Average Error: 32.8 → 4.4
Time: 1.0min
Precision: binary64
Cost: 65736
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
\[\begin{array}{l} t_1 := {\left(\left(\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\frac{1}{\sin k}}\right) \cdot \sqrt[3]{\frac{1}{\tan k}}\right) \cdot \frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)}^{3}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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) (cbrt (/ 1.0 (sin k)))) (cbrt (/ 1.0 (tan k))))
           (/ (/ (* (cbrt l) (cbrt 2.0)) t) (cbrt (+ 2.0 (pow (/ k t) 2.0)))))
          3.0)))
   (if (<= t -2e-16)
     t_1
     (if (<= t 1.0)
       (* (* 2.0 (/ (/ l k) (* t k))) (/ (/ l (sin k)) (tan k)))
       t_1))))
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) * cbrt((1.0 / sin(k)))) * cbrt((1.0 / tan(k)))) * (((cbrt(l) * cbrt(2.0)) / t) / cbrt((2.0 + pow((k / t), 2.0))))), 3.0);
	double tmp;
	if (t <= -2e-16) {
		tmp = t_1;
	} else if (t <= 1.0) {
		tmp = (2.0 * ((l / k) / (t * k))) * ((l / sin(k)) / tan(k));
	} else {
		tmp = t_1;
	}
	return tmp;
}
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) * Math.cbrt((1.0 / Math.sin(k)))) * Math.cbrt((1.0 / Math.tan(k)))) * (((Math.cbrt(l) * Math.cbrt(2.0)) / t) / Math.cbrt((2.0 + Math.pow((k / t), 2.0))))), 3.0);
	double tmp;
	if (t <= -2e-16) {
		tmp = t_1;
	} else if (t <= 1.0) {
		tmp = (2.0 * ((l / k) / (t * k))) * ((l / Math.sin(k)) / Math.tan(k));
	} else {
		tmp = t_1;
	}
	return tmp;
}
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(Float64(Float64(cbrt(l) * cbrt(Float64(1.0 / sin(k)))) * cbrt(Float64(1.0 / tan(k)))) * Float64(Float64(Float64(cbrt(l) * cbrt(2.0)) / t) / cbrt(Float64(2.0 + (Float64(k / t) ^ 2.0))))) ^ 3.0
	tmp = 0.0
	if (t <= -2e-16)
		tmp = t_1;
	elseif (t <= 1.0)
		tmp = Float64(Float64(2.0 * Float64(Float64(l / k) / Float64(t * k))) * Float64(Float64(l / sin(k)) / tan(k)));
	else
		tmp = t_1;
	end
	return tmp
end
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[(N[(N[(N[Power[l, 1/3], $MachinePrecision] * N[Power[N[(1.0 / N[Sin[k], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision] * N[Power[N[(1.0 / N[Tan[k], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Power[l, 1/3], $MachinePrecision] * N[Power[2.0, 1/3], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] / N[Power[N[(2.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]}, If[LessEqual[t, -2e-16], t$95$1, If[LessEqual[t, 1.0], N[(N[(2.0 * N[(N[(l / k), $MachinePrecision] / N[(t * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$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)}
\begin{array}{l}
t_1 := {\left(\left(\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\frac{1}{\sin k}}\right) \cdot \sqrt[3]{\frac{1}{\tan k}}\right) \cdot \frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)}^{3}\\
\mathbf{if}\;t \leq -2 \cdot 10^{-16}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t \leq 1:\\
\;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes
  2. if t < -2e-16 or 1 < t

    1. Initial program 23.0

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
    2. Simplified21.2

      \[\leadsto \color{blue}{\frac{\frac{2}{\frac{{t}^{3}}{\ell}}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\frac{\ell}{\sin k}}{\tan k}} \]
      Proof
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (Rewrite<= associate-/r*_binary64 (/.f64 l (*.f64 (sin.f64 k) (tan.f64 k))))): 10 points increase in error, 5 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) l) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k))))): 16 points increase in error, 13 points decrease in error
      (/.f64 (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 (/.f64 (pow.f64 t 3) l) l))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 4 points increase in error, 2 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-/r*_binary64 (/.f64 (pow.f64 t 3) (*.f64 l l)))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 36 points increase in error, 2 points decrease in error
      (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))): 1 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (*.f64 (sin.f64 k) (tan.f64 k))))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 1 points increase in error, 4 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 2 points increase in error, 25 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 1 points increase in error, 2 points decrease in error
    3. Applied egg-rr19.2

      \[\leadsto \color{blue}{\left(\frac{{\left(\frac{\sqrt[3]{2}}{\frac{t}{\sqrt[3]{\ell}}}\right)}^{2}}{\sqrt{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \frac{\frac{\sqrt[3]{2}}{\frac{t}{\sqrt[3]{\ell}}}}{\sqrt{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)} \cdot \frac{\frac{\ell}{\sin k}}{\tan k} \]
    4. Applied egg-rr13.9

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\frac{\ell}{\sin k}}{\tan k}} \cdot \frac{\frac{\sqrt[3]{2} \cdot \sqrt[3]{\ell}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)}^{3}} \]
    5. Applied egg-rr6.4

      \[\leadsto {\left(\color{blue}{\left(\sqrt[3]{\frac{\ell}{\sin k}} \cdot \sqrt[3]{\frac{1}{\tan k}}\right)} \cdot \frac{\frac{\sqrt[3]{2} \cdot \sqrt[3]{\ell}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)}^{3} \]
    6. Applied egg-rr2.4

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

    if -2e-16 < t < 1

    1. Initial program 50.3

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
    2. Simplified45.9

      \[\leadsto \color{blue}{\frac{\frac{2}{\frac{{t}^{3}}{\ell}}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\frac{\ell}{\sin k}}{\tan k}} \]
      Proof
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (Rewrite<= associate-/r*_binary64 (/.f64 l (*.f64 (sin.f64 k) (tan.f64 k))))): 10 points increase in error, 5 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) l) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k))))): 16 points increase in error, 13 points decrease in error
      (/.f64 (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 (/.f64 (pow.f64 t 3) l) l))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 4 points increase in error, 2 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-/r*_binary64 (/.f64 (pow.f64 t 3) (*.f64 l l)))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 36 points increase in error, 2 points decrease in error
      (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))): 1 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (*.f64 (sin.f64 k) (tan.f64 k))))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 1 points increase in error, 4 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 2 points increase in error, 25 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 1 points increase in error, 2 points decrease in error
    3. Taylor expanded in t around 0 21.6

      \[\leadsto \color{blue}{\left(2 \cdot \frac{\ell}{{k}^{2} \cdot t}\right)} \cdot \frac{\frac{\ell}{\sin k}}{\tan k} \]
    4. Simplified8.1

      \[\leadsto \color{blue}{\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right)} \cdot \frac{\frac{\ell}{\sin k}}{\tan k} \]
      Proof
      (*.f64 2 (/.f64 (/.f64 l k) (*.f64 t k))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (/.f64 l k) k) t))): 48 points increase in error, 30 points decrease in error
      (*.f64 2 (/.f64 (Rewrite<= associate-/r*_binary64 (/.f64 l (*.f64 k k))) t)): 25 points increase in error, 26 points decrease in error
      (*.f64 2 (/.f64 (/.f64 l (Rewrite<= unpow2_binary64 (pow.f64 k 2))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= associate-/r*_binary64 (/.f64 l (*.f64 (pow.f64 k 2) t)))): 18 points increase in error, 29 points decrease in error
  3. Recombined 2 regimes into one program.
  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;{\left(\left(\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\frac{1}{\sin k}}\right) \cdot \sqrt[3]{\frac{1}{\tan k}}\right) \cdot \frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)}^{3}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\frac{1}{\sin k}}\right) \cdot \sqrt[3]{\frac{1}{\tan k}}\right) \cdot \frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)}^{3}\\ \end{array} \]

Alternatives

Alternative 1
Error6.2
Cost59472
\[\begin{array}{l} t_1 := \frac{\ell}{\sin k}\\ t_2 := t \cdot {\left(\sqrt[3]{k}\right)}^{2}\\ t_3 := \left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_2} \cdot \frac{\sqrt[3]{\ell}}{t_2}\right) \cdot \frac{\ell}{t_2}\\ t_4 := {\left(\frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \frac{\sqrt[3]{t_1}}{\sqrt[3]{\tan k}}\right)}^{3}\\ \mathbf{if}\;t \leq -1.5711259095703903 \cdot 10^{+178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{t_1}{\tan k}\\ \mathbf{elif}\;t \leq 8.964143212456244 \cdot 10^{+188}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 2
Error6.2
Cost59472
\[\begin{array}{l} t_1 := \frac{\ell}{\sin k}\\ t_2 := \sqrt[3]{t_1}\\ t_3 := \sqrt[3]{\tan k}\\ t_4 := \frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\\ t_5 := t \cdot {\left(\sqrt[3]{k}\right)}^{2}\\ t_6 := \left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_5} \cdot \frac{\sqrt[3]{\ell}}{t_5}\right) \cdot \frac{\ell}{t_5}\\ \mathbf{if}\;t \leq -1.5711259095703903 \cdot 10^{+178}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;{\left(t_4 \cdot \frac{t_2}{t_3}\right)}^{3}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{t_1}{\tan k}\\ \mathbf{elif}\;t \leq 8.964143212456244 \cdot 10^{+188}:\\ \;\;\;\;{\left(t_4 \cdot \left(t_2 \cdot \frac{1}{t_3}\right)\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]
Alternative 3
Error6.1
Cost59472
\[\begin{array}{l} t_1 := t \cdot {\left(\sqrt[3]{k}\right)}^{2}\\ t_2 := \left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_1} \cdot \frac{\sqrt[3]{\ell}}{t_1}\right) \cdot \frac{\ell}{t_1}\\ t_3 := \frac{\ell}{\sin k}\\ t_4 := {\left(\frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \left(\sqrt[3]{\frac{1}{\tan k}} \cdot \sqrt[3]{t_3}\right)\right)}^{3}\\ \mathbf{if}\;t \leq -1.0009745919733462 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{t_3}{\tan k}\\ \mathbf{elif}\;t \leq 8.964143212456244 \cdot 10^{+188}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error6.1
Cost59472
\[\begin{array}{l} t_1 := \sqrt[3]{\frac{1}{\tan k}}\\ t_2 := \frac{\ell}{\sin k}\\ t_3 := \frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\\ t_4 := t \cdot {\left(\sqrt[3]{k}\right)}^{2}\\ t_5 := \left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_4} \cdot \frac{\sqrt[3]{\ell}}{t_4}\right) \cdot \frac{\ell}{t_4}\\ \mathbf{if}\;t \leq -1.5711259095703903 \cdot 10^{+178}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;{\left(t_3 \cdot \left(t_1 \cdot \frac{1}{\sqrt[3]{\frac{\sin k}{\ell}}}\right)\right)}^{3}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{t_2}{\tan k}\\ \mathbf{elif}\;t \leq 8.964143212456244 \cdot 10^{+188}:\\ \;\;\;\;{\left(t_3 \cdot \left(t_1 \cdot \sqrt[3]{t_2}\right)\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]
Alternative 5
Error7.0
Cost59080
\[\begin{array}{l} t_1 := \frac{\ell}{\sin k}\\ t_2 := {\left(\frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \frac{\sqrt[3]{t_1}}{\sqrt[3]{\tan k}}\right)}^{3}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{t_1}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error11.3
Cost52940
\[\begin{array}{l} t_1 := \left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ t_2 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ \mathbf{if}\;k \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{{t_2}^{2}}{k} \cdot \frac{t_2}{k}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+51}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \frac{1}{\sqrt[3]{\tan k \cdot \frac{\sin k}{\ell}}}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error7.0
Cost52936
\[\begin{array}{l} t_1 := \frac{\ell}{\sin k}\\ t_2 := {\left(\left(\sqrt[3]{\frac{1}{\tan k}} \cdot \sqrt[3]{t_1}\right) \cdot \left(\sqrt[3]{\ell \cdot 2} \cdot \frac{\frac{1}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}}\right)\right)}^{3}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{t_1}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error11.5
Cost52812
\[\begin{array}{l} t_1 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ t_2 := \frac{\frac{\ell}{\sin k}}{\tan k}\\ t_3 := \left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot t_2\\ \mathbf{if}\;k \leq -1:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{{t_1}^{2}}{k} \cdot \frac{t_1}{k}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+51}:\\ \;\;\;\;{\left(\sqrt[3]{t_2} \cdot \left(\frac{\sqrt[3]{\ell}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \frac{\sqrt[3]{2}}{t}\right)\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 9
Error11.4
Cost52812
\[\begin{array}{l} t_1 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ t_2 := \frac{\frac{\ell}{\sin k}}{\tan k}\\ t_3 := \left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot t_2\\ \mathbf{if}\;k \leq -1:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{{t_1}^{2}}{k} \cdot \frac{t_1}{k}\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+51}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}}{\sqrt[3]{2 + {\left(\frac{k}{t}\right)}^{2}}} \cdot \sqrt[3]{t_2}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 10
Error10.7
Cost40396
\[\begin{array}{l} t_1 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ t_2 := {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;t \leq -5.369051671770017 \cdot 10^{+128}:\\ \;\;\;\;\frac{{t_1}^{2}}{k} \cdot \frac{t_1}{k}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\frac{{\left(\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}\right)}^{3}}{\left(2 + t_2\right) \cdot \left(\tan k \cdot \frac{\sin k}{\ell}\right)}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(\sin k \cdot {\left({t}^{0.75} \cdot \left({t}^{0.75} \cdot \frac{1}{\ell}\right)\right)}^{2}\right)\right) \cdot \left(1 + \left(1 + t_2\right)\right)}\\ \end{array} \]
Alternative 11
Error9.9
Cost39880
\[\begin{array}{l} t_1 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ t_2 := {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;t \leq -5.369051671770017 \cdot 10^{+128}:\\ \;\;\;\;\frac{{t_1}^{2}}{k} \cdot \frac{t_1}{k}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\frac{{\left(\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{2}}{t}\right)}^{3}}{\left(2 + t_2\right) \cdot \left(\tan k \cdot \frac{\sin k}{\ell}\right)}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{elif}\;t \leq 8.964143212456244 \cdot 10^{+188}:\\ \;\;\;\;\frac{2}{\left(1 + \left(1 + t_2\right)\right) \cdot \left(\tan k \cdot \left(\sin k \cdot {\left(\frac{{t}^{1.5}}{\ell}\right)}^{2}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{{\left(\sqrt[3]{k} \cdot \sqrt{t}\right)}^{3}}\right)}^{2}\\ \end{array} \]
Alternative 12
Error11.2
Cost33676
\[\begin{array}{l} t_1 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{{t_1}^{2}}{k} \cdot \frac{t_1}{k}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{elif}\;t \leq 8.964143212456244 \cdot 10^{+188}:\\ \;\;\;\;\frac{2}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\tan k \cdot \left(\sin k \cdot {\left(\frac{{t}^{1.5}}{\ell}\right)}^{2}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{{\left(\sqrt[3]{k} \cdot \sqrt{t}\right)}^{3}}\right)}^{2}\\ \end{array} \]
Alternative 13
Error11.3
Cost33156
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{\sin k}}{\tan k}\\ t_2 := \frac{\sqrt[3]{\ell}}{\frac{t}{\sqrt[3]{\ell}}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{{t_2}^{2}}{k} \cdot \frac{t_2}{k}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot t_1\\ \mathbf{elif}\;t \leq 1.669633423954766 \cdot 10^{+122}:\\ \;\;\;\;t_1 \cdot \frac{\frac{2}{t \cdot \left(t \cdot \frac{t}{\ell}\right)}}{2 + {\left(\frac{k}{t}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{{\left(\sqrt[3]{k} \cdot \sqrt{t}\right)}^{3}}\right)}^{2}\\ \end{array} \]
Alternative 14
Error11.4
Cost26444
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\frac{\ell}{k}}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot t_1\\ \mathbf{elif}\;t \leq 1.669633423954766 \cdot 10^{+122}:\\ \;\;\;\;t_1 \cdot \frac{\frac{2}{t \cdot \left(t \cdot \frac{t}{\ell}\right)}}{2 + {\left(\frac{k}{t}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{{\left(\sqrt[3]{k} \cdot \sqrt{t}\right)}^{3}}\right)}^{2}\\ \end{array} \]
Alternative 15
Error11.9
Cost21004
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\frac{\ell}{k}}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot t_1\\ \mathbf{elif}\;t \leq 1.669633423954766 \cdot 10^{+122}:\\ \;\;\;\;t_1 \cdot \frac{\frac{\ell}{t} \cdot \frac{\frac{2}{t}}{t}}{2 + {\left(\frac{k}{t}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt{\ell \cdot \frac{\ell}{t}}}{t}}{k}\right)}^{2}\\ \end{array} \]
Alternative 16
Error11.9
Cost21004
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\frac{\ell}{k}}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot t_1\\ \mathbf{elif}\;t \leq 1.669633423954766 \cdot 10^{+122}:\\ \;\;\;\;t_1 \cdot \frac{\frac{2}{t \cdot \left(t \cdot \frac{t}{\ell}\right)}}{2 + {\left(\frac{k}{t}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt{\ell \cdot \frac{\ell}{t}}}{t}}{k}\right)}^{2}\\ \end{array} \]
Alternative 17
Error11.8
Cost19912
\[\begin{array}{l} t_1 := \left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;k \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 10^{-10}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\frac{\ell}{k}}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 18
Error15.0
Cost14288
\[\begin{array}{l} t_1 := \left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;k \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{1}{t} \cdot \frac{\ell}{t \cdot \frac{t}{\ell}}}{k \cdot k}\\ \mathbf{elif}\;k \leq -2.2 \cdot 10^{-265}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt{\ell \cdot \frac{\ell}{t}}}{t}}{k}\right)}^{2}\\ \mathbf{elif}\;k \leq 10^{-10}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error18.3
Cost14024
\[\begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{\left(\ell \cdot 2\right) \cdot \frac{\ell}{\sin k \cdot \tan k}}{k \cdot \left(t \cdot k\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt{\ell \cdot \frac{\ell}{t}}}{t}}{k}\right)}^{2}\\ \end{array} \]
Alternative 20
Error16.0
Cost14024
\[\begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{\frac{\ell}{k \cdot \left(t \cdot k\right)} \cdot \left(2 \cdot \frac{\ell}{\sin k}\right)}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt{\ell \cdot \frac{\ell}{t}}}{t}}{k}\right)}^{2}\\ \end{array} \]
Alternative 21
Error23.4
Cost13704
\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;\left(2 \cdot \frac{\ell}{t \cdot {k}^{2}}\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\sqrt{\ell \cdot \frac{\ell}{t}}}{t}}{k}\right)}^{2}\\ \end{array} \]
Alternative 22
Error23.8
Cost13512
\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;\left(2 \cdot \frac{\ell}{t \cdot {k}^{2}}\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\ell}{k}}{{t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 23
Error23.2
Cost13512
\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;\left(2 \cdot \frac{\ell}{t \cdot {k}^{2}}\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\ell \cdot \frac{{t}^{-1.5}}{k}\right)}^{2}\\ \end{array} \]
Alternative 24
Error23.3
Cost13512
\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;\left(2 \cdot \frac{\ell}{t \cdot {k}^{2}}\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 25
Error24.3
Cost7560
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;\left(2 \cdot \frac{\ell}{t \cdot {k}^{2}}\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 26
Error24.1
Cost7304
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{{k}^{4}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 27
Error28.1
Cost1092
\[\begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{1}{t} \cdot \frac{\ell}{t \cdot \frac{t}{\ell}}}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \end{array} \]
Alternative 28
Error28.8
Cost832
\[\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t} \]

Error

Reproduce

herbie shell --seed 2022302 
(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))))