Error

Derivation

1. Split input into 5 regimes

2. if t < -3.17789192275232e+19

   1. Initial program 22.2

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

   3. Applied add-cube-cbrt22.3

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

   4. Applied times-frac18.5

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

   5. Applied simplify18.5

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

   6. Applied simplify9.9

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

   8. Applied tan-quot9.9

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

   9. Applied associate-*r/9.9

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

   10. Applied associate-*l/9.9

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

   11. Applied associate-/r/9.9

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

   12. Applied simplify7.4

       \[\leadsto \color{blue}{\frac{2}{\left(\left(\sin k \cdot \frac{t}{\ell}\right) \cdot \left(\frac{t}{\ell} \cdot t\right)\right) \cdot \left((\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_* \cdot \sin k\right)}} \cdot \cos k\]
   13. Using strategy rm

   14. Applied associate-/r*7.4

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

   if -3.17789192275232e+19 < t < 2.922224006859559e-05

   1. Initial program 47.3

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

   3. Applied add-cube-cbrt47.3

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

   4. Applied times-frac45.6

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

   5. Applied simplify45.6

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

   6. Applied simplify35.6

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

   8. Applied tan-quot35.6

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

   9. Applied associate-*r/35.6

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

   10. Applied associate-*l/35.6

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

   11. Applied associate-/r/35.6

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

   12. Applied simplify33.5

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

   13. Taylor expanded around inf 32.7

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

   14. Applied simplify4.1

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

   16. Applied associate-*r*2.6

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

   if 2.922224006859559e-05 < t < 1.3586215161890917e+152

   1. Initial program 23.9

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

   3. Applied add-cube-cbrt24.1

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

   4. Applied times-frac20.7

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

   5. Applied simplify20.6

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

   6. Applied simplify13.6

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

   8. Applied tan-quot13.6

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

   9. Applied associate-*r/13.6

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

   10. Applied associate-*l/13.6

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

   11. Applied associate-/r/13.6

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

   12. Applied simplify9.2

       \[\leadsto \color{blue}{\frac{2}{\left(\left(\sin k \cdot \frac{t}{\ell}\right) \cdot \left(\frac{t}{\ell} \cdot t\right)\right) \cdot \left((\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_* \cdot \sin k\right)}} \cdot \cos k\]
   13. Using strategy rm

   14. Applied associate-*l/9.2

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

   15. Applied associate-*r/9.4

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

   16. Applied associate-*l/7.2

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

   17. Applied associate-/r/7.1

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

   if 1.3586215161890917e+152 < t < 7.632480244337274e+258

   1. Initial program 22.2

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

   3. Applied add-cube-cbrt22.2

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

   4. Applied times-frac20.4

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

   5. Applied simplify20.4

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

   6. Applied simplify8.7

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

   8. Applied tan-quot8.7

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

   9. Applied frac-times20.0

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

   10. Applied associate-*l/19.9

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

   11. Applied frac-times19.9

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

   12. Applied associate-*l/19.9

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

   13. Applied simplify8.7

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

   if 7.632480244337274e+258 < t

   1. Initial program 20.2

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

   3. Applied add-cube-cbrt20.2

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

   4. Applied times-frac13.1

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

   5. Applied simplify13.1

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

   6. Applied simplify8.4

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

   8. Applied tan-quot8.4

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

   9. Applied associate-*r/8.4

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

   10. Applied associate-*l/8.4

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

   11. Applied associate-/r/8.4

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

   12. Applied simplify7.1

       \[\leadsto \color{blue}{\frac{2}{\left(\left(\sin k \cdot \frac{t}{\ell}\right) \cdot \left(\frac{t}{\ell} \cdot t\right)\right) \cdot \left((\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_* \cdot \sin k\right)}} \cdot \cos k\]
   13. Using strategy rm

   14. Applied associate-/r*7.1

       \[\leadsto \color{blue}{\frac{\frac{2}{\left(\sin k \cdot \frac{t}{\ell}\right) \cdot \left(\frac{t}{\ell} \cdot t\right)}}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_* \cdot \sin k}} \cdot \cos k\]
3. Recombined 5 regimes into one program.

Runtime

Time bar (total: 3.6m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))))