Toniolo and Linder, Equation (10+)

Average Error: 32.5 → 17.9

Time: 34.1s

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 -1.361561607826163938590433986165123404617 \cdot 10^{74}:\\ \;\;\;\;\frac{\frac{2}{\left(\left(\frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell}}\right) \cdot \frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell}\right) \cdot \sin k}}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \mathbf{elif}\;\ell \le -3.671469527357900756356766403755497030844 \cdot 10^{-125}:\\ \;\;\;\;\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{elif}\;\ell \le 1.147150844170901392374916916178894499446 \cdot 10^{-119}:\\ \;\;\;\;\frac{2}{\left(\left(\left(\frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell}}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}\\ \mathbf{elif}\;\ell \le 2.547304444790666703643914625432659827925 \cdot 10^{119}:\\ \;\;\;\;\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(\frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell}}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}\\ \end{array}\]

C

double f(double t, double l, double k) {
        double r135312 = 2.0;
        double r135313 = t;
        double r135314 = 3.0;
        double r135315 = pow(r135313, r135314);
        double r135316 = l;
        double r135317 = r135316 * r135316;
        double r135318 = r135315 / r135317;
        double r135319 = k;
        double r135320 = sin(r135319);
        double r135321 = r135318 * r135320;
        double r135322 = tan(r135319);
        double r135323 = r135321 * r135322;
        double r135324 = 1.0;
        double r135325 = r135319 / r135313;
        double r135326 = pow(r135325, r135312);
        double r135327 = r135324 + r135326;
        double r135328 = r135327 + r135324;
        double r135329 = r135323 * r135328;
        double r135330 = r135312 / r135329;
        return r135330;
}

↓

double f(double t, double l, double k) {
        double r135331 = l;
        double r135332 = -1.361561607826164e+74;
        bool r135333 = r135331 <= r135332;
        double r135334 = 2.0;
        double r135335 = t;
        double r135336 = cbrt(r135335);
        double r135337 = r135336 * r135336;
        double r135338 = 3.0;
        double r135339 = 2.0;
        double r135340 = r135338 / r135339;
        double r135341 = pow(r135337, r135340);
        double r135342 = cbrt(r135331);
        double r135343 = r135342 * r135342;
        double r135344 = r135341 / r135343;
        double r135345 = r135341 / r135342;
        double r135346 = r135344 * r135345;
        double r135347 = pow(r135336, r135338);
        double r135348 = r135347 / r135331;
        double r135349 = r135346 * r135348;
        double r135350 = k;
        double r135351 = sin(r135350);
        double r135352 = r135349 * r135351;
        double r135353 = r135334 / r135352;
        double r135354 = tan(r135350);
        double r135355 = 1.0;
        double r135356 = r135350 / r135335;
        double r135357 = pow(r135356, r135334);
        double r135358 = r135355 + r135357;
        double r135359 = r135358 + r135355;
        double r135360 = r135354 * r135359;
        double r135361 = r135353 / r135360;
        double r135362 = -3.671469527357901e-125;
        bool r135363 = r135331 <= r135362;
        double r135364 = 3.0;
        double r135365 = pow(r135335, r135364);
        double r135366 = pow(r135351, r135339);
        double r135367 = r135365 * r135366;
        double r135368 = cos(r135350);
        double r135369 = pow(r135331, r135339);
        double r135370 = r135368 * r135369;
        double r135371 = r135367 / r135370;
        double r135372 = r135334 * r135371;
        double r135373 = 1.0;
        double r135374 = -1.0;
        double r135375 = pow(r135374, r135338);
        double r135376 = r135373 / r135375;
        double r135377 = pow(r135376, r135355);
        double r135378 = pow(r135350, r135339);
        double r135379 = r135378 * r135366;
        double r135380 = r135335 * r135379;
        double r135381 = r135380 / r135370;
        double r135382 = r135377 * r135381;
        double r135383 = r135372 - r135382;
        double r135384 = r135334 / r135383;
        double r135385 = 1.1471508441709014e-119;
        bool r135386 = r135331 <= r135385;
        double r135387 = 0.3333333333333333;
        double r135388 = r135387 * r135338;
        double r135389 = pow(r135335, r135388);
        double r135390 = r135389 / r135331;
        double r135391 = r135346 * r135390;
        double r135392 = r135391 * r135351;
        double r135393 = r135392 * r135360;
        double r135394 = r135334 / r135393;
        double r135395 = 2.5473044447906667e+119;
        bool r135396 = r135331 <= r135395;
        double r135397 = r135396 ? r135384 : r135394;
        double r135398 = r135386 ? r135394 : r135397;
        double r135399 = r135363 ? r135384 : r135398;
        double r135400 = r135333 ? r135361 : r135399;
        return r135400;
}

Error

Bits error versus t

Bits error versus l

Bits error versus k

Derivation

1. Split input into 3 regimes

2. if l < -1.361561607826164e+74

   1. Initial program 53.0

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

   3. Applied add-cube-cbrt 53.1

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

   4. Applied unpow-prod-down 53.1

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

   5. Applied times-frac 38.5

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

   7. Applied add-cube-cbrt 38.5

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

   8. Applied sqr-pow 38.5

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

   9. Applied times-frac 27.9

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

   11. Applied associate-*l* 27.9

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

   13. Applied associate-/r* 28.1

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

   if -1.361561607826164e+74 < l < -3.671469527357901e-125 or 1.1471508441709014e-119 < l < 2.5473044447906667e+119

   1. Initial program 25.5

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

   2. Taylor expanded around -inf 16.8

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

   if -3.671469527357901e-125 < l < 1.1471508441709014e-119 or 2.5473044447906667e+119 < l

   1. Initial program 32.2

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

   3. Applied add-cube-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 23.5

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

   7. Applied add-cube-cbrt 23.5

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

   8. Applied sqr-pow 23.5

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

   9. Applied times-frac 16.3

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

   11. Applied associate-*l* 15.9

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

   13. Applied pow1/3 39.8

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

   14. Applied pow-pow 15.9

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

4. Final simplification 17.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -1.361561607826163938590433986165123404617 \cdot 10^{74}:\\ \;\;\;\;\frac{\frac{2}{\left(\left(\frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell}}\right) \cdot \frac{{\left(\sqrt[3]{t}\right)}^{3}}{\ell}\right) \cdot \sin k}}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\\ \mathbf{elif}\;\ell \le -3.671469527357900756356766403755497030844 \cdot 10^{-125}:\\ \;\;\;\;\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{elif}\;\ell \le 1.147150844170901392374916916178894499446 \cdot 10^{-119}:\\ \;\;\;\;\frac{2}{\left(\left(\left(\frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell}}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}\\ \mathbf{elif}\;\ell \le 2.547304444790666703643914625432659827925 \cdot 10^{119}:\\ \;\;\;\;\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(\frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{\left(\frac{3}{2}\right)}}{\sqrt[3]{\ell}}\right) \cdot \frac{{t}^{\left(\frac{1}{3} \cdot 3\right)}}{\ell}\right) \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019347 
(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))))