Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

Average Error: 5.8 → 1.5

Time: 26.3s

Precision: 64

Math

\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot y - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 2.5255778798157246 \cdot 10^{255}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(t \cdot z\right) \cdot x\right) \cdot 18\right) \cdot y - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r110302 = x;
        double r110303 = 18.0;
        double r110304 = r110302 * r110303;
        double r110305 = y;
        double r110306 = r110304 * r110305;
        double r110307 = z;
        double r110308 = r110306 * r110307;
        double r110309 = t;
        double r110310 = r110308 * r110309;
        double r110311 = a;
        double r110312 = 4.0;
        double r110313 = r110311 * r110312;
        double r110314 = r110313 * r110309;
        double r110315 = r110310 - r110314;
        double r110316 = b;
        double r110317 = c;
        double r110318 = r110316 * r110317;
        double r110319 = r110315 + r110318;
        double r110320 = r110302 * r110312;
        double r110321 = i;
        double r110322 = r110320 * r110321;
        double r110323 = r110319 - r110322;
        double r110324 = j;
        double r110325 = 27.0;
        double r110326 = r110324 * r110325;
        double r110327 = k;
        double r110328 = r110326 * r110327;
        double r110329 = r110323 - r110328;
        return r110329;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r110330 = x;
        double r110331 = 18.0;
        double r110332 = r110330 * r110331;
        double r110333 = y;
        double r110334 = r110332 * r110333;
        double r110335 = z;
        double r110336 = r110334 * r110335;
        double r110337 = t;
        double r110338 = r110336 * r110337;
        double r110339 = a;
        double r110340 = 4.0;
        double r110341 = r110339 * r110340;
        double r110342 = r110341 * r110337;
        double r110343 = r110338 - r110342;
        double r110344 = b;
        double r110345 = c;
        double r110346 = r110344 * r110345;
        double r110347 = r110343 + r110346;
        double r110348 = r110330 * r110340;
        double r110349 = i;
        double r110350 = r110348 * r110349;
        double r110351 = r110347 - r110350;
        double r110352 = -inf.0;
        bool r110353 = r110351 <= r110352;
        double r110354 = r110337 * r110335;
        double r110355 = r110354 * r110332;
        double r110356 = r110355 * r110333;
        double r110357 = r110356 - r110342;
        double r110358 = r110346 + r110357;
        double r110359 = r110358 - r110350;
        double r110360 = j;
        double r110361 = 27.0;
        double r110362 = r110360 * r110361;
        double r110363 = k;
        double r110364 = r110362 * r110363;
        double r110365 = cbrt(r110364);
        double r110366 = r110365 * r110365;
        double r110367 = r110366 * r110365;
        double r110368 = r110359 - r110367;
        double r110369 = 2.5255778798157246e+255;
        bool r110370 = r110351 <= r110369;
        double r110371 = r110333 * r110331;
        double r110372 = r110330 * r110371;
        double r110373 = r110372 * r110335;
        double r110374 = r110373 * r110337;
        double r110375 = r110374 - r110342;
        double r110376 = r110375 + r110346;
        double r110377 = r110376 - r110350;
        double r110378 = r110361 * r110363;
        double r110379 = r110378 * r110360;
        double r110380 = r110377 - r110379;
        double r110381 = r110354 * r110330;
        double r110382 = r110381 * r110331;
        double r110383 = r110382 * r110333;
        double r110384 = r110383 - r110342;
        double r110385 = r110346 + r110384;
        double r110386 = r110385 - r110350;
        double r110387 = r110386 - r110364;
        double r110388 = r110370 ? r110380 : r110387;
        double r110389 = r110353 ? r110368 : r110388;
        return r110389;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Derivation

1. Split input into 3 regimes

2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0

   1. Initial program 64.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   2. Using strategy rm

   3. Applied associate-*l* 63.8

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   4. Simplified 63.8

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \color{blue}{\left(y \cdot 18\right)}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   5. Using strategy rm

   6. Applied pow1 63.8

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot \color{blue}{{t}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   7. Applied pow1 63.8

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot \color{blue}{{z}^{1}}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   8. Applied pow1 63.8

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot \color{blue}{{18}^{1}}\right)\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   9. Applied pow1 63.8

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(\color{blue}{{y}^{1}} \cdot {18}^{1}\right)\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   10. Applied pow-prod-down 63.8

       \[\leadsto \left(\left(\left(\left(\left(x \cdot \color{blue}{{\left(y \cdot 18\right)}^{1}}\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   11. Applied pow1 63.8

       \[\leadsto \left(\left(\left(\left(\left(\color{blue}{{x}^{1}} \cdot {\left(y \cdot 18\right)}^{1}\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   12. Applied pow-prod-down 63.8

       \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(x \cdot \left(y \cdot 18\right)\right)}^{1}} \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   13. Applied pow-prod-down 63.8

       \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right)}^{1}} \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   14. Applied pow-prod-down 63.8

       \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   15. Simplified 36.6

       \[\leadsto \left(\left(\left({\color{blue}{\left(\left(t \cdot z\right) \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   16. Using strategy rm

   17. Applied associate-*r* 4.6

       \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot y\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   18. Using strategy rm

   19. Applied add-cube-cbrt 4.7

       \[\leadsto \left(\left(\left({\left(\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot y\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{\left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}}\]

   if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 2.5255778798157246e+255

   1. Initial program 0.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   2. Using strategy rm

   3. Applied associate-*l* 0.4

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   4. Simplified 0.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \color{blue}{\left(y \cdot 18\right)}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   5. Using strategy rm

   6. Applied pow1 0.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot \color{blue}{{k}^{1}}\]

   7. Applied pow1 0.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot \color{blue}{{27}^{1}}\right) \cdot {k}^{1}\]

   8. Applied pow1 0.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\color{blue}{{j}^{1}} \cdot {27}^{1}\right) \cdot {k}^{1}\]

   9. Applied pow-prod-down 0.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{{\left(j \cdot 27\right)}^{1}} \cdot {k}^{1}\]

   10. Applied pow-prod-down 0.4

       \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{{\left(\left(j \cdot 27\right) \cdot k\right)}^{1}}\]

   11. Simplified 0.5

       \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - {\color{blue}{\left(\left(27 \cdot k\right) \cdot j\right)}}^{1}\]

   if 2.5255778798157246e+255 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

   1. Initial program 23.9

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   2. Using strategy rm

   3. Applied associate-*l* 23.7

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   4. Simplified 23.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \color{blue}{\left(y \cdot 18\right)}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   5. Using strategy rm

   6. Applied pow1 23.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot \color{blue}{{t}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   7. Applied pow1 23.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot \color{blue}{{z}^{1}}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   8. Applied pow1 23.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot \color{blue}{{18}^{1}}\right)\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   9. Applied pow1 23.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(\color{blue}{{y}^{1}} \cdot {18}^{1}\right)\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   10. Applied pow-prod-down 23.7

       \[\leadsto \left(\left(\left(\left(\left(x \cdot \color{blue}{{\left(y \cdot 18\right)}^{1}}\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   11. Applied pow1 23.7

       \[\leadsto \left(\left(\left(\left(\left(\color{blue}{{x}^{1}} \cdot {\left(y \cdot 18\right)}^{1}\right) \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   12. Applied pow-prod-down 23.7

       \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(x \cdot \left(y \cdot 18\right)\right)}^{1}} \cdot {z}^{1}\right) \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   13. Applied pow-prod-down 23.7

       \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right)}^{1}} \cdot {t}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   14. Applied pow-prod-down 23.7

       \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

   15. Simplified 18.6

       \[\leadsto \left(\left(\left({\color{blue}{\left(\left(t \cdot z\right) \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   16. Using strategy rm

   17. Applied associate-*r* 7.8

       \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot y\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
   18. Using strategy rm

   19. Applied associate-*r* 7.6

       \[\leadsto \left(\left(\left({\left(\color{blue}{\left(\left(\left(t \cdot z\right) \cdot x\right) \cdot 18\right)} \cdot y\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
3. Recombined 3 regimes into one program.

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot y - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 2.5255778798157246 \cdot 10^{255}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(t \cdot z\right) \cdot x\right) \cdot 18\right) \cdot y - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))