Toniolo and Linder, Equation (10+)

Average Error: 32.1 → 17.5

Time: 26.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\ell \le -2.484239696005438759151946975339159010231 \cdot 10^{123}:\\ \;\;\;\;\frac{2}{\left(\left(\left(\left({\left(\sqrt[3]{t}\right)}^{3} \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \mathbf{elif}\;\ell \le -25217102.0555565096437931060791015625:\\ \;\;\;\;\frac{2}{2 \cdot \left({\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{{\left(\sqrt[3]{-1}\right)}^{9} \cdot \left({t}^{3} \cdot {\left(\sin k\right)}^{2}\right)}{\cos k \cdot {\ell}^{2}}\right) + {\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{{\left(\sqrt[3]{-1}\right)}^{9} \cdot \left({\left(\sin k\right)}^{2} \cdot \left({k}^{2} \cdot t\right)\right)}{\cos k \cdot {\ell}^{2}}}\\ \mathbf{elif}\;\ell \le 2.297049428607241564178931690682164825056 \cdot 10^{-139}:\\ \;\;\;\;\frac{2}{\left(\left(\left({\left(\sqrt[3]{t}\right)}^{3} \cdot \frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell}\right) \cdot \left(\frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell} \cdot \sin k\right)\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \mathbf{elif}\;\ell \le 5.548140519913770723669052513231581727514 \cdot 10^{121}:\\ \;\;\;\;\frac{2}{2 \cdot \frac{{t}^{3} \cdot {\left(\sin k\right)}^{2}}{\cos k \cdot {\ell}^{2}} - {\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{t \cdot \left({k}^{2} \cdot {\left(\sin k\right)}^{2}\right)}{\cos k \cdot {\ell}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\left(\left(\left({\left(\sqrt[3]{t}\right)}^{3} \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \end{array}\]

C

double f(double t, double l, double k) {
        double r118321 = 2.0;
        double r118322 = t;
        double r118323 = 3.0;
        double r118324 = pow(r118322, r118323);
        double r118325 = l;
        double r118326 = r118325 * r118325;
        double r118327 = r118324 / r118326;
        double r118328 = k;
        double r118329 = sin(r118328);
        double r118330 = r118327 * r118329;
        double r118331 = tan(r118328);
        double r118332 = r118330 * r118331;
        double r118333 = 1.0;
        double r118334 = r118328 / r118322;
        double r118335 = pow(r118334, r118321);
        double r118336 = r118333 + r118335;
        double r118337 = r118336 + r118333;
        double r118338 = r118332 * r118337;
        double r118339 = r118321 / r118338;
        return r118339;
}

↓

double f(double t, double l, double k) {
        double r118340 = l;
        double r118341 = -2.4842396960054388e+123;
        bool r118342 = r118340 <= r118341;
        double r118343 = 2.0;
        double r118344 = t;
        double r118345 = cbrt(r118344);
        double r118346 = 3.0;
        double r118347 = pow(r118345, r118346);
        double r118348 = 0.3333333333333333;
        double r118349 = r118348 * r118346;
        double r118350 = pow(r118344, r118349);
        double r118351 = r118350 / r118340;
        double r118352 = r118347 * r118351;
        double r118353 = r118352 * r118351;
        double r118354 = k;
        double r118355 = sin(r118354);
        double r118356 = r118353 * r118355;
        double r118357 = tan(r118354);
        double r118358 = r118356 * r118357;
        double r118359 = 1.0;
        double r118360 = r118354 / r118344;
        double r118361 = pow(r118360, r118343);
        double r118362 = r118359 + r118361;
        double r118363 = r118362 + r118359;
        double r118364 = r118358 * r118363;
        double r118365 = r118343 / r118364;
        double r118366 = -25217102.05555651;
        bool r118367 = r118340 <= r118366;
        double r118368 = 1.0;
        double r118369 = -1.0;
        double r118370 = pow(r118369, r118346);
        double r118371 = r118368 / r118370;
        double r118372 = pow(r118371, r118359);
        double r118373 = cbrt(r118369);
        double r118374 = 9.0;
        double r118375 = pow(r118373, r118374);
        double r118376 = 3.0;
        double r118377 = pow(r118344, r118376);
        double r118378 = 2.0;
        double r118379 = pow(r118355, r118378);
        double r118380 = r118377 * r118379;
        double r118381 = r118375 * r118380;
        double r118382 = cos(r118354);
        double r118383 = pow(r118340, r118378);
        double r118384 = r118382 * r118383;
        double r118385 = r118381 / r118384;
        double r118386 = r118372 * r118385;
        double r118387 = r118343 * r118386;
        double r118388 = pow(r118354, r118378);
        double r118389 = r118388 * r118344;
        double r118390 = r118379 * r118389;
        double r118391 = r118375 * r118390;
        double r118392 = r118391 / r118384;
        double r118393 = r118372 * r118392;
        double r118394 = r118387 + r118393;
        double r118395 = r118343 / r118394;
        double r118396 = 2.2970494286072416e-139;
        bool r118397 = r118340 <= r118396;
        double r118398 = r118347 / r118340;
        double r118399 = r118347 * r118398;
        double r118400 = r118351 * r118355;
        double r118401 = r118399 * r118400;
        double r118402 = r118401 * r118357;
        double r118403 = r118402 * r118363;
        double r118404 = r118343 / r118403;
        double r118405 = 5.548140519913771e+121;
        bool r118406 = r118340 <= r118405;
        double r118407 = r118380 / r118384;
        double r118408 = r118343 * r118407;
        double r118409 = r118388 * r118379;
        double r118410 = r118344 * r118409;
        double r118411 = r118410 / r118384;
        double r118412 = r118372 * r118411;
        double r118413 = r118408 - r118412;
        double r118414 = r118343 / r118413;
        double r118415 = r118406 ? r118414 : r118365;
        double r118416 = r118397 ? r118404 : r118415;
        double r118417 = r118367 ? r118395 : r118416;
        double r118418 = r118342 ? r118365 : r118417;
        return r118418;
}

Error

Bits error versus t

Bits error versus l

Bits error versus k

Derivation

1. Split input into 4 regimes

2. if l < -2.4842396960054388e+123 or 5.548140519913771e+121 < l

   1. Initial program 59.0

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

   3. Applied add-cube-cbrt 59.1

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

   4. Applied unpow-prod-down 59.1

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

   5. Applied times-frac 41.7

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

   7. Applied *-un-lft-identity 41.7

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

   8. Applied unpow-prod-down 41.7

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

   9. Applied times-frac 27.4

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

   10. Simplified 27.4

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

   12. Applied pow1/3 47.0

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

   13. Applied pow-pow 27.2

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

   15. Applied pow1/3 47.0

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

   16. Applied pow-pow 27.0

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

   if -2.4842396960054388e+123 < l < -25217102.05555651

   1. Initial program 31.9

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

   3. Applied add-cube-cbrt 32.2

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

   4. Applied unpow-prod-down 32.2

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

   5. Applied times-frac 28.4

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

   6. Taylor expanded around -inf 25.5

      \[\leadsto \frac{2}{\color{blue}{2 \cdot \left({\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{{\left(\sqrt[3]{-1}\right)}^{9} \cdot \left({t}^{3} \cdot {\left(\sin k\right)}^{2}\right)}{\cos k \cdot {\ell}^{2}}\right) + {\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{{\left(\sqrt[3]{-1}\right)}^{9} \cdot \left({\left(\sin k\right)}^{2} \cdot \left({k}^{2} \cdot t\right)\right)}{\cos k \cdot {\ell}^{2}}}}\]

   if -25217102.05555651 < l < 2.2970494286072416e-139

   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. Using strategy rm

   3. Applied add-cube-cbrt 23.1

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

   4. Applied unpow-prod-down 23.1

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

   5. Applied times-frac 17.7

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

   7. Applied *-un-lft-identity 17.7

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

   8. Applied unpow-prod-down 17.7

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

   9. Applied times-frac 14.2

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

   10. Simplified 14.2

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

   12. Applied pow1/3 39.1

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

   13. Applied pow-pow 14.1

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

   15. Applied associate-*l* 11.5

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

   if 2.2970494286072416e-139 < l < 5.548140519913771e+121

   1. Initial program 26.5

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

   2. Taylor expanded around -inf 17.9

      \[\leadsto \frac{2}{\color{blue}{2 \cdot \frac{{t}^{3} \cdot {\left(\sin k\right)}^{2}}{\cos k \cdot {\ell}^{2}} - {\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{t \cdot \left({k}^{2} \cdot {\left(\sin k\right)}^{2}\right)}{\cos k \cdot {\ell}^{2}}}}\]
3. Recombined 4 regimes into one program.

4. Final simplification 17.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -2.484239696005438759151946975339159010231 \cdot 10^{123}:\\ \;\;\;\;\frac{2}{\left(\left(\left(\left({\left(\sqrt[3]{t}\right)}^{3} \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \mathbf{elif}\;\ell \le -25217102.0555565096437931060791015625:\\ \;\;\;\;\frac{2}{2 \cdot \left({\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{{\left(\sqrt[3]{-1}\right)}^{9} \cdot \left({t}^{3} \cdot {\left(\sin k\right)}^{2}\right)}{\cos k \cdot {\ell}^{2}}\right) + {\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{{\left(\sqrt[3]{-1}\right)}^{9} \cdot \left({\left(\sin k\right)}^{2} \cdot \left({k}^{2} \cdot t\right)\right)}{\cos k \cdot {\ell}^{2}}}\\ \mathbf{elif}\;\ell \le 2.297049428607241564178931690682164825056 \cdot 10^{-139}:\\ \;\;\;\;\frac{2}{\left(\left(\left({\left(\sqrt[3]{t}\right)}^{3} \cdot \frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell}\right) \cdot \left(\frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell} \cdot \sin k\right)\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \mathbf{elif}\;\ell \le 5.548140519913770723669052513231581727514 \cdot 10^{121}:\\ \;\;\;\;\frac{2}{2 \cdot \frac{{t}^{3} \cdot {\left(\sin k\right)}^{2}}{\cos k \cdot {\ell}^{2}} - {\left(\frac{1}{{-1}^{3}}\right)}^{1} \cdot \frac{t \cdot \left({k}^{2} \cdot {\left(\sin k\right)}^{2}\right)}{\cos k \cdot {\ell}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\left(\left(\left({\left(\sqrt[3]{t}\right)}^{3} \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  :precision binary64
  (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))))