Toniolo and Linder, Equation (10+)

Average Error: 49.97% → 10.74%

Time: 49.2s

Precision: binary64

Cost: 46276

Math

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

↓

\[\begin{array}{l} t_1 := {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+32}:\\ \;\;\;\;\frac{2}{{\left(\frac{\sqrt[3]{\sin k}}{\frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + t_1\right)\right)\right)}\\ \mathbf{elif}\;t \leq 460:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\ell \cdot \frac{-\cos k}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(t \cdot \left(\left(\tan k \cdot \left(2 + t_1\right)\right) \cdot \left(\left(t \cdot \sin k\right) \cdot \frac{t}{\ell}\right)\right)\right) \cdot \frac{1}{\ell}}\\ \end{array} \]

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 (pow (/ k t) 2.0)))
   (if (<= t -3e+32)
     (/
      2.0
      (*
       (pow (/ (cbrt (sin k)) (/ (cbrt l) (/ t (cbrt l)))) 3.0)
       (* (tan k) (+ 1.0 (+ 1.0 t_1)))))
     (if (<= t 460.0)
       (/
        2.0
        (* (/ k (/ l (pow (sin k) 2.0))) (/ (- t) (* l (/ (- (cos k)) k)))))
       (/
        2.0
        (*
         (* t (* (* (tan k) (+ 2.0 t_1)) (* (* t (sin k)) (/ t l))))
         (/ 1.0 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 = pow((k / t), 2.0);
	double tmp;
	if (t <= -3e+32) {
		tmp = 2.0 / (pow((cbrt(sin(k)) / (cbrt(l) / (t / cbrt(l)))), 3.0) * (tan(k) * (1.0 + (1.0 + t_1))));
	} else if (t <= 460.0) {
		tmp = 2.0 / ((k / (l / pow(sin(k), 2.0))) * (-t / (l * (-cos(k) / k))));
	} else {
		tmp = 2.0 / ((t * ((tan(k) * (2.0 + t_1)) * ((t * sin(k)) * (t / l)))) * (1.0 / 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 = Math.pow((k / t), 2.0);
	double tmp;
	if (t <= -3e+32) {
		tmp = 2.0 / (Math.pow((Math.cbrt(Math.sin(k)) / (Math.cbrt(l) / (t / Math.cbrt(l)))), 3.0) * (Math.tan(k) * (1.0 + (1.0 + t_1))));
	} else if (t <= 460.0) {
		tmp = 2.0 / ((k / (l / Math.pow(Math.sin(k), 2.0))) * (-t / (l * (-Math.cos(k) / k))));
	} else {
		tmp = 2.0 / ((t * ((Math.tan(k) * (2.0 + t_1)) * ((t * Math.sin(k)) * (t / l)))) * (1.0 / 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(k / t) ^ 2.0
	tmp = 0.0
	if (t <= -3e+32)
		tmp = Float64(2.0 / Float64((Float64(cbrt(sin(k)) / Float64(cbrt(l) / Float64(t / cbrt(l)))) ^ 3.0) * Float64(tan(k) * Float64(1.0 + Float64(1.0 + t_1)))));
	elseif (t <= 460.0)
		tmp = Float64(2.0 / Float64(Float64(k / Float64(l / (sin(k) ^ 2.0))) * Float64(Float64(-t) / Float64(l * Float64(Float64(-cos(k)) / k)))));
	else
		tmp = Float64(2.0 / Float64(Float64(t * Float64(Float64(tan(k) * Float64(2.0 + t_1)) * Float64(Float64(t * sin(k)) * Float64(t / l)))) * Float64(1.0 / 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[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[t, -3e+32], N[(2.0 / N[(N[Power[N[(N[Power[N[Sin[k], $MachinePrecision], 1/3], $MachinePrecision] / N[(N[Power[l, 1/3], $MachinePrecision] / N[(t / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision] * N[(N[Tan[k], $MachinePrecision] * N[(1.0 + N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 460.0], N[(2.0 / N[(N[(k / N[(l / N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((-t) / N[(l * N[((-N[Cos[k], $MachinePrecision]) / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(t * N[(N[(N[Tan[k], $MachinePrecision] * N[(2.0 + t$95$1), $MachinePrecision]), $MachinePrecision] * N[(N[(t * N[Sin[k], $MachinePrecision]), $MachinePrecision] * N[(t / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e32

   1. Initial program 34.3

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

   2. Simplified 34.31

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

      [Start] 34.3	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 34.31	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      +-commutative [=>] 34.31	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\right)} \]

   3. Applied egg-rr 8.56

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

   4. Applied egg-rr 8.56

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

   5. Simplified 8.57

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

      [Start] 8.56	\[ \frac{2}{{\left(\frac{\frac{\sqrt[3]{\sin k}}{\frac{\sqrt[3]{\ell}}{t}}}{\sqrt[3]{\ell}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      associate-/r/ [=>] 8.58	\[ \frac{2}{{\left(\frac{\color{blue}{\frac{\sqrt[3]{\sin k}}{\sqrt[3]{\ell}} \cdot t}}{\sqrt[3]{\ell}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-lft-identity [<=] 8.58	\[ \frac{2}{{\left(\frac{\frac{\sqrt[3]{\sin k}}{\sqrt[3]{\ell}} \cdot t}{\color{blue}{1 \cdot \sqrt[3]{\ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      times-frac [=>] 8.57	\[ \frac{2}{{\color{blue}{\left(\frac{\frac{\sqrt[3]{\sin k}}{\sqrt[3]{\ell}}}{1} \cdot \frac{t}{\sqrt[3]{\ell}}\right)}}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      associate-/r* [<=] 8.57	\[ \frac{2}{{\left(\color{blue}{\frac{\sqrt[3]{\sin k}}{\sqrt[3]{\ell} \cdot 1}} \cdot \frac{t}{\sqrt[3]{\ell}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-rgt-identity [=>] 8.57	\[ \frac{2}{{\left(\frac{\sqrt[3]{\sin k}}{\color{blue}{\sqrt[3]{\ell}}} \cdot \frac{t}{\sqrt[3]{\ell}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]

   6. Applied egg-rr 8.57

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

   if -3e32 < t < 460

   1. Initial program 73.49

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

   2. Simplified 73.4

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

      [Start] 73.49	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 73.4	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      +-commutative [=>] 73.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\right)} \]

   3. Taylor expanded in t around 0 42.56

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

   4. Simplified 37.1

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

      [Start] 42.56	\[ \frac{2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}} \]
      times-frac [=>] 45.03	\[ \frac{2}{\color{blue}{\frac{{k}^{2}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}}} \]
      unpow2 [=>] 45.03	\[ \frac{2}{\frac{\color{blue}{k \cdot k}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}} \]
      *-commutative [=>] 45.03	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{\color{blue}{t \cdot {\sin k}^{2}}}{{\ell}^{2}}} \]
      unpow2 [=>] 45.03	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{t \cdot {\sin k}^{2}}{\color{blue}{\ell \cdot \ell}}} \]
      times-frac [=>] 37.1	\[ \frac{2}{\frac{k \cdot k}{\cos k} \cdot \color{blue}{\left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}} \]

   5. Applied egg-rr 19.64

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

   6. Simplified 11.56

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

      [Start] 19.64	\[ \frac{2}{\frac{k \cdot \left(-t\right)}{\frac{\ell}{{\sin k}^{2}} \cdot \left(\frac{\cos k}{k} \cdot \left(-\ell\right)\right)}} \]
      times-frac [=>] 11.56	\[ \frac{2}{\color{blue}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\frac{\cos k}{k} \cdot \left(-\ell\right)}}} \]

   if 460 < t

   1. Initial program 33.85

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

   2. Simplified 42.31

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

      [Start] 33.85	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 33.85	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      distribute-rgt1-in [<=] 33.85	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      *-commutative [=>] 33.85	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      associate-*l* [=>] 33.85	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-*l* [=>] 42.1	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      distribute-lft-in [=>] 42.1	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \color{blue}{\left(\tan k \cdot 1 + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)}\right)} \]
      *-rgt-identity [=>] 42.1	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\color{blue}{\tan k} + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)} \]
      distribute-lft-in [=>] 42.1	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \color{blue}{\left(\sin k \cdot \tan k + \sin k \cdot \left(\tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]

   3. Applied egg-rr 33.33

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

   4. Applied egg-rr 10.31

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

   5. Applied egg-rr 11.7

      \[\leadsto \frac{2}{\color{blue}{\left(\left(\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\left(t \cdot \sin k\right) \cdot \frac{t}{\ell}\right)\right) \cdot t\right) \cdot \frac{1}{\ell}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 10.74

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+32}:\\ \;\;\;\;\frac{2}{{\left(\frac{\sqrt[3]{\sin k}}{\frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 460:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\ell \cdot \frac{-\cos k}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(t \cdot \left(\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\left(t \cdot \sin k\right) \cdot \frac{t}{\ell}\right)\right)\right) \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternatives

Alternative 1
Error	12.38%
Cost	39812

\[\begin{array}{l} t_1 := {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+29}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(1 + \left(1 + t_1\right)\right)\right) \cdot \left(\sin k \cdot {\left(\frac{t}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3}\right)}\\ \mathbf{elif}\;t \leq 63000:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\ell \cdot \frac{-\cos k}{k}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(t \cdot \left(\left(\tan k \cdot \left(2 + t_1\right)\right) \cdot \left(\left(t \cdot \sin k\right) \cdot \frac{t}{\ell}\right)\right)\right) \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 2
Error	12.76%
Cost	21004

\[\begin{array}{l} t_1 := \frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\ell \cdot \frac{-\cos k}{k}}}\\ \mathbf{if}\;k \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+59}:\\ \;\;\;\;\frac{2}{\left(\frac{t}{\ell} \cdot \left(t \cdot \frac{t}{\ell}\right)\right) \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	11.59%
Cost	21004

\[\begin{array}{l} t_1 := \frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\ell \cdot \frac{-\cos k}{k}}}\\ \mathbf{if}\;k \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{2}{\frac{t \cdot \left(\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\sin k \cdot \frac{t}{\ell}\right)\right)}{\frac{\ell}{t}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	24.12%
Cost	20884

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\\ t_2 := {\sin k}^{2}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-229}:\\ \;\;\;\;\cos k \cdot \frac{2}{k \cdot \left(k \cdot \frac{t_2}{\ell \cdot \frac{\ell}{t}}\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-160}:\\ \;\;\;\;\left(\ell \cdot \ell\right) \cdot \left(2 \cdot \frac{\cos k}{\left(k \cdot k\right) \cdot \left(t \cdot t_2\right)}\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;\ell \cdot \left(\frac{\frac{\cos k}{k}}{k \cdot t_2} \cdot \left(\ell \cdot \frac{2}{t}\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+77}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\frac{\ell}{k}}{{t}^{3}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 5
Error	23.78%
Cost	20884

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\\ t_2 := {\sin k}^{2}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-23}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-230}:\\ \;\;\;\;\cos k \cdot \frac{2}{k \cdot \left(k \cdot \frac{t_2}{\ell \cdot \frac{\ell}{t}}\right)}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;\left(\ell \cdot \ell\right) \cdot \left(2 \cdot \frac{\cos k}{\left(k \cdot k\right) \cdot \left(t \cdot t_2\right)}\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-25}:\\ \;\;\;\;\ell \cdot \frac{2 \cdot \frac{\cos k}{k \cdot k}}{t_2 \cdot \frac{t}{\ell}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+76}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\frac{\ell}{k}}{{t}^{3}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 6
Error	13.6%
Cost	20748

\[\begin{array}{l} t_1 := \frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}}} \cdot \frac{-t}{\ell \cdot \frac{-\cos k}{k}}}\\ \mathbf{if}\;k \leq -2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{2}{\left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right) \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	25.59%
Cost	20620

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{2}{\left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right) \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-35}:\\ \;\;\;\;2 \cdot \frac{\cos k \cdot \left(\ell \cdot \ell\right)}{\left(k \cdot k\right) \cdot \left(t \cdot {\sin k}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	23.83%
Cost	20620

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-23}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-31}:\\ \;\;\;\;\ell \cdot \left(\frac{\frac{\cos k}{k}}{k \cdot {\sin k}^{2}} \cdot \left(\ell \cdot \frac{2}{t}\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\frac{\ell}{k}}{{t}^{3}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 9
Error	19.25%
Cost	20620

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\ell}{{\sin k}^{2}} \cdot \left(\frac{\cos k}{k} \cdot \frac{\ell}{t}\right)}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{\ell}{k \cdot {t}^{3}} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 10
Error	17.53%
Cost	20620

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{\frac{t \cdot k}{\frac{\ell}{{\sin k}^{2}} \cdot \left(\ell \cdot \frac{\cos k}{k}\right)}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{\ell}{k \cdot {t}^{3}} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+107}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 11
Error	28.43%
Cost	15324

\[\begin{array}{l} t_1 := \frac{2}{\left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right) \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ t_2 := \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{1 - \cos \left(k + k\right)}{\ell \cdot \frac{2 \cdot \ell}{t}}}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.16666666666666666, \frac{\ell}{k \cdot \frac{k}{\ell}}, \frac{-\ell}{\frac{{k}^{4}}{\ell}}\right)}{t} \cdot -2\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{\ell}{k \cdot {t}^{3}} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 12
Error	28.44%
Cost	15324

\[\begin{array}{l} t_1 := \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{1 - \cos \left(k + k\right)}{\ell \cdot \frac{2 \cdot \ell}{t}}}\\ t_2 := \frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{t_2 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.16666666666666666, \frac{\ell}{k \cdot \frac{k}{\ell}}, \frac{-\ell}{\frac{{k}^{4}}{\ell}}\right)}{t} \cdot -2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{\ell}{k \cdot {t}^{3}} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{2}{t_2 \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{{\left(t \cdot k\right)}^{2}}{\frac{\ell}{t}}}\\ \end{array} \]

Alternative 13
Error	25.94%
Cost	14604

\[\begin{array}{l} t_1 := \frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{1 - \cos \left(k + k\right)}{\ell \cdot \frac{2 \cdot \ell}{t}}}\\ \mathbf{if}\;k \leq -1.6 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{elif}\;k \leq 2800000000:\\ \;\;\;\;\frac{2}{\frac{t \cdot \left(\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \frac{t \cdot k}{\ell}\right)}{\frac{\ell}{t}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	29.48%
Cost	14412

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-266}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \frac{1 - \cos \left(k + k\right)}{\ell \cdot \frac{2 \cdot \ell}{t}}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.16666666666666666, \frac{\ell}{k \cdot \frac{k}{\ell}}, \frac{-\ell}{\frac{{k}^{4}}{\ell}}\right)}{t} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	29.37%
Cost	7753

\[\begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-34} \lor \neg \left(t \leq 1.02 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{k \cdot k}{\ell}\right)}\\ \end{array} \]

Alternative 16
Error	29.71%
Cost	1865

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-18} \lor \neg \left(t \leq 1.76 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{t + \frac{t \cdot -6}{k \cdot k}}{t \cdot \frac{t \cdot \frac{k \cdot k}{\ell}}{\ell \cdot -0.16666666666666666}}\\ \end{array} \]

Alternative 17
Error	31.21%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-17} \lor \neg \left(t \leq 2.1 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(-0.16666666666666666 \cdot \left(\left(\frac{\ell}{k} \cdot \frac{\ell}{k}\right) \cdot \frac{1 + \frac{-6}{k \cdot k}}{t}\right)\right)\\ \end{array} \]

Alternative 18
Error	30.88%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-18} \lor \neg \left(t \leq 3.8 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\frac{6}{k \cdot k} + -1}{k \cdot k} \cdot \left(0.16666666666666666 \cdot \frac{\ell}{\frac{t}{\ell}}\right)\right)\\ \end{array} \]

Alternative 19
Error	47%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-18} \lor \neg \left(t \leq 1.2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot k} \cdot \frac{\ell}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \frac{\ell}{k \cdot k}}{t}\right)\\ \end{array} \]

Alternative 20
Error	40.54%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-18} \lor \neg \left(t \leq 1.2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{\ell}{\left(t \cdot t\right) \cdot \left(k \cdot \left(k \cdot \frac{t}{\ell}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \frac{\ell}{k \cdot k}}{t}\right)\\ \end{array} \]

Alternative 21
Error	38.83%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-18} \lor \neg \left(t \leq 1.2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{\ell}{\frac{k \cdot \left(t \cdot t\right)}{\frac{\ell}{t \cdot k}}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \frac{\ell}{k \cdot k}}{t}\right)\\ \end{array} \]

Alternative 22
Error	33.05%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-17} \lor \neg \left(t \leq 6 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{\frac{\ell}{t \cdot k} \cdot \frac{\ell}{t}}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \frac{\ell}{k \cdot k}}{t}\right)\\ \end{array} \]

Alternative 23
Error	39.33%
Cost	1096

\[\begin{array}{l} t_1 := \frac{\ell}{t \cdot k}\\ t_2 := k \cdot \left(t \cdot t\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{\ell \cdot t_1}{t_2}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \frac{\ell}{k \cdot k}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{t_2}{t_1}}\\ \end{array} \]

Alternative 24
Error	58.38%
Cost	832

\[2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \ell}{t \cdot \left(k \cdot k\right)}\right) \]

Alternative 25
Error	58.67%
Cost	832

\[2 \cdot \left(-0.16666666666666666 \cdot \frac{\ell \cdot \frac{\ell}{k \cdot k}}{t}\right) \]

Reproduce

herbie shell --seed 2023102 
(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))))