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

Average Error: 5.7 → 1.9

Time: 22.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -18869685775798424479823402359192282988540:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \le 1.786777171204849913027233772322421856416 \cdot 10^{-6}:\\ \;\;\;\;\left(\left(b \cdot c + \left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\sqrt[3]{27 \cdot \left(k \cdot j\right)} \cdot \sqrt[3]{27 \cdot \left(k \cdot j\right)}\right) \cdot \sqrt[3]{27 \cdot \left(k \cdot j\right)}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r594214 = x;
        double r594215 = 18.0;
        double r594216 = r594214 * r594215;
        double r594217 = y;
        double r594218 = r594216 * r594217;
        double r594219 = z;
        double r594220 = r594218 * r594219;
        double r594221 = t;
        double r594222 = r594220 * r594221;
        double r594223 = a;
        double r594224 = 4.0;
        double r594225 = r594223 * r594224;
        double r594226 = r594225 * r594221;
        double r594227 = r594222 - r594226;
        double r594228 = b;
        double r594229 = c;
        double r594230 = r594228 * r594229;
        double r594231 = r594227 + r594230;
        double r594232 = r594214 * r594224;
        double r594233 = i;
        double r594234 = r594232 * r594233;
        double r594235 = r594231 - r594234;
        double r594236 = j;
        double r594237 = 27.0;
        double r594238 = r594236 * r594237;
        double r594239 = k;
        double r594240 = r594238 * r594239;
        double r594241 = r594235 - r594240;
        return r594241;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r594242 = t;
        double r594243 = -1.8869685775798424e+40;
        bool r594244 = r594242 <= r594243;
        double r594245 = b;
        double r594246 = c;
        double r594247 = r594245 * r594246;
        double r594248 = 18.0;
        double r594249 = x;
        double r594250 = z;
        double r594251 = y;
        double r594252 = r594250 * r594251;
        double r594253 = r594249 * r594252;
        double r594254 = r594248 * r594253;
        double r594255 = r594242 * r594254;
        double r594256 = a;
        double r594257 = 4.0;
        double r594258 = r594256 * r594257;
        double r594259 = r594258 * r594242;
        double r594260 = r594255 - r594259;
        double r594261 = r594247 + r594260;
        double r594262 = r594249 * r594257;
        double r594263 = i;
        double r594264 = r594262 * r594263;
        double r594265 = r594261 - r594264;
        double r594266 = 27.0;
        double r594267 = k;
        double r594268 = j;
        double r594269 = r594267 * r594268;
        double r594270 = r594266 * r594269;
        double r594271 = r594265 - r594270;
        double r594272 = 1.78677717120485e-06;
        bool r594273 = r594242 <= r594272;
        double r594274 = r594248 * r594251;
        double r594275 = r594250 * r594242;
        double r594276 = r594274 * r594275;
        double r594277 = r594249 * r594276;
        double r594278 = r594277 - r594259;
        double r594279 = r594247 + r594278;
        double r594280 = r594279 - r594264;
        double r594281 = r594268 * r594266;
        double r594282 = r594281 * r594267;
        double r594283 = r594280 - r594282;
        double r594284 = r594249 * r594248;
        double r594285 = r594284 * r594251;
        double r594286 = r594285 * r594250;
        double r594287 = r594286 * r594242;
        double r594288 = r594287 - r594259;
        double r594289 = r594288 + r594247;
        double r594290 = r594289 - r594264;
        double r594291 = cbrt(r594270);
        double r594292 = r594291 * r594291;
        double r594293 = r594292 * r594291;
        double r594294 = r594290 - r594293;
        double r594295 = r594273 ? r594283 : r594294;
        double r594296 = r594244 ? r594271 : r594295;
        return r594296;
}

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

Target

Original	5.7
Target	1.7
Herbie	1.9

\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if t < -1.8869685775798424e+40

   1. Initial program 1.6

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

   3. Applied associate-*l* 1.7

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

   5. Applied pow1 1.7

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

   6. Applied pow1 1.7

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

   7. Applied pow-prod-down 1.7

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

   8. Applied pow1 1.7

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

   9. Applied pow-prod-down 1.7

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

   10. Simplified 1.6

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

   12. Applied pow1 1.6

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

   13. Applied pow1 1.6

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

   14. Applied pow1 1.6

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

   15. Applied pow1 1.6

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

   16. Applied pow1 1.6

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

   17. Applied pow-prod-down 1.6

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

   18. Applied pow-prod-down 1.6

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

   19. Applied pow-prod-down 1.6

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

   20. Applied pow-prod-down 1.6

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

   21. Simplified 1.6

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

   if -1.8869685775798424e+40 < t < 1.78677717120485e-06

   1. Initial program 7.7

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

   3. Applied pow1 7.7

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

   4. Applied pow1 7.7

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

   5. Applied pow1 7.7

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

   6. Applied pow1 7.7

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

   7. Applied pow1 7.7

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

   8. Applied pow-prod-down 7.7

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

   9. Applied pow-prod-down 7.7

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

   10. Applied pow-prod-down 7.7

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

   11. Applied pow-prod-down 7.7

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

   12. Simplified 1.9

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

   if 1.78677717120485e-06 < t

   1. Initial program 1.9

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

   3. Applied associate-*l* 1.9

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

   5. Applied pow1 1.9

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

   6. Applied pow1 1.9

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

   7. Applied pow-prod-down 1.9

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

   8. Applied pow1 1.9

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

   9. Applied pow-prod-down 1.9

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

   10. Simplified 1.8

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

   12. Applied add-cube-cbrt 2.0

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

4. Final simplification 1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -18869685775798424479823402359192282988540:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \le 1.786777171204849913027233772322421856416 \cdot 10^{-6}:\\ \;\;\;\;\left(\left(b \cdot c + \left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\sqrt[3]{27 \cdot \left(k \cdot j\right)} \cdot \sqrt[3]{27 \cdot \left(k \cdot j\right)}\right) \cdot \sqrt[3]{27 \cdot \left(k \cdot j\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 165.680279438052224) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))