Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 11.6 → 11.3

Time: 23.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;c \le -1.911661663231193133152425417101608962071 \cdot 10^{-99}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \left(t \cdot j\right)\right) \cdot \sqrt[3]{c} + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \mathbf{elif}\;c \le 3.281737004707663056029424521453613958063 \cdot 10^{145}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;c \le 2.662534141559160429989964984960950739743 \cdot 10^{222}:\\ \;\;\;\;\left(\left(t \cdot j\right) \cdot c + \left(-i \cdot \left(y \cdot j\right)\right)\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{elif}\;c \le 4.731713770906781313248457864535070930729 \cdot 10^{243}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-\sqrt[3]{{\left(i \cdot \left(y \cdot j\right)\right)}^{3}}\right)\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r96867 = x;
        double r96868 = y;
        double r96869 = z;
        double r96870 = r96868 * r96869;
        double r96871 = t;
        double r96872 = a;
        double r96873 = r96871 * r96872;
        double r96874 = r96870 - r96873;
        double r96875 = r96867 * r96874;
        double r96876 = b;
        double r96877 = c;
        double r96878 = r96877 * r96869;
        double r96879 = i;
        double r96880 = r96879 * r96872;
        double r96881 = r96878 - r96880;
        double r96882 = r96876 * r96881;
        double r96883 = r96875 - r96882;
        double r96884 = j;
        double r96885 = r96877 * r96871;
        double r96886 = r96879 * r96868;
        double r96887 = r96885 - r96886;
        double r96888 = r96884 * r96887;
        double r96889 = r96883 + r96888;
        return r96889;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r96890 = c;
        double r96891 = -1.911661663231193e-99;
        bool r96892 = r96890 <= r96891;
        double r96893 = x;
        double r96894 = y;
        double r96895 = z;
        double r96896 = r96894 * r96895;
        double r96897 = t;
        double r96898 = a;
        double r96899 = r96897 * r96898;
        double r96900 = r96896 - r96899;
        double r96901 = r96893 * r96900;
        double r96902 = b;
        double r96903 = r96890 * r96895;
        double r96904 = i;
        double r96905 = r96904 * r96898;
        double r96906 = r96903 - r96905;
        double r96907 = r96902 * r96906;
        double r96908 = r96901 - r96907;
        double r96909 = cbrt(r96890);
        double r96910 = r96909 * r96909;
        double r96911 = j;
        double r96912 = r96897 * r96911;
        double r96913 = r96910 * r96912;
        double r96914 = r96913 * r96909;
        double r96915 = r96894 * r96911;
        double r96916 = r96904 * r96915;
        double r96917 = -r96916;
        double r96918 = r96914 + r96917;
        double r96919 = r96908 + r96918;
        double r96920 = 3.281737004707663e+145;
        bool r96921 = r96890 <= r96920;
        double r96922 = cbrt(r96907);
        double r96923 = r96922 * r96922;
        double r96924 = r96923 * r96922;
        double r96925 = r96901 - r96924;
        double r96926 = r96890 * r96897;
        double r96927 = r96904 * r96894;
        double r96928 = r96926 - r96927;
        double r96929 = r96911 * r96928;
        double r96930 = r96925 + r96929;
        double r96931 = 2.6625341415591604e+222;
        bool r96932 = r96890 <= r96931;
        double r96933 = r96912 * r96890;
        double r96934 = r96933 + r96917;
        double r96935 = -r96907;
        double r96936 = r96934 + r96935;
        double r96937 = 4.731713770906781e+243;
        bool r96938 = r96890 <= r96937;
        double r96939 = r96902 * r96890;
        double r96940 = r96895 * r96939;
        double r96941 = -r96905;
        double r96942 = r96941 * r96902;
        double r96943 = r96940 + r96942;
        double r96944 = r96901 - r96943;
        double r96945 = r96911 * r96890;
        double r96946 = r96897 * r96945;
        double r96947 = r96946 + r96917;
        double r96948 = r96944 + r96947;
        double r96949 = 3.0;
        double r96950 = pow(r96916, r96949);
        double r96951 = cbrt(r96950);
        double r96952 = -r96951;
        double r96953 = r96933 + r96952;
        double r96954 = r96908 + r96953;
        double r96955 = r96938 ? r96948 : r96954;
        double r96956 = r96932 ? r96936 : r96955;
        double r96957 = r96921 ? r96930 : r96956;
        double r96958 = r96892 ? r96919 : r96957;
        return r96958;
}

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

Derivation

1. Split input into 5 regimes

2. if c < -1.911661663231193e-99

   1. Initial program 13.5

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

   3. Applied sub-neg 13.5

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

   4. Applied distribute-lft-in 13.5

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

   5. Simplified 13.9

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

   7. Applied distribute-rgt-neg-out 13.9

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

   8. Simplified 13.4

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

   10. Applied associate-*r* 11.8

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

   12. Applied add-cube-cbrt 12.0

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

   13. Applied associate-*r* 12.0

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

   14. Simplified 12.0

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

   if -1.911661663231193e-99 < c < 3.281737004707663e+145

   1. Initial program 9.3

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

   3. Applied add-cube-cbrt 9.6

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

   if 3.281737004707663e+145 < c < 2.6625341415591604e+222

   1. Initial program 21.8

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

   3. Applied sub-neg 21.8

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

   4. Applied distribute-lft-in 21.8

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

   5. Simplified 24.7

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

   7. Applied distribute-rgt-neg-out 24.7

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

   8. Simplified 22.8

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

   10. Applied associate-*r* 15.2

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

   11. Taylor expanded around 0 23.6

       \[\leadsto \left(\color{blue}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot \left(y \cdot j\right)\right)\right)\]

   if 2.6625341415591604e+222 < c < 4.731713770906781e+243

   1. Initial program 26.1

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

   3. Applied sub-neg 26.1

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

   4. Applied distribute-lft-in 26.1

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

   5. Simplified 22.1

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

   7. Applied distribute-rgt-neg-out 22.1

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

   8. Simplified 20.5

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

   10. Applied sub-neg 20.5

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

   11. Applied distribute-lft-in 20.5

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

   12. Simplified 18.8

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

   13. Simplified 18.8

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

   if 4.731713770906781e+243 < c

   1. Initial program 21.6

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

   3. Applied sub-neg 21.6

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

   4. Applied distribute-lft-in 21.6

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

   5. Simplified 24.4

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

   7. Applied distribute-rgt-neg-out 24.4

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

   8. Simplified 22.3

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

   10. Applied associate-*r* 13.6

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

   12. Applied add-cbrt-cube 19.6

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

   13. Applied add-cbrt-cube 32.0

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

   14. Applied cbrt-unprod 32.5

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

   15. Applied add-cbrt-cube 40.1

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

   16. Applied cbrt-unprod 40.5

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

   17. Simplified 19.1

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-\sqrt[3]{\color{blue}{{\left(i \cdot \left(y \cdot j\right)\right)}^{3}}}\right)\right)\]
3. Recombined 5 regimes into one program.

4. Final simplification 11.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \le -1.911661663231193133152425417101608962071 \cdot 10^{-99}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \left(t \cdot j\right)\right) \cdot \sqrt[3]{c} + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \mathbf{elif}\;c \le 3.281737004707663056029424521453613958063 \cdot 10^{145}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;c \le 2.662534141559160429989964984960950739743 \cdot 10^{222}:\\ \;\;\;\;\left(\left(t \cdot j\right) \cdot c + \left(-i \cdot \left(y \cdot j\right)\right)\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{elif}\;c \le 4.731713770906781313248457864535070930729 \cdot 10^{243}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-\sqrt[3]{{\left(i \cdot \left(y \cdot j\right)\right)}^{3}}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))