Average Error: 31.8 → 11.2
Time: 4.4m
Precision: 64
Internal Precision: 576
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 8.303061663433523 \cdot 10^{-218}:\\ \;\;\;\;\left(\left(\frac{\sqrt[3]{\frac{2}{t}}}{\frac{\sqrt[3]{\sin k}}{\sqrt[3]{\frac{\ell}{t}}}} \cdot \frac{\cos k}{\left(1 + 1\right) + \frac{k}{t} \cdot \frac{k}{t}}\right) \cdot \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sqrt[3]{\sin k} \cdot \sqrt[3]{\sin k}}{\sqrt[3]{\frac{\ell}{t}} \cdot \sqrt[3]{\frac{\ell}{t}}}}\right) \cdot \frac{\frac{\ell}{t}}{\sin k}\\ \mathbf{elif}\;t \le 1.6274586930172435 \cdot 10^{-40}:\\ \;\;\;\;\left(t \cdot \left(\frac{\cos k}{\left(1 + \left(1 - 1\right)\right) \cdot \left(k \cdot \frac{k}{t}\right) + t \cdot \left({1}^{3} + {1}^{3}\right)} \cdot \frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}}}\right)\right) \cdot \frac{\frac{\ell}{t}}{\sin k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\cos k}{\left(1 + 1\right) + \frac{k}{t} \cdot \frac{k}{t}} \cdot \frac{\sqrt{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}}\right)\\ \end{array}\]

Error

Bits error versus t

Bits error versus l

Bits error versus k

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if t < 8.303061663433523e-218

    1. Initial program 34.7

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

    2. Initial simplification27.2

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

    4. Applied *-un-lft-identity27.2

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

    5. Applied tan-quot27.2

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

    6. Applied associate-*r/27.2

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

    7. Applied associate-/r/27.2

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

    8. Applied times-frac27.2

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

    9. Simplified19.4

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

    11. Applied *-un-lft-identity19.4

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

    12. Applied times-frac17.9

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

    13. Applied associate-*l*16.2

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

    14. Simplified16.1

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

    16. Applied add-cube-cbrt16.3

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

    17. Applied add-cube-cbrt16.4

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

    18. Applied times-frac16.4

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

    19. Applied add-cube-cbrt16.5

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

    20. Applied times-frac16.5

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

    21. Applied associate-*l*14.6

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

    if 8.303061663433523e-218 < t < 1.6274586930172435e-40

    1. Initial program 49.6

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

    2. Initial simplification33.4

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

    4. Applied *-un-lft-identity33.4

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

    5. Applied tan-quot33.4

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

    6. Applied associate-*r/33.4

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

    7. Applied associate-/r/33.4

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

    8. Applied times-frac33.4

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

    9. Simplified30.7

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

    11. Applied *-un-lft-identity30.7

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

    12. Applied times-frac30.6

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

    13. Applied associate-*l*25.2

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

    14. Simplified25.2

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

    16. Applied flip3-+25.2

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

    17. Applied associate-*r/25.1

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

    18. Applied frac-add25.1

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

    19. Applied associate-/r/24.8

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

    20. Applied associate-*r*21.3

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

    21. Simplified21.3

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

    if 1.6274586930172435e-40 < t

    1. Initial program 21.7

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

    2. Initial simplification17.5

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

    4. Applied *-un-lft-identity17.5

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

    5. Applied tan-quot17.5

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

    6. Applied associate-*r/17.5

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

    7. Applied associate-/r/17.5

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

    8. Applied times-frac17.5

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

    9. Simplified5.9

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

    11. Applied add-sqr-sqrt6.0

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

    12. Applied times-frac3.3

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

    13. Applied associate-*l*2.6

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

  4. Final simplification11.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 8.303061663433523 \cdot 10^{-218}:\\ \;\;\;\;\left(\left(\frac{\sqrt[3]{\frac{2}{t}}}{\frac{\sqrt[3]{\sin k}}{\sqrt[3]{\frac{\ell}{t}}}} \cdot \frac{\cos k}{\left(1 + 1\right) + \frac{k}{t} \cdot \frac{k}{t}}\right) \cdot \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sqrt[3]{\sin k} \cdot \sqrt[3]{\sin k}}{\sqrt[3]{\frac{\ell}{t}} \cdot \sqrt[3]{\frac{\ell}{t}}}}\right) \cdot \frac{\frac{\ell}{t}}{\sin k}\\ \mathbf{elif}\;t \le 1.6274586930172435 \cdot 10^{-40}:\\ \;\;\;\;\left(t \cdot \left(\frac{\cos k}{\left(1 + \left(1 - 1\right)\right) \cdot \left(k \cdot \frac{k}{t}\right) + t \cdot \left({1}^{3} + {1}^{3}\right)} \cdot \frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}}}\right)\right) \cdot \frac{\frac{\ell}{t}}{\sin k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\cos k}{\left(1 + 1\right) + \frac{k}{t} \cdot \frac{k}{t}} \cdot \frac{\sqrt{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}}\right)\\ \end{array}\]

Runtime

Time bar (total: 4.4m)Debug logProfile

herbie shell --seed 2018220 
(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))))