Average Error: 32.3 → 12.6
Time: 25.3s
Precision: binary64
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -7.399879496769818 \cdot 10^{-126} \lor \neg \left(t \leq 0.1482355226089767\right):\\ \;\;\;\;\frac{2}{\frac{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\tan k \cdot \left(\left(\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}\right) \cdot \left(\left(\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}\right) \cdot \left(\frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell} \cdot \sin k\right)\right)\right)\right)}{\sqrt[3]{\ell} \cdot \frac{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}{\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{{\left(\sin k\right)}^{2}}{\ell \cdot \ell} \cdot \left(\frac{t \cdot \left(k \cdot k\right)}{\cos k} + 2 \cdot \frac{{t}^{3}}{\cos k}\right)}\\ \end{array}\]
\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}
\mathbf{if}\;t \leq -7.399879496769818 \cdot 10^{-126} \lor \neg \left(t \leq 0.1482355226089767\right):\\
\;\;\;\;\frac{2}{\frac{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\tan k \cdot \left(\left(\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}\right) \cdot \left(\left(\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}\right) \cdot \left(\frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell} \cdot \sin k\right)\right)\right)\right)}{\sqrt[3]{\ell} \cdot \frac{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}{\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{2}{\frac{{\left(\sin k\right)}^{2}}{\ell \cdot \ell} \cdot \left(\frac{t \cdot \left(k \cdot k\right)}{\cos k} + 2 \cdot \frac{{t}^{3}}{\cos k}\right)}\\

\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
 (if (or (<= t -7.399879496769818e-126) (not (<= t 0.1482355226089767)))
   (/
    2.0
    (/
     (*
      (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))
      (*
       (tan k)
       (*
        (* (cbrt (pow (cbrt t) 3.0)) (cbrt (pow (cbrt t) 3.0)))
        (*
         (* (cbrt (pow (cbrt t) 3.0)) (cbrt (pow (cbrt t) 3.0)))
         (* (/ (pow (cbrt t) 3.0) l) (sin k))))))
     (*
      (cbrt l)
      (/
       (* (cbrt l) (cbrt l))
       (* (cbrt (pow (cbrt t) 3.0)) (cbrt (pow (cbrt t) 3.0)))))))
   (/
    2.0
    (*
     (/ (pow (sin k) 2.0) (* l l))
     (+ (/ (* t (* k k)) (cos k)) (* 2.0 (/ (pow t 3.0) (cos k))))))))
double code(double t, double l, double k) {
	return (2.0 / ((double) (((double) (((double) ((((double) pow(t, 3.0)) / ((double) (l * l))) * ((double) sin(k)))) * ((double) tan(k)))) * ((double) (((double) (1.0 + ((double) pow((k / t), 2.0)))) + 1.0)))));
}
↓
double code(double t, double l, double k) {
	double tmp;
	if (((t <= -7.399879496769818e-126) || !(t <= 0.1482355226089767))) {
		tmp = (2.0 / (((double) (((double) (1.0 + ((double) (1.0 + ((double) pow((k / t), 2.0)))))) * ((double) (((double) tan(k)) * ((double) (((double) (((double) cbrt(((double) pow(((double) cbrt(t)), 3.0)))) * ((double) cbrt(((double) pow(((double) cbrt(t)), 3.0)))))) * ((double) (((double) (((double) cbrt(((double) pow(((double) cbrt(t)), 3.0)))) * ((double) cbrt(((double) pow(((double) cbrt(t)), 3.0)))))) * ((double) ((((double) pow(((double) cbrt(t)), 3.0)) / l) * ((double) sin(k)))))))))))) / ((double) (((double) cbrt(l)) * (((double) (((double) cbrt(l)) * ((double) cbrt(l)))) / ((double) (((double) cbrt(((double) pow(((double) cbrt(t)), 3.0)))) * ((double) cbrt(((double) pow(((double) cbrt(t)), 3.0)))))))))));
	} else {
		tmp = (2.0 / ((double) ((((double) pow(((double) sin(k)), 2.0)) / ((double) (l * l))) * ((double) ((((double) (t * ((double) (k * k)))) / ((double) cos(k))) + ((double) (2.0 * (((double) pow(t, 3.0)) / ((double) cos(k))))))))));
	}
	return tmp;
}

Error

Bits error versus t

Bits error versus l

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -7.3998794967698181e-126 or 0.14823552260897671 < t

    1. Initial program 23.6

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

    3. Applied add-cube-cbrt_binary6423.7

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

    4. Applied unpow-prod-down_binary6423.7

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

    5. Applied times-frac_binary6417.0

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

    6. Applied associate-*l*_binary6415.2

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

    8. Applied unpow-prod-down_binary6415.2

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

    9. Applied associate-/l*_binary6410.1

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

    11. Applied add-cube-cbrt_binary6410.1

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

    12. Applied add-cube-cbrt_binary6410.2

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

    13. Applied times-frac_binary6410.2

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

    14. Applied add-cube-cbrt_binary6410.2

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

    15. Applied times-frac_binary6410.2

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

    16. Applied associate-*l*_binary649.0

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

    17. Simplified9.0

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

    19. Applied associate-*l/_binary649.0

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

    20. Applied associate-*r/_binary649.0

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

    21. Applied frac-times_binary649.6

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

    22. Applied associate-*l/_binary647.9

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

    23. Applied associate-*l/_binary647.5

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

    24. Simplified7.5

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

    if -7.3998794967698181e-126 < t < 0.14823552260897671

    1. Initial program 54.4

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

    2. Taylor expanded around inf 36.8

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

    3. Simplified25.5

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

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.399879496769818 \cdot 10^{-126} \lor \neg \left(t \leq 0.1482355226089767\right):\\ \;\;\;\;\frac{2}{\frac{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \left(\tan k \cdot \left(\left(\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}\right) \cdot \left(\left(\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}\right) \cdot \left(\frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell} \cdot \sin k\right)\right)\right)\right)}{\sqrt[3]{\ell} \cdot \frac{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}{\sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{t}\right)}^{3}}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{{\left(\sin k\right)}^{2}}{\ell \cdot \ell} \cdot \left(\frac{t \cdot \left(k \cdot k\right)}{\cos k} + 2 \cdot \frac{{t}^{3}}{\cos k}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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))))