\mathsf{log1p}\left(\color{blue}{\ell \cdot \left(\ell \cdot \frac{2}{\tan k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)\right)}\right)}\right)} - 1 \]
      associate-/r* [=>] 35.7	\[ e^{\mathsf{log1p}\left(\ell \cdot \left(\ell \cdot \color{blue}{\frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)}}\right)\right)} - 1 \]

   4. Simplified 50.4%

      \[\leadsto \color{blue}{\ell \cdot \frac{\ell \cdot \frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)}} \]
      Step-by-step derivation

      [Start] 35.7	\[ e^{\mathsf{log1p}\left(\ell \cdot \left(\ell \cdot \frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)}\right)\right)} - 1 \]
      expm1-def [=>] 45.4	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\ell \cdot \left(\ell \cdot \frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)}\right)\right)\right)} \]
      expm1-log1p [=>] 47.5	\[ \color{blue}{\ell \cdot \left(\ell \cdot \frac{\frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)}\right)} \]
      associate-*r/ [=>] 50.4	\[ \ell \cdot \color{blue}{\frac{\ell \cdot \frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left({t}^{3} \cdot \sin k\right)}} \]
      *-commutative [<=] 50.4	\[ \ell \cdot \frac{\ell \cdot \frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \color{blue}{\left(\sin k \cdot {t}^{3}\right)}} \]

   5. Applied egg-rr 59.2%

      \[\leadsto \ell \cdot \color{blue}{\left(\frac{\ell}{{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t\right)}^{2}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t}\right)} \]
      Step-by-step derivation

      [Start] 50.4	\[ \ell \cdot \frac{\ell \cdot \frac{2}{\tan k}}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)} \]
      add-cube-cbrt [=>] 50.2	\[ \ell \cdot \frac{\ell \cdot \frac{2}{\tan k}}{\color{blue}{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)} \cdot \sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)}\right) \cdot \sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)}}} \]
      times-frac [=>] 49.2	\[ \ell \cdot \color{blue}{\left(\frac{\ell}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)} \cdot \sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot {t}^{3}\right)}}\right)} \]

   6. Applied egg-rr 68.0%

      \[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{\ell \cdot \frac{2}{\tan k}}}{t \cdot \sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k}} \cdot \sqrt[3]{\ell}\right)}^{3}} \]
      Step-by-step derivation

      [Start] 59.2	\[ \ell \cdot \left(\frac{\ell}{{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t\right)}^{2}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t}\right) \]
      add-cube-cbrt [=>] 59.1	\[ \color{blue}{\left(\sqrt[3]{\ell \cdot \left(\frac{\ell}{{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t\right)}^{2}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t}\right)} \cdot \sqrt[3]{\ell \cdot \left(\frac{\ell}{{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t\right)}^{2}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t}\right)}\right) \cdot \sqrt[3]{\ell \cdot \left(\frac{\ell}{{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t\right)}^{2}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t}\right)}} \]
      pow3 [=>] 59.1	\[ \color{blue}{{\left(\sqrt[3]{\ell \cdot \left(\frac{\ell}{{\left(\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t\right)}^{2}} \cdot \frac{\frac{2}{\tan k}}{\sqrt[3]{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \sin k} \cdot t}\right)}\right)}^{3}} \]

   if 8.5999999999999996e-293 < k < 6e-152

   1. Initial program 8.7%

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

   2. Simplified 3.9%

      \[\leadsto \color{blue}{\frac{2}{\left({t}^{3} \cdot \left(\sin k \cdot \tan k\right)\right) \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \left(\ell \cdot \ell\right)} \]
      Step-by-step derivation

      [Start] 8.7	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 8.7	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      associate-*l/ [=>] 12.6	\[ \frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\color{blue}{\frac{{t}^{3} \cdot \sin k}{\ell \cdot \ell}} \cdot \tan k\right)} \]
      associate-*l/ [=>] 12.6	\[ \frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \color{blue}{\frac{\left({t}^{3} \cdot \sin k\right) \cdot \tan k}{\ell \cdot \ell}}} \]
      associate-*r/ [=>] 12.6	\[ \frac{2}{\color{blue}{\frac{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left({t}^{3} \cdot \sin k\right) \cdot \tan k\right)}{\ell \cdot \ell}}} \]
      associate-/r/ [=>] 12.6	\[ \color{blue}{\frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left({t}^{3} \cdot \sin k\right) \cdot \tan k\right)} \cdot \left(\ell \cdot \ell\right)} \]

   3. Taylor expanded in k around 0 4.0%

      \[\leadsto \color{blue}{\frac{{\ell}^{2}}{{k}^{2} \cdot {t}^{3}}} \]

   4. Simplified 4.0%

      \[\leadsto \color{blue}{\frac{\ell}{{t}^{3}} \cdot \frac{\ell}{k \cdot k}} \]
      Step-by-step derivation

      [Start] 4.0	\[ \frac{{\ell}^{2}}{{k}^{2} \cdot {t}^{3}} \]
      unpow2 [=>] 4.0	\[ \frac{\color{blue}{\ell \cdot \ell}}{{k}^{2} \cdot {t}^{3}} \]
      *-commutative [=>] 4.0	\[ \frac{\ell \cdot \ell}{\color{blue}{{t}^{3} \cdot {k}^{2}}} \]
      times-frac [=>] 4.0	\[ \color{blue}{\frac{\ell}{{t}^{3}} \cdot \frac{\ell}{{k}^{2}}} \]
      unpow2 [=>] 4.0	\[ \frac{\ell}{{t}^{3}} \cdot \frac{\ell}{\color{blue}{k \cdot k}} \]

   5. Applied egg-rr 4.0%

      \[\leadsto \color{blue}{\left(\frac{1}{t} \cdot \frac{\ell}{t \cdot t}\right)} \cdot \frac{\ell}{k \cdot k} \]
      Step-by-step derivation

      [Start] 4.0	\[ \frac{\ell}{{t}^{3}} \cdot \frac{\ell}{k \cdot k} \]
      *-un-lft-identity [=>] 4.0	\[ \frac{\color{blue}{1 \cdot \ell}}{{t}^{3}} \cdot \frac{\ell}{k \cdot k} \]
      cube-mult [=>] 4.0	\[ \frac{1 \cdot \ell}{\color{blue}{t \cdot \left(t \cdot t\right)}} \cdot \frac{\ell}{k \cdot k} \]
      times-frac [=>] 4.0	\[ \color{blue}{\left(\frac{1}{t} \cdot \frac{\ell}{t \cdot t}\right)} \cdot \frac{\ell}{k \cdot k} \]

   6. Applied egg-rr 4.0%

      \[\leadsto \color{blue}{\frac{\frac{\ell}{t}}{t \cdot t}} \cdot \frac{\ell}{k \cdot k} \]
      Step-by-step derivation

      [Start] 4.0	\[ \left(\frac{1}{t} \cdot \frac{\ell}{t \cdot t}\right) \cdot \frac{\ell}{k \cdot k} \]
      associate-/r* [=>] 3.9	\[ \left(\frac{1}{t} \cdot \color{blue}{\frac{\frac{\ell}{t}}{t}}\right) \cdot \frac{\ell}{k \cdot k} \]
      frac-times [=>] 4.0	\[ \color{blue}{\frac{1 \cdot \frac{\ell}{t}}{t \cdot t}} \cdot \frac{\ell}{k \cdot k} \]
      *-un-lft-identity [<=] 4.0	\[ \frac{\color{blue}{\frac{\ell}{t}}}{t \cdot t} \cdot \frac{\ell}{k \cdot k} \]

   7. Applied egg-rr 35.7%

      \[\leadsto \color{blue}{\frac{\frac{\ell}{t}}{\frac{{\left(t \cdot k\right)}^{2}}{\ell}}} \]
      Step-by-step derivation

      [Start] 4.0	\[ \frac{\frac{\ell}{t}}{t \cdot t} \cdot \frac{\ell}{k \cdot k} \]
      frac-times [=>] 3.9	\[ \color{blue}{\frac{\frac{\ell}{t} \cdot \ell}{\left(t \cdot t\right) \cdot \left(k \cdot k\right)}} \]
      associate-/l* [=>] 3.9	\[ \color{blue}{\frac{\frac{\ell}{t}}{\frac{\left(t \cdot t\right) \cdot \left(k \cdot k\right)}{\ell}}} \]
      pow2 [=>] 3.9	\[ \frac{\frac{\ell}{t}}{\frac{\color{blue}{{t}^{2}} \cdot \left(k \cdot k\right)}{\ell}} \]
      pow2 [=>] 3.9	\[ \frac{\frac{\ell}{t}}{\frac{{t}^{2} \cdot \color{blue}{{k}^{2}}}{\ell}} \]
      pow-prod-down [=>] 35.7	\[ \frac{\frac{\ell}{t}}{\frac{\color{blue}{{\left(t \cdot k\right)}^{2}}}{\ell}} \]

   if 6e-152 < k < 5.1999999999999998e92

   1. Initial program 38.8%

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

   2. Simplified 42.0%

      \[\leadsto \color{blue}{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot \left(\frac{\ell}{{t}^{3}} \cdot \ell\right)} \]
      Step-by-step derivation

      [Start] 38.8	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 38.8	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      associate-/l/ [<=] 38.8	\[ \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}} \]
      *-commutative [=>] 38.8	\[ \frac{\frac{2}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}}{\color{blue}{\sin k \cdot \frac{{t}^{3}}{\ell \cdot \ell}}} \]
      associate-*r/ [=>] 37.9	\[ \frac{\frac{2}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}}{\color{blue}{\frac{\sin k \cdot {t}^{3}}{\ell \cdot \ell}}} \]
      associate-/l* [=>] 38.8	\[ \frac{\frac{2}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}}{\color{blue}{\frac{\sin k}{\frac{\ell \cdot \ell}{{t}^{3}}}}} \]
      associate-/r/ [=>] 38.8	\[ \color{blue}{\frac{\frac{2}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}}{\sin k} \cdot \frac{\ell \cdot \ell}{{t}^{3}}} \]

   3. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}} \]
      Step-by-step derivation

      [Start] 42.0	\[ \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot \left(\frac{\ell}{{t}^{3}} \cdot \ell\right) \]
      add-cube-cbrt [=>] 41.9	\[ \color{blue}{\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot \left(\frac{\ell}{{t}^{3}} \cdot \ell\right)} \cdot \sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot \left(\frac{\ell}{{t}^{3}} \cdot \ell\right)}\right) \cdot \sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot \left(\frac{\ell}{{t}^{3}} \cdot \ell\right)}} \]
      pow3 [=>] 41.9	\[ \color{blue}{{\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot \left(\frac{\ell}{{t}^{3}} \cdot \ell\right)}\right)}^{3}} \]
      cbrt-prod [=>] 41.9	\[ {\color{blue}{\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \sqrt[3]{\frac{\ell}{{t}^{3}} \cdot \ell}\right)}}^{3} \]
      associate-*l/ [=>] 38.8	\[ {\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \sqrt[3]{\color{blue}{\frac{\ell \cdot \ell}{{t}^{3}}}}\right)}^{3} \]
      cbrt-div [=>] 40.5	\[ {\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \color{blue}{\frac{\sqrt[3]{\ell \cdot \ell}}{\sqrt[3]{{t}^{3}}}}\right)}^{3} \]
      cbrt-unprod [<=] 43.5	\[ {\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{\color{blue}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{{t}^{3}}}\right)}^{3} \]
      pow2 [=>] 43.5	\[ {\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{2}}}{\sqrt[3]{{t}^{3}}}\right)}^{3} \]
      rem-cbrt-cube [=>] 63.5	\[ {\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{\color{blue}{t}}\right)}^{3} \]

   if 5.1999999999999998e92 < k

   1. Initial program 54.6%

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

   2. Simplified 54.6%

      \[\leadsto \color{blue}{\frac{2}{\left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right) \cdot \left(\sin k \cdot \tan k\right)}} \]
      Step-by-step derivation

      [Start] 54.6	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 54.6	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      associate-*l* [=>] 54.6	\[ \frac{2}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \tan k\right)\right)}} \]
      associate-*r* [=>] 54.6	\[ \frac{2}{\color{blue}{\left(\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right) \cdot \left(\sin k \cdot \tan k\right)}} \]
      +-commutative [=>] 54.6	\[ \frac{2}{\left(\color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)} \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right) \cdot \left(\sin k \cdot \tan k\right)} \]
      associate-+r+ [=>] 54.6	\[ \frac{2}{\left(\color{blue}{\left(\left(1 + 1\right) + {\left(\frac{k}{t}\right)}^{2}\right)} \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right) \cdot \left(\sin k \cdot \tan k\right)} \]
      metadata-eval [=>] 54.6	\[ \frac{2}{\left(\left(\color{blue}{2} + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right) \cdot \left(\sin k \cdot \tan k\right)} \]

   3. Taylor expanded in k around inf 72.0%

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

   4. Simplified 70.3%

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

      [Start] 72.0	\[ \frac{2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}} \]
      unpow2 [=>] 72.0	\[ \frac{2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot \color{blue}{\left(\ell \cdot \ell\right)}}} \]
      times-frac [=>] 70.1	\[ \frac{2}{\color{blue}{\frac{{k}^{2}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{\ell \cdot \ell}}} \]
      unpow2 [=>] 70.1	\[ \frac{2}{\frac{\color{blue}{k \cdot k}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{\ell \cdot \ell}} \]
      *-commutative [=>] 70.1	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{\color{blue}{t \cdot {\sin k}^{2}}}{\ell \cdot \ell}} \]
      times-frac [=>] 70.3	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \color{blue}{\left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}} \]

   5. Taylor expanded in k around inf 72.0%

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

   6. Simplified 77.3%

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

      [Start] 72.0	\[ \frac{2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}} \]
      unpow2 [=>] 72.0	\[ \frac{2}{\frac{\color{blue}{\left(k \cdot k\right)} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}} \]
      associate-/l* [=>] 70.0	\[ \frac{2}{\color{blue}{\frac{k \cdot k}{\frac{\cos k \cdot {\ell}^{2}}{{\sin k}^{2} \cdot t}}}} \]
      unpow2 [=>] 70.0	\[ \frac{2}{\frac{k \cdot k}{\frac{\cos k \cdot \color{blue}{\left(\ell \cdot \ell\right)}}{{\sin k}^{2} \cdot t}}} \]
      *-commutative [<=] 70.0	\[ \frac{2}{\frac{k \cdot k}{\frac{\cos k \cdot \left(\ell \cdot \ell\right)}{\color{blue}{t \cdot {\sin k}^{2}}}}} \]
      associate-/l* [=>] 75.4	\[ \frac{2}{\color{blue}{\frac{k}{\frac{\frac{\cos k \cdot \left(\ell \cdot \ell\right)}{t \cdot {\sin k}^{2}}}{k}}}} \]
      associate-/r/ [=>] 75.4	\[ \frac{2}{\color{blue}{\frac{k}{\frac{\cos k \cdot \left(\ell \cdot \ell\right)}{t \cdot {\sin k}^{2}}} \cdot k}} \]
      times-frac [=>] 75.4	\[ \frac{2}{\frac{k}{\color{blue}{\frac{\cos k}{t} \cdot \frac{\ell \cdot \ell}{{\sin k}^{2}}}} \cdot k} \]
      associate-*r/ [<=] 75.3	\[ \frac{2}{\frac{k}{\frac{\cos k}{t} \cdot \color{blue}{\left(\ell \cdot \frac{\ell}{{\sin k}^{2}}\right)}} \cdot k} \]
      associate-/r/ [<=] 75.4	\[ \frac{2}{\frac{k}{\color{blue}{\frac{\cos k}{\frac{t}{\ell \cdot \frac{\ell}{{\sin k}^{2}}}}}} \cdot k} \]
      associate-/l* [<=] 76.8	\[ \frac{2}{\color{blue}{\frac{k \cdot \frac{t}{\ell \cdot \frac{\ell}{{\sin k}^{2}}}}{\cos k}} \cdot k} \]
      *-commutative [=>] 76.8	\[ \frac{2}{\color{blue}{k \cdot \frac{k \cdot \frac{t}{\ell \cdot \frac{\ell}{{\sin k}^{2}}}}{\cos k}}} \]
      associate-/l* [=>] 75.4	\[ \frac{2}{k \cdot \color{blue}{\frac{k}{\frac{\cos k}{\frac{t}{\ell \cdot \frac{\ell}{{\sin k}^{2}}}}}}} \]

   7. Applied egg-rr 90.4%

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

      [Start] 77.3	\[ \frac{2}{k \cdot \frac{k}{\left(\ell \cdot \frac{\ell}{t}\right) \cdot \frac{\cos k}{{\sin k}^{2}}}} \]
      clear-num [=>] 77.2	\[ \frac{2}{k \cdot \color{blue}{\frac{1}{\frac{\left(\ell \cdot \frac{\ell}{t}\right) \cdot \frac{\cos k}{{\sin k}^{2}}}{k}}}} \]
      un-div-inv [=>] 77.2	\[ \frac{2}{\color{blue}{\frac{k}{\frac{\left(\ell \cdot \frac{\ell}{t}\right) \cdot \frac{\cos k}{{\sin k}^{2}}}{k}}}} \]
      associate-*l* [=>] 77.3	\[ \frac{2}{\frac{k}{\frac{\color{blue}{\ell \cdot \left(\frac{\ell}{t} \cdot \frac{\cos k}{{\sin k}^{2}}\right)}}{k}}} \]
      associate-/l* [=>] 90.5	\[ \frac{2}{\frac{k}{\color{blue}{\frac{\ell}{\frac{k}{\frac{\ell}{t} \cdot \frac{\cos k}{{\sin k}^{2}}}}}}} \]
      div-inv [=>] 90.5	\[ \frac{2}{\frac{k}{\frac{\ell}{\frac{k}{\frac{\ell}{t} \cdot \color{blue}{\left(\cos k \cdot \frac{1}{{\sin k}^{2}}\right)}}}}} \]
      associate-*r* [=>] 90.4	\[ \frac{2}{\frac{k}{\frac{\ell}{\frac{k}{\color{blue}{\left(\frac{\ell}{t} \cdot \cos k\right) \cdot \frac{1}{{\sin k}^{2}}}}}}} \]
      pow-flip [=>] 90.4	\[ \frac{2}{\frac{k}{\frac{\ell}{\frac{k}{\left(\frac{\ell}{t} \cdot \cos k\right) \cdot \color{blue}{{\sin k}^{\left(-2\right)}}}}}} \]
      metadata-eval [=>] 90.4	\[ \frac{2}{\frac{k}{\frac{\ell}{\frac{k}{\left(\frac{\ell}{t} \cdot \cos k\right) \cdot {\sin k}^{\color{blue}{-2}}}}}} \]

   8. Simplified 94.2%

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

      [Start] 90.4	\[ \frac{2}{\frac{k}{\frac{\ell}{\frac{k}{\left(\frac{\ell}{t} \cdot \cos k\right) \cdot {\sin k}^{-2}}}}} \]
      associate-/r/ [=>] 90.4	\[ \frac{2}{\color{blue}{\frac{k}{\ell} \cdot \frac{k}{\left(\frac{\ell}{t} \cdot \cos k\right) \cdot {\sin k}^{-2}}}} \]
      *-commutative [=>] 90.4	\[ \frac{2}{\color{blue}{\frac{k}{\left(\frac{\ell}{t} \cdot \cos k\right) \cdot {\sin k}^{-2}} \cdot \frac{k}{\ell}}} \]
      times-frac [<=] 70.1	\[ \frac{2}{\color{blue}{\frac{k \cdot k}{\left(\left(\frac{\ell}{t} \cdot \cos k\right) \cdot {\sin k}^{-2}\right) \cdot \ell}}} \]
      associate-*l* [=>] 70.1	\[ \frac{2}{\frac{k \cdot k}{\color{blue}{\left(\frac{\ell}{t} \cdot \left(\cos k \cdot {\sin k}^{-2}\right)\right)} \cdot \ell}} \]
      associate-*l* [=>] 70.1	\[ \frac{2}{\frac{k \cdot k}{\color{blue}{\frac{\ell}{t} \cdot \left(\left(\cos k \cdot {\sin k}^{-2}\right) \cdot \ell\right)}}} \]
      *-commutative [=>] 70.1	\[ \frac{2}{\frac{k \cdot k}{\frac{\ell}{t} \cdot \color{blue}{\left(\ell \cdot \left(\cos k \cdot {\sin k}^{-2}\right)\right)}}} \]
      associate-*r* [=>] 70.1	\[ \frac{2}{\frac{k \cdot k}{\frac{\ell}{t} \cdot \color{blue}{\left(\left(\ell \cdot \cos k\right) \cdot {\sin k}^{-2}\right)}}} \]
      associate-*l/ [=>] 70.0	\[ \frac{2}{\frac{k \cdot k}{\color{blue}{\frac{\ell \cdot \left(\left(\ell \cdot \cos k\right) \cdot {\sin k}^{-2}\right)}{t}}}} \]
      associate-*r* [<=] 70.0	\[ \frac{2}{\frac{k \cdot k}{\frac{\ell \cdot \color{blue}{\left(\ell \cdot \left(\cos k \cdot {\sin k}^{-2}\right)\right)}}{t}}} \]
      associate-*l* [<=] 70.0	\[ \frac{2}{\frac{k \cdot k}{\frac{\color{blue}{\left(\ell \cdot \ell\right) \cdot \left(\cos k \cdot {\sin k}^{-2}\right)}}{t}}} \]
      *-commutative [=>] 70.0	\[ \frac{2}{\frac{k \cdot k}{\frac{\color{blue}{\left(\cos k \cdot {\sin k}^{-2}\right) \cdot \left(\ell \cdot \ell\right)}}{t}}} \]
      associate-*r/ [<=] 70.0	\[ \frac{2}{\frac{k \cdot k}{\color{blue}{\left(\cos k \cdot {\sin k}^{-2}\right) \cdot \frac{\ell \cdot \ell}{t}}}} \]
      associate-/r* [=>] 70.0	\[ \frac{2}{\color{blue}{\frac{\frac{k \cdot k}{\cos k \cdot {\sin k}^{-2}}}{\frac{\ell \cdot \ell}{t}}}} \]
      associate-/r/ [=>] 72.0	\[ \frac{2}{\color{blue}{\frac{\frac{k \cdot k}{\cos k \cdot {\sin k}^{-2}}}{\ell \cdot \ell} \cdot t}} \]
      *-commutative [=>] 72.0	\[ \frac{2}{\color{blue}{t \cdot \frac{\frac{k \cdot k}{\cos k \cdot {\sin k}^{-2}}}{\ell \cdot \ell}}} \]

3. Recombined 5 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{+194}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{-293}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\ell \cdot \frac{2}{\tan k}}}{t \cdot \sqrt[3]{\sin k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \cdot \sqrt[3]{\ell}\right)}^{3}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-152}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{{\left(k \cdot t\right)}^{2}}{\ell}}\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;{\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	58.5%
Cost	101772

\[\begin{array}{l} t_1 := {\left(\frac{k}{t}\right)}^{2}\\ t_2 := 1 + \left(t_1 + 1\right)\\ t_3 := \frac{2}{\left(\tan k \cdot \left(\sin k \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right)\right) \cdot t_2}\\ t_4 := \frac{\ell \cdot \frac{1}{k}}{t}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;\frac{\ell}{\frac{{t}^{3}}{\frac{\ell}{\sin k \cdot \left(2 + t_1\right)}} \cdot \left(\tan k \cdot 0.5\right)}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_4 \cdot \frac{t_4}{t}\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{2}{\left(\sin k \cdot \left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right)\right) \cdot \left(\tan k \cdot t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \end{array} \]

Alternative 2
Accuracy	61.9%
Cost	46480

\[\begin{array}{l} t_1 := {\left(\sqrt[3]{\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)}} \cdot \frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}\\ t_2 := \frac{\ell \cdot \frac{1}{k}}{t}\\ \mathbf{if}\;k \leq -2.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-151}:\\ \;\;\;\;t_2 \cdot \frac{t_2}{t}\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternative 3
Accuracy	58.4%
Cost	45960

\[\begin{array}{l} \mathbf{if}\;k \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{-293}:\\ \;\;\;\;{\left(\sqrt[3]{\ell} \cdot \frac{\sqrt[3]{\ell \cdot \frac{2}{\tan k}}}{\sqrt[3]{2} \cdot \left(t \cdot \sqrt[3]{\sin k}\right)}\right)}^{3}\\ \mathbf{elif}\;k \leq 2.85 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{{\left(k \cdot t\right)}^{2}}{\ell}}\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{2}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}}{\sin k} \cdot {\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternative 4
Accuracy	58.9%
Cost	40212

\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{1}{k}}{t}\\ t_2 := \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\sin k \cdot \tan k\right)} \cdot {\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{if}\;k \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{elif}\;k \leq -1.32 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{-152}:\\ \;\;\;\;t_1 \cdot \frac{t_1}{t}\\ \mathbf{elif}\;k \leq 0.00035:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternative 5
Accuracy	59.6%
Cost	40212

\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{1}{k}}{t}\\ t_2 := \frac{\frac{2}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}}{\sin k} \cdot {\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{if}\;k \leq -3 \cdot 10^{+33}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{elif}\;k \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -7.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \mathbf{elif}\;k \leq 2.85 \cdot 10^{-151}:\\ \;\;\;\;t_1 \cdot \frac{t_1}{t}\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternative 6
Accuracy	59.0%
Cost	27080

\[\begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+105}:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-2}{-2 - {\left(\frac{k}{t}\right)}^{2}} \cdot \left(\frac{\ell}{\frac{\tan k}{{t}^{-3}}} \cdot \frac{\ell}{\sin k}\right)\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{+85}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{{\left(k \cdot t\right)}^{2}}{\ell}}\\ \end{array} \]

Alternative 7
Accuracy	56.9%
Cost	20868

\[\begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{2}{\left(\sin k \cdot \left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right)\right) \cdot \left(\tan k \cdot \left(1 + \left({\left(\frac{k}{t}\right)}^{2} + 1\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+81}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{{\left(k \cdot t\right)}^{2}}{\ell}}\\ \end{array} \]

Alternative 8
Accuracy	59.4%
Cost	20620

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{{\sin k}^{2} \cdot t}\right)\\ \mathbf{if}\;k \leq -1.25 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -31500000:\\ \;\;\;\;\ell \cdot \frac{\ell \cdot \frac{2}{\tan k}}{k \cdot \left(k \cdot \left(\sin k \cdot t\right)\right)}\\ \mathbf{elif}\;k \leq 0.00016:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	59.2%
Cost	20620

\[\begin{array}{l} t_1 := {\sin k}^{2} \cdot t\\ t_2 := 2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t_1}\right)\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -11000000:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\cos k}{k \cdot k} \cdot \frac{\ell}{t_1}\right)\right)\\ \mathbf{elif}\;k \leq 0.00029:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	59.0%
Cost	20620

\[\begin{array}{l} t_1 := {\sin k}^{2} \cdot t\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{+155}:\\ \;\;\;\;2 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{\cos k}{t_1}\right)\\ \mathbf{elif}\;k \leq -34000000000:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\cos k}{k \cdot k} \cdot \frac{\ell}{t_1}\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternative 11
Accuracy	58.3%
Cost	20488

\[\begin{array}{l} \mathbf{if}\;k \leq -12000000:\\ \;\;\;\;\frac{2}{\frac{k \cdot \left({\sin k}^{2} \cdot \frac{t}{\ell}\right)}{\ell \cdot \frac{\cos k}{k}}}\\ \mathbf{elif}\;k \leq 0.00019:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{\frac{k}{\cos k}}{\ell} \cdot \frac{\frac{k}{{\sin k}^{-2}}}{\ell}\right)}\\ \end{array} \]

Alternative 12
Accuracy	56.8%
Cost	14024

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+33}:\\ \;\;\;\;\ell \cdot \frac{\ell \cdot \frac{2}{\tan k}}{k \cdot \left(k \cdot \left(\sin k \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\frac{{\left(k \cdot t\right)}^{2}}{\ell}}\\ \end{array} \]

Alternative 13
Accuracy	50.6%
Cost	7753

\[\begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-27} \lor \neg \left(t \leq 3.6 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{k \cdot k}{\ell}\right)}\\ \end{array} \]

Alternative 14
Accuracy	50.0%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-34} \lor \neg \left(t \leq 1.32 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \end{array} \]

Alternative 15
Accuracy	49.7%
Cost	7176

\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{1}{k}}{t}\\ t_2 := \ell \cdot \frac{\ell}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-96}:\\ \;\;\;\;t_1 \cdot \frac{t_1}{t}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-48}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{t_2}{k \cdot k} + t_2 \cdot -0.16666666666666666}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{\ell}{k \cdot t}\right)}^{2}}{t}\\ \end{array} \]

Alternative 16
Accuracy	49.2%
Cost	1737

\[\begin{array}{l} t_1 := \ell \cdot \frac{\ell}{t}\\ t_2 := \frac{\ell \cdot \frac{1}{k}}{t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-97} \lor \neg \left(t \leq 8.2 \cdot 10^{-79}\right):\\ \;\;\;\;t_2 \cdot \frac{t_2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{t_1}{k \cdot k} + t_1 \cdot -0.16666666666666666}}\\ \end{array} \]

Alternative 17
Accuracy	46.9%
Cost	1353

\[\begin{array}{l} t_1 := \ell \cdot \frac{1}{k}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-97} \lor \neg \left(t \leq 7.6 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{t_1}{t} \cdot \frac{t_1}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{\ell \cdot \frac{\ell}{t}}{k \cdot k}}}\\ \end{array} \]

Alternative 18
Accuracy	48.8%
Cost	1353

\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{1}{k}}{t}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-97} \lor \neg \left(t \leq 3.6 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{t_1 \cdot t_1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{\ell \cdot \frac{\ell}{t}}{k \cdot k}}}\\ \end{array} \]

Alternative 19
Accuracy	48.9%
Cost	1353

\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{1}{k}}{t}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-97} \lor \neg \left(t \leq 6 \cdot 10^{-82}\right):\\ \;\;\;\;t_1 \cdot \frac{t_1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{\ell \cdot \frac{\ell}{t}}{k \cdot k}}}\\ \end{array} \]

Alternative 20
Accuracy	42.9%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-149} \lor \neg \left(t \leq 1.02 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{\ell}{k}}{k \cdot \left(\frac{t}{\ell} \cdot \left(t \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{\ell \cdot \ell}{t \cdot \left(k \cdot k\right)}}}\\ \end{array} \]

Alternative 21
Accuracy	45.0%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-95} \lor \neg \left(t \leq 2.6 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{\frac{\ell}{k}}{k \cdot \left(\frac{t}{\ell} \cdot \left(t \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{k \cdot \frac{k}{\frac{\ell \cdot \frac{\ell}{t}}{k \cdot k}}}\\ \end{array} \]

Alternative 22
Accuracy	32.5%
Cost	832

\[\frac{\frac{\ell}{t}}{t \cdot t} \cdot \frac{\ell}{k \cdot k} \]

Alternative 23
Accuracy	38.6%
Cost	832

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

Alternative 24
Accuracy	37.6%
Cost	832

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

Reproduce

herbie shell --seed 2023157 
(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))))