Toniolo and Linder, Equation (10+)

Average Accuracy: 49.3% → 81.6%

Time: 1.0min

Precision: binary64

Cost: 46344

Math

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

↓

\[\begin{array}{l} t_1 := {\left(\sqrt[3]{\ell}\right)}^{2}\\ t_2 := \tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ t_3 := \sqrt[3]{\sin k}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{{\left(\frac{t \cdot t_3}{t_1}\right)}^{3} \cdot t_2}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t_2 \cdot {\left(t_3 \cdot \frac{t}{t_1}\right)}^{3}}\\ \end{array} \]

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 (cbrt l) 2.0))
        (t_2 (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))
        (t_3 (cbrt (sin k))))
   (if (<= t -7.5e-42)
     (/ 2.0 (* (pow (/ (* t t_3) t_1) 3.0) t_2))
     (if (<= t 2.1e-66)
       (/ 2.0 (* (/ k (/ (cos k) k)) (* (/ t l) (/ (pow (sin k) 2.0) l))))
       (/ 2.0 (* t_2 (pow (* t_3 (/ t t_1)) 3.0)))))))

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(cbrt(l), 2.0);
	double t_2 = tan(k) * (1.0 + (1.0 + pow((k / t), 2.0)));
	double t_3 = cbrt(sin(k));
	double tmp;
	if (t <= -7.5e-42) {
		tmp = 2.0 / (pow(((t * t_3) / t_1), 3.0) * t_2);
	} else if (t <= 2.1e-66) {
		tmp = 2.0 / ((k / (cos(k) / k)) * ((t / l) * (pow(sin(k), 2.0) / l)));
	} else {
		tmp = 2.0 / (t_2 * pow((t_3 * (t / t_1)), 3.0));
	}
	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(Math.cbrt(l), 2.0);
	double t_2 = Math.tan(k) * (1.0 + (1.0 + Math.pow((k / t), 2.0)));
	double t_3 = Math.cbrt(Math.sin(k));
	double tmp;
	if (t <= -7.5e-42) {
		tmp = 2.0 / (Math.pow(((t * t_3) / t_1), 3.0) * t_2);
	} else if (t <= 2.1e-66) {
		tmp = 2.0 / ((k / (Math.cos(k) / k)) * ((t / l) * (Math.pow(Math.sin(k), 2.0) / l)));
	} else {
		tmp = 2.0 / (t_2 * Math.pow((t_3 * (t / t_1)), 3.0));
	}
	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 = cbrt(l) ^ 2.0
	t_2 = Float64(tan(k) * Float64(1.0 + Float64(1.0 + (Float64(k / t) ^ 2.0))))
	t_3 = cbrt(sin(k))
	tmp = 0.0
	if (t <= -7.5e-42)
		tmp = Float64(2.0 / Float64((Float64(Float64(t * t_3) / t_1) ^ 3.0) * t_2));
	elseif (t <= 2.1e-66)
		tmp = Float64(2.0 / Float64(Float64(k / Float64(cos(k) / k)) * Float64(Float64(t / l) * Float64((sin(k) ^ 2.0) / l))));
	else
		tmp = Float64(2.0 / Float64(t_2 * (Float64(t_3 * Float64(t / t_1)) ^ 3.0)));
	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[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$2 = N[(N[Tan[k], $MachinePrecision] * N[(1.0 + N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[Sin[k], $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[t, -7.5e-42], N[(2.0 / N[(N[Power[N[(N[(t * t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], 3.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-66], N[(2.0 / N[(N[(k / N[(N[Cos[k], $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision] * N[(N[(t / l), $MachinePrecision] * N[(N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(t$95$2 * N[Power[N[(t$95$3 * N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999972e-42

   1. Initial program 64.9%

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

   2. Simplified 64.9%

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

      [Start] 64.9	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 64.9	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      +-commutative [=>] 64.9	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\right)} \]

   3. Applied egg-rr 88.5%

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

      [Start] 64.9	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      add-cube-cbrt [=>] 64.8	\[ \frac{2}{\color{blue}{\left(\left(\sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k} \cdot \sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}\right) \cdot \sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}\right)} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      pow3 [=>] 64.8	\[ \frac{2}{\color{blue}{{\left(\sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}\right)}^{3}} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-commutative [=>] 64.8	\[ \frac{2}{{\left(\sqrt[3]{\color{blue}{\sin k \cdot \frac{{t}^{3}}{\ell \cdot \ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      cbrt-prod [=>] 64.7	\[ \frac{2}{{\color{blue}{\left(\sqrt[3]{\sin k} \cdot \sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell}}\right)}}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      cbrt-div [=>] 66.0	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \color{blue}{\frac{\sqrt[3]{{t}^{3}}}{\sqrt[3]{\ell \cdot \ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      rem-cbrt-cube [=>] 72.0	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{\color{blue}{t}}{\sqrt[3]{\ell \cdot \ell}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      cbrt-prod [=>] 88.5	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{t}{\color{blue}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      pow2 [=>] 88.5	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{t}{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{2}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]

   4. Simplified 88.5%

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

      [Start] 88.5	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{t}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      associate-*r/ [=>] 88.5	\[ \frac{2}{{\color{blue}{\left(\frac{\sqrt[3]{\sin k} \cdot t}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]

   if -7.49999999999999972e-42 < t < 2.1e-66

   1. Initial program 12.5%

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

   2. Simplified 12.4%

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

      [Start] 12.5	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      *-commutative [=>] 12.5	\[ \frac{2}{\color{blue}{\left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      distribute-rgt1-in [<=] 12.5	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right)}} \]
      *-commutative [=>] 12.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      associate-*l* [=>] 12.6	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]
      associate-*l* [=>] 12.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \color{blue}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}} \]
      distribute-lft-in [=>] 12.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \color{blue}{\left(\tan k \cdot 1 + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)}\right)} \]
      *-rgt-identity [=>] 12.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\color{blue}{\tan k} + \tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)} \]
      distribute-lft-in [=>] 12.5	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k + \frac{{t}^{3}}{\ell \cdot \ell} \cdot \color{blue}{\left(\sin k \cdot \tan k + \sin k \cdot \left(\tan k \cdot {\left(\frac{k}{t}\right)}^{2}\right)\right)}} \]

   3. Applied egg-rr 13.9%

      \[\leadsto \frac{2}{\color{blue}{{\left(\frac{{t}^{1.5}}{\ell}\right)}^{2}} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      Proof

      [Start] 12.4	\[ \frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      add-sqr-sqrt [=>] 4.7	\[ \frac{2}{\color{blue}{\left(\sqrt{\frac{{t}^{3}}{\ell \cdot \ell}} \cdot \sqrt{\frac{{t}^{3}}{\ell \cdot \ell}}\right)} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      pow2 [=>] 4.7	\[ \frac{2}{\color{blue}{{\left(\sqrt{\frac{{t}^{3}}{\ell \cdot \ell}}\right)}^{2}} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      sqrt-div [=>] 4.7	\[ \frac{2}{{\color{blue}{\left(\frac{\sqrt{{t}^{3}}}{\sqrt{\ell \cdot \ell}}\right)}}^{2} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      sqrt-prod [=>] 2.9	\[ \frac{2}{{\left(\frac{\sqrt{{t}^{3}}}{\color{blue}{\sqrt{\ell} \cdot \sqrt{\ell}}}\right)}^{2} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      add-sqr-sqrt [<=] 5.3	\[ \frac{2}{{\left(\frac{\sqrt{{t}^{3}}}{\color{blue}{\ell}}\right)}^{2} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      sqrt-pow1 [=>] 13.9	\[ \frac{2}{{\left(\frac{\color{blue}{{t}^{\left(\frac{3}{2}\right)}}}{\ell}\right)}^{2} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      metadata-eval [=>] 13.9	\[ \frac{2}{{\left(\frac{{t}^{\color{blue}{1.5}}}{\ell}\right)}^{2} \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 58.9%

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

   5. Simplified 65.5%

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

      [Start] 58.9	\[ \frac{2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot {\ell}^{2}}} \]
      times-frac [=>] 54.7	\[ \frac{2}{\color{blue}{\frac{{k}^{2}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}}} \]
      unpow2 [=>] 54.7	\[ \frac{2}{\frac{\color{blue}{k \cdot k}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}} \]
      associate-/l* [=>] 54.7	\[ \frac{2}{\color{blue}{\frac{k}{\frac{\cos k}{k}}} \cdot \frac{{\sin k}^{2} \cdot t}{{\ell}^{2}}} \]
      *-commutative [=>] 54.7	\[ \frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \frac{\color{blue}{t \cdot {\sin k}^{2}}}{{\ell}^{2}}} \]
      unpow2 [=>] 54.7	\[ \frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \frac{t \cdot {\sin k}^{2}}{\color{blue}{\ell \cdot \ell}}} \]
      times-frac [=>] 65.5	\[ \frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \color{blue}{\left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}} \]

   if 2.1e-66 < t

   1. Initial program 63.6%

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

   2. Simplified 63.6%

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

      [Start] 63.6	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 63.6	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      +-commutative [=>] 63.6	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\right)} \]

   3. Applied egg-rr 87.8%

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

      [Start] 63.6	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      add-cube-cbrt [=>] 63.5	\[ \frac{2}{\color{blue}{\left(\left(\sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k} \cdot \sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}\right) \cdot \sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}\right)} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      pow3 [=>] 63.5	\[ \frac{2}{\color{blue}{{\left(\sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}\right)}^{3}} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      *-commutative [=>] 63.5	\[ \frac{2}{{\left(\sqrt[3]{\color{blue}{\sin k \cdot \frac{{t}^{3}}{\ell \cdot \ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      cbrt-prod [=>] 63.4	\[ \frac{2}{{\color{blue}{\left(\sqrt[3]{\sin k} \cdot \sqrt[3]{\frac{{t}^{3}}{\ell \cdot \ell}}\right)}}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      cbrt-div [=>] 64.8	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \color{blue}{\frac{\sqrt[3]{{t}^{3}}}{\sqrt[3]{\ell \cdot \ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      rem-cbrt-cube [=>] 70.8	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{\color{blue}{t}}{\sqrt[3]{\ell \cdot \ell}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      cbrt-prod [=>] 87.8	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{t}{\color{blue}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]
      pow2 [=>] 87.8	\[ \frac{2}{{\left(\sqrt[3]{\sin k} \cdot \frac{t}{\color{blue}{{\left(\sqrt[3]{\ell}\right)}^{2}}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{{\left(\frac{t \cdot \sqrt[3]{\sin k}}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3} \cdot \left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot {\left(\sqrt[3]{\sin k} \cdot \frac{t}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	79.0%
Cost	46348

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ t_2 := \frac{2}{{\left(\frac{t}{{\left(\sqrt[3]{\ell}\right)}^{2}} \cdot \sqrt[3]{\tan k \cdot \left(\sin k \cdot t_1\right)}\right)}^{3}}\\ t_3 := \frac{2}{t_1 \cdot \left(\frac{{t}^{3}}{\frac{\ell}{\sin k}} \cdot \frac{\tan k}{\ell}\right)}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \end{array} \]

Alternative 2
Accuracy	79.0%
Cost	46348

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ t_2 := \frac{2}{{\left(\frac{\sqrt[3]{\sin k \cdot \left(\tan k \cdot t_1\right)}}{\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t}}\right)}^{3}}\\ t_3 := \frac{2}{t_1 \cdot \left(\frac{{t}^{3}}{\frac{\ell}{\sin k}} \cdot \frac{\tan k}{\ell}\right)}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \end{array} \]

Alternative 3
Accuracy	81.6%
Cost	46345

\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-40} \lor \neg \left(t \leq 5 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot {\left(\sqrt[3]{\sin k} \cdot \frac{t}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \end{array} \]

Alternative 4
Accuracy	79.0%
Cost	39940

\[\begin{array}{l} t_1 := \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\frac{{t}^{3}}{\frac{\ell}{\sin k}} \cdot \frac{\tan k}{\ell}\right)}\\ t_2 := t \cdot \sqrt[3]{\frac{\sin k \cdot 0.5}{\ell}}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{0.5}{{t_2}^{2}} \cdot \frac{\ell}{t_2}}{\tan k}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \end{array} \]

Alternative 5
Accuracy	79.0%
Cost	39940

\[\begin{array}{l} t_1 := \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\frac{{t}^{3}}{\frac{\ell}{\sin k}} \cdot \frac{\tan k}{\ell}\right)}\\ t_2 := t \cdot \sqrt[3]{\frac{\sin k \cdot 0.5}{\ell}}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{\ell}{{t_2}^{2}} \cdot \frac{0.5}{t_2}}{\tan k}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \end{array} \]

Alternative 6
Accuracy	80.6%
Cost	39816

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ t_2 := \frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ t_3 := \frac{2}{t_1 \cdot \left(\frac{{t}^{3}}{\frac{\ell}{\sin k}} \cdot \frac{\tan k}{\ell}\right)}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{2}{\left(t_1 \cdot \left(\sin k \cdot \tan k\right)\right) \cdot {\left(\frac{t}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3}}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	78.1%
Cost	27344

\[\begin{array}{l} t_1 := \frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\frac{{t}^{3}}{\frac{\ell}{\sin k}} \cdot \frac{\tan k}{\ell}\right)}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{\ell \cdot 0.5}{{\left(t \cdot \sqrt[3]{\frac{\sin k \cdot 0.5}{\ell}}\right)}^{3}}}{\tan k}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-65}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \end{array} \]

Alternative 8
Accuracy	75.0%
Cost	20872

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{2}{\left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right) \cdot \left(\sin k \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right)}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+32}:\\ \;\;\;\;\frac{\ell \cdot 0.5}{\left(\tan k \cdot \left({t}^{3} \cdot 0.5\right)\right) \cdot \frac{k}{\ell}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	73.6%
Cost	20868

\[\begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \left(\sin k \cdot \left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right)\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \end{array} \]

Alternative 10
Accuracy	72.9%
Cost	20489

\[\begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+22} \lor \neg \left(t \leq 5.2 \cdot 10^{-65}\right):\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\left(\ell \cdot \ell\right) \cdot \frac{2 \cdot \frac{\cos k}{k \cdot k}}{t \cdot {\sin k}^{2}}\\ \end{array} \]

Alternative 11
Accuracy	74.8%
Cost	20489

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+30} \lor \neg \left(t \leq 1.25 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{\frac{\ell}{t}}{k \cdot \left(t \cdot \sqrt[3]{k}\right)} \cdot \frac{\ell}{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{k}{\frac{\cos k}{k}} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \end{array} \]

Alternative 12
Accuracy	68.6%
Cost	20488

\[\begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+23}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\ell}}{t \cdot \sqrt[3]{k}}\right)}^{3} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot \frac{\cos k}{\frac{\left(k \cdot k\right) \cdot \left(t \cdot {\sin k}^{2}\right)}{\ell \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 13
Accuracy	68.6%
Cost	20488

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\ell}}{t \cdot \sqrt[3]{k}}\right)}^{3} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-64}:\\ \;\;\;\;\left(\ell \cdot \ell\right) \cdot \frac{2 \cdot \frac{\cos k}{k \cdot k}}{t \cdot {\sin k}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 14
Accuracy	59.2%
Cost	20368

\[\begin{array}{l} t_1 := {\left(\frac{\sqrt[3]{\ell \cdot \frac{\ell}{k}}}{t \cdot \sqrt[3]{k}}\right)}^{3}\\ t_2 := \tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ \mathbf{if}\;k \leq -5.2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-268}:\\ \;\;\;\;\frac{2}{t_2 \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-205}:\\ \;\;\;\;\frac{\ell \cdot \ell}{{\left(t \cdot {\left(\sqrt[3]{k}\right)}^{2}\right)}^{3}}\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+152}:\\ \;\;\;\;\frac{2}{t_2 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot \frac{t \cdot t}{\ell}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	63.0%
Cost	20360

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-126}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(\frac{\cos k}{{k}^{3}} \cdot \frac{\ell \cdot \ell}{t \cdot \sin k}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 16
Accuracy	63.1%
Cost	20360

\[\begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 10^{-99}:\\ \;\;\;\;2 \cdot \left(\frac{\cos k}{{k}^{3}} \cdot \frac{\frac{\ell \cdot \ell}{t}}{\sin k}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 17
Accuracy	57.8%
Cost	20304

\[\begin{array}{l} t_1 := \tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ t_2 := \sqrt{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-162}:\\ \;\;\;\;\frac{t_2}{k \cdot \left(t \cdot \frac{k}{\ell}\right)} \cdot \frac{t_2}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot \frac{t \cdot t}{\ell}\right)\right)}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+215}:\\ \;\;\;\;\frac{\ell \cdot \ell}{{\left(t \cdot {\left(\sqrt[3]{k}\right)}^{2}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 18
Accuracy	60.2%
Cost	20104

\[\begin{array}{l} t_1 := \tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-155}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\ell}}{t \cdot \sqrt[3]{k}}\right)}^{3} \cdot \frac{\ell}{k}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot \left(\left(t \cdot t\right) \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 19
Accuracy	59.5%
Cost	14860

\[\begin{array}{l} t_1 := \frac{2}{\left(\tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\right) \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot \left(\left(t \cdot t\right) \cdot \frac{1}{\ell}\right)\right)\right)}\\ t_2 := \sqrt{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{t_2}{k \cdot \left(t \cdot \frac{k}{\ell}\right)} \cdot \frac{t_2}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 20
Accuracy	59.5%
Cost	14860

\[\begin{array}{l} t_1 := \tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ t_2 := \sqrt{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-162}:\\ \;\;\;\;\frac{t_2}{k \cdot \left(t \cdot \frac{k}{\ell}\right)} \cdot \frac{t_2}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot \left(\left(t \cdot t\right) \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 21
Accuracy	59.1%
Cost	14732

\[\begin{array}{l} t_1 := \tan k \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)\\ \mathbf{if}\;\ell \leq 6.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(\left(t \cdot t\right) \cdot \left(t \cdot \frac{1}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{-106}:\\ \;\;\;\;\frac{\ell}{{\left(t \cdot \frac{k}{\sqrt{\ell}}\right)}^{2}} \cdot \frac{1}{t}\\ \mathbf{elif}\;\ell \leq 9.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot \frac{t \cdot t}{\ell}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{{\left(\frac{t \cdot k}{\sqrt{\ell}}\right)}^{2}}\\ \end{array} \]

Alternative 22
Accuracy	57.2%
Cost	14284

\[\begin{array}{l} t_1 := \sqrt{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{\left(t \cdot t\right) \cdot \left(t \cdot k\right)}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-103}:\\ \;\;\;\;\frac{2}{\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \frac{k \cdot k}{\frac{\ell \cdot \ell}{{t}^{3}}}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{t_1}{k \cdot \left(t \cdot \frac{k}{\ell}\right)} \cdot \frac{t_1}{t}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 23
Accuracy	58.4%
Cost	14020

\[\begin{array}{l} t_1 := \frac{k}{\sqrt{\ell}}\\ \mathbf{if}\;\ell \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{\ell}{t} \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t}}{t_1} \cdot \frac{\frac{\ell}{t}}{t \cdot t_1}\\ \end{array} \]

Alternative 24
Accuracy	58.8%
Cost	13836

\[\begin{array}{l} \mathbf{if}\;\ell \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{\ell}{t} \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{-103}:\\ \;\;\;\;\frac{\ell}{{\left(t \cdot \frac{k}{\sqrt{\ell}}\right)}^{2}} \cdot \frac{1}{t}\\ \mathbf{elif}\;\ell \leq 1.85 \cdot 10^{-72}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{{\left(t \cdot \sqrt[3]{k}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{{\left(\frac{t \cdot k}{\sqrt{\ell}}\right)}^{2}}\\ \end{array} \]

Alternative 25
Accuracy	56.0%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;t \leq 3.9 \cdot 10^{-156}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{{\left(t \cdot \sqrt[3]{k}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 26
Accuracy	56.2%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;t \leq 2.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{\ell}{\frac{k}{\ell} \cdot {\left(t \cdot \sqrt[3]{k}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 27
Accuracy	56.6%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;\ell \leq 1.85 \cdot 10^{-72}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{{\left(t \cdot \sqrt[3]{k}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{{\left(t \cdot \frac{k}{\sqrt{\ell}}\right)}^{2}}\\ \end{array} \]

Alternative 28
Accuracy	57.1%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;\ell \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{{\left(t \cdot \sqrt[3]{k}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{{\left(\frac{t \cdot k}{\sqrt{\ell}}\right)}^{2}}\\ \end{array} \]

Alternative 29
Accuracy	57.1%
Cost	13512

\[\begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{\left(t \cdot t\right) \cdot \left(t \cdot k\right)}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{\frac{2}{t}}{\left(t \cdot t\right) \cdot \left(\tan k \cdot \frac{\frac{k}{\ell}}{\ell \cdot 0.5}\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 30
Accuracy	54.9%
Cost	7752

\[\begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{\left(t \cdot t\right) \cdot \left(t \cdot k\right)}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-99}:\\ \;\;\;\;\frac{\frac{2}{t}}{\left(t \cdot t\right) \cdot \left(\tan k \cdot \frac{\frac{k}{\ell}}{\ell \cdot 0.5}\right)}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\frac{1}{t} \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\right)\\ \end{array} \]

Alternative 31
Accuracy	55.1%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{\left(t \cdot t\right) \cdot \left(t \cdot k\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{1}{t \cdot t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\frac{1}{t} \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\right)\\ \end{array} \]

Alternative 32
Accuracy	55.3%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{\left(t \cdot t\right) \cdot \left(t \cdot k\right)}\\ \mathbf{elif}\;t \leq 1000000000:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{t} \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \end{array} \]

Alternative 33
Accuracy	53.1%
Cost	832

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

Alternative 34
Accuracy	53.8%
Cost	832

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

Reproduce

herbie shell --seed 2023139 
(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))))