Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.2 → 11.1

Time: 23.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -8.484491448467913911670391729773340407491 \cdot 10^{163}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(c \cdot j\right) \cdot a + \left(-\left(y \cdot j\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \le -1.14585642471154897748655973054367810659 \cdot 10^{44}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - \left(z \cdot \left(c \cdot b\right) + \left(b \cdot \left(-i\right)\right) \cdot t\right)\right) + \left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;i \le -3.021474117192716423446625066638916660611 \cdot 10^{-33}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(-y \cdot \left(i \cdot j\right)\right) + \left(a \cdot j\right) \cdot c\right)\\ \mathbf{elif}\;i \le 1.095860812157643621114714876614430524753 \cdot 10^{-193}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - \left(z \cdot \left(c \cdot b\right) + \left(b \cdot \left(-i\right)\right) \cdot t\right)\right) + \left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;i \le 2.718855256653906167827645742203364148304 \cdot 10^{-39}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(-y \cdot \left(i \cdot j\right)\right) + \left(a \cdot j\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(c \cdot \left(b \cdot z\right) + \left(-i\right) \cdot \left(b \cdot t\right)\right)\right) + \left(c \cdot a - y \cdot i\right) \cdot j\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r548170 = x;
        double r548171 = y;
        double r548172 = z;
        double r548173 = r548171 * r548172;
        double r548174 = t;
        double r548175 = a;
        double r548176 = r548174 * r548175;
        double r548177 = r548173 - r548176;
        double r548178 = r548170 * r548177;
        double r548179 = b;
        double r548180 = c;
        double r548181 = r548180 * r548172;
        double r548182 = i;
        double r548183 = r548174 * r548182;
        double r548184 = r548181 - r548183;
        double r548185 = r548179 * r548184;
        double r548186 = r548178 - r548185;
        double r548187 = j;
        double r548188 = r548180 * r548175;
        double r548189 = r548171 * r548182;
        double r548190 = r548188 - r548189;
        double r548191 = r548187 * r548190;
        double r548192 = r548186 + r548191;
        return r548192;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r548193 = i;
        double r548194 = -8.484491448467914e+163;
        bool r548195 = r548193 <= r548194;
        double r548196 = y;
        double r548197 = z;
        double r548198 = r548196 * r548197;
        double r548199 = t;
        double r548200 = a;
        double r548201 = r548199 * r548200;
        double r548202 = r548198 - r548201;
        double r548203 = x;
        double r548204 = r548202 * r548203;
        double r548205 = b;
        double r548206 = c;
        double r548207 = r548197 * r548206;
        double r548208 = r548199 * r548193;
        double r548209 = r548207 - r548208;
        double r548210 = r548205 * r548209;
        double r548211 = r548204 - r548210;
        double r548212 = j;
        double r548213 = r548206 * r548212;
        double r548214 = r548213 * r548200;
        double r548215 = r548196 * r548212;
        double r548216 = r548215 * r548193;
        double r548217 = -r548216;
        double r548218 = r548214 + r548217;
        double r548219 = r548211 + r548218;
        double r548220 = -1.145856424711549e+44;
        bool r548221 = r548193 <= r548220;
        double r548222 = cbrt(r548199);
        double r548223 = r548200 * r548203;
        double r548224 = r548222 * r548223;
        double r548225 = -r548222;
        double r548226 = r548224 * r548225;
        double r548227 = r548226 * r548222;
        double r548228 = r548203 * r548197;
        double r548229 = r548228 * r548196;
        double r548230 = r548227 + r548229;
        double r548231 = r548206 * r548205;
        double r548232 = r548197 * r548231;
        double r548233 = -r548193;
        double r548234 = r548205 * r548233;
        double r548235 = r548234 * r548199;
        double r548236 = r548232 + r548235;
        double r548237 = r548230 - r548236;
        double r548238 = r548206 * r548200;
        double r548239 = r548196 * r548193;
        double r548240 = r548238 - r548239;
        double r548241 = r548240 * r548212;
        double r548242 = r548237 + r548241;
        double r548243 = -3.0214741171927164e-33;
        bool r548244 = r548193 <= r548243;
        double r548245 = r548230 - r548210;
        double r548246 = r548193 * r548212;
        double r548247 = r548196 * r548246;
        double r548248 = -r548247;
        double r548249 = r548200 * r548212;
        double r548250 = r548249 * r548206;
        double r548251 = r548248 + r548250;
        double r548252 = r548245 + r548251;
        double r548253 = 1.0958608121576436e-193;
        bool r548254 = r548193 <= r548253;
        double r548255 = 2.7188552566539062e-39;
        bool r548256 = r548193 <= r548255;
        double r548257 = r548205 * r548197;
        double r548258 = r548206 * r548257;
        double r548259 = r548205 * r548199;
        double r548260 = r548233 * r548259;
        double r548261 = r548258 + r548260;
        double r548262 = r548204 - r548261;
        double r548263 = r548262 + r548241;
        double r548264 = r548256 ? r548252 : r548263;
        double r548265 = r548254 ? r548242 : r548264;
        double r548266 = r548244 ? r548252 : r548265;
        double r548267 = r548221 ? r548242 : r548266;
        double r548268 = r548195 ? r548219 : r548267;
        return r548268;
}

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

Target

Original	12.2
Target	19.6
Herbie	11.1

\[\begin{array}{l} \mathbf{if}\;x \lt -1.469694296777705016266218530347997287942 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.21135273622268028942701600607048800714 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

1. Split input into 4 regimes

2. if i < -8.484491448467914e+163

   1. Initial program 20.6

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

   3. Applied sub-neg 20.6

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

   4. Applied distribute-lft-in 20.6

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

   5. Simplified 20.1

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

   6. Simplified 14.1

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

   if -8.484491448467914e+163 < i < -1.145856424711549e+44 or -3.0214741171927164e-33 < i < 1.0958608121576436e-193

   1. Initial program 10.7

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

   3. Applied sub-neg 10.7

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

   4. Applied distribute-lft-in 10.7

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

   5. Simplified 10.5

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

   6. Simplified 10.4

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

   8. Applied associate-*r* 9.9

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

   10. Applied add-cube-cbrt 10.0

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

   11. Applied associate-*r* 10.0

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

   12. Simplified 10.0

       \[\leadsto \left(\left(y \cdot \left(x \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{t} \cdot \left(\left(-a\right) \cdot x\right)\right) \cdot \sqrt[3]{t}\right)} \cdot \sqrt[3]{t}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
   13. Using strategy rm

   14. Applied sub-neg 10.0

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

   15. Applied distribute-lft-in 10.0

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

   16. Simplified 10.8

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

   17. Simplified 10.7

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

   if -1.145856424711549e+44 < i < -3.0214741171927164e-33 or 1.0958608121576436e-193 < i < 2.7188552566539062e-39

   1. Initial program 9.0

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

   3. Applied sub-neg 9.0

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

   4. Applied distribute-lft-in 9.0

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

   5. Simplified 8.2

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

   6. Simplified 8.8

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

   8. Applied associate-*r* 8.0

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

   10. Applied add-cube-cbrt 8.1

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

   11. Applied associate-*r* 8.1

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

   12. Simplified 8.1

       \[\leadsto \left(\left(y \cdot \left(x \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{t} \cdot \left(\left(-a\right) \cdot x\right)\right) \cdot \sqrt[3]{t}\right)} \cdot \sqrt[3]{t}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
   13. Using strategy rm

   14. Applied sub-neg 8.1

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

   15. Applied distribute-lft-in 8.1

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

   16. Simplified 9.1

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

   17. Simplified 9.0

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

   if 2.7188552566539062e-39 < i

   1. Initial program 15.7

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

   3. Applied sub-neg 15.7

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

   4. Applied distribute-lft-in 15.7

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

   5. Simplified 16.1

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

   6. Simplified 13.1

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

4. Final simplification 11.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -8.484491448467913911670391729773340407491 \cdot 10^{163}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(c \cdot j\right) \cdot a + \left(-\left(y \cdot j\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \le -1.14585642471154897748655973054367810659 \cdot 10^{44}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - \left(z \cdot \left(c \cdot b\right) + \left(b \cdot \left(-i\right)\right) \cdot t\right)\right) + \left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;i \le -3.021474117192716423446625066638916660611 \cdot 10^{-33}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(-y \cdot \left(i \cdot j\right)\right) + \left(a \cdot j\right) \cdot c\right)\\ \mathbf{elif}\;i \le 1.095860812157643621114714876614430524753 \cdot 10^{-193}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - \left(z \cdot \left(c \cdot b\right) + \left(b \cdot \left(-i\right)\right) \cdot t\right)\right) + \left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;i \le 2.718855256653906167827645742203364148304 \cdot 10^{-39}:\\ \;\;\;\;\left(\left(\left(\left(\sqrt[3]{t} \cdot \left(a \cdot x\right)\right) \cdot \left(-\sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(-y \cdot \left(i \cdot j\right)\right) + \left(a \cdot j\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(c \cdot \left(b \cdot z\right) + \left(-i\right) \cdot \left(b \cdot t\right)\right)\right) + \left(c \cdot a - y \cdot i\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))