Average Error: 25.1 → 26.6
Time: 2.3m
Precision: 64
\[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y5 \le -8.103181025477281 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(y2 \cdot \left(y1 \cdot \left(y4 \cdot k\right)\right) - \left(j \cdot y3\right) \cdot \left(y4 \cdot y1\right)\right) + \left(y2 \cdot k - j \cdot y3\right) \cdot \left(\left(-y5\right) \cdot y0\right)\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\\ \mathbf{elif}\;y5 \le 1.522479190400549 \cdot 10^{-296}:\\ \;\;\;\;\left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \left(\left(\left(y \cdot y5\right) \cdot y3\right) \cdot a - \left(\left(\left(t \cdot y5\right) \cdot y2\right) \cdot a + \left(y4 \cdot \left(y \cdot c\right)\right) \cdot y3\right)\right)\right) + \left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\\ \mathbf{elif}\;y5 \le 1.1351536813200046 \cdot 10^{-198}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)} \cdot \left(\sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)} \cdot \sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(c \cdot z\right)\right) - \left(a \cdot \left(t \cdot \left(b \cdot z\right)\right) + \left(\left(y \cdot c\right) \cdot x\right) \cdot i\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right) + \left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\\ \end{array}\]
\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)
↓
\begin{array}{l}
\mathbf{if}\;y5 \le -8.103181025477281 \cdot 10^{-243}:\\
\;\;\;\;\left(\left(y2 \cdot \left(y1 \cdot \left(y4 \cdot k\right)\right) - \left(j \cdot y3\right) \cdot \left(y4 \cdot y1\right)\right) + \left(y2 \cdot k - j \cdot y3\right) \cdot \left(\left(-y5\right) \cdot y0\right)\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\\

\mathbf{elif}\;y5 \le 1.522479190400549 \cdot 10^{-296}:\\
\;\;\;\;\left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \left(\left(\left(y \cdot y5\right) \cdot y3\right) \cdot a - \left(\left(\left(t \cdot y5\right) \cdot y2\right) \cdot a + \left(y4 \cdot \left(y \cdot c\right)\right) \cdot y3\right)\right)\right) + \left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\\

\mathbf{elif}\;y5 \le 1.1351536813200046 \cdot 10^{-198}:\\
\;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)} \cdot \left(\sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)} \cdot \sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(c \cdot z\right)\right) - \left(a \cdot \left(t \cdot \left(b \cdot z\right)\right) + \left(\left(y \cdot c\right) \cdot x\right) \cdot i\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right) + \left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
        double r3935693 = x;
        double r3935694 = y;
        double r3935695 = r3935693 * r3935694;
        double r3935696 = z;
        double r3935697 = t;
        double r3935698 = r3935696 * r3935697;
        double r3935699 = r3935695 - r3935698;
        double r3935700 = a;
        double r3935701 = b;
        double r3935702 = r3935700 * r3935701;
        double r3935703 = c;
        double r3935704 = i;
        double r3935705 = r3935703 * r3935704;
        double r3935706 = r3935702 - r3935705;
        double r3935707 = r3935699 * r3935706;
        double r3935708 = j;
        double r3935709 = r3935693 * r3935708;
        double r3935710 = k;
        double r3935711 = r3935696 * r3935710;
        double r3935712 = r3935709 - r3935711;
        double r3935713 = y0;
        double r3935714 = r3935713 * r3935701;
        double r3935715 = y1;
        double r3935716 = r3935715 * r3935704;
        double r3935717 = r3935714 - r3935716;
        double r3935718 = r3935712 * r3935717;
        double r3935719 = r3935707 - r3935718;
        double r3935720 = y2;
        double r3935721 = r3935693 * r3935720;
        double r3935722 = y3;
        double r3935723 = r3935696 * r3935722;
        double r3935724 = r3935721 - r3935723;
        double r3935725 = r3935713 * r3935703;
        double r3935726 = r3935715 * r3935700;
        double r3935727 = r3935725 - r3935726;
        double r3935728 = r3935724 * r3935727;
        double r3935729 = r3935719 + r3935728;
        double r3935730 = r3935697 * r3935708;
        double r3935731 = r3935694 * r3935710;
        double r3935732 = r3935730 - r3935731;
        double r3935733 = y4;
        double r3935734 = r3935733 * r3935701;
        double r3935735 = y5;
        double r3935736 = r3935735 * r3935704;
        double r3935737 = r3935734 - r3935736;
        double r3935738 = r3935732 * r3935737;
        double r3935739 = r3935729 + r3935738;
        double r3935740 = r3935697 * r3935720;
        double r3935741 = r3935694 * r3935722;
        double r3935742 = r3935740 - r3935741;
        double r3935743 = r3935733 * r3935703;
        double r3935744 = r3935735 * r3935700;
        double r3935745 = r3935743 - r3935744;
        double r3935746 = r3935742 * r3935745;
        double r3935747 = r3935739 - r3935746;
        double r3935748 = r3935710 * r3935720;
        double r3935749 = r3935708 * r3935722;
        double r3935750 = r3935748 - r3935749;
        double r3935751 = r3935733 * r3935715;
        double r3935752 = r3935735 * r3935713;
        double r3935753 = r3935751 - r3935752;
        double r3935754 = r3935750 * r3935753;
        double r3935755 = r3935747 + r3935754;
        return r3935755;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
        double r3935756 = y5;
        double r3935757 = -8.103181025477281e-243;
        bool r3935758 = r3935756 <= r3935757;
        double r3935759 = y2;
        double r3935760 = y1;
        double r3935761 = y4;
        double r3935762 = k;
        double r3935763 = r3935761 * r3935762;
        double r3935764 = r3935760 * r3935763;
        double r3935765 = r3935759 * r3935764;
        double r3935766 = j;
        double r3935767 = y3;
        double r3935768 = r3935766 * r3935767;
        double r3935769 = r3935761 * r3935760;
        double r3935770 = r3935768 * r3935769;
        double r3935771 = r3935765 - r3935770;
        double r3935772 = r3935759 * r3935762;
        double r3935773 = r3935772 - r3935768;
        double r3935774 = -r3935756;
        double r3935775 = y0;
        double r3935776 = r3935774 * r3935775;
        double r3935777 = r3935773 * r3935776;
        double r3935778 = r3935771 + r3935777;
        double r3935779 = b;
        double r3935780 = r3935779 * r3935761;
        double r3935781 = i;
        double r3935782 = r3935756 * r3935781;
        double r3935783 = r3935780 - r3935782;
        double r3935784 = t;
        double r3935785 = r3935784 * r3935766;
        double r3935786 = y;
        double r3935787 = r3935786 * r3935762;
        double r3935788 = r3935785 - r3935787;
        double r3935789 = r3935783 * r3935788;
        double r3935790 = c;
        double r3935791 = r3935775 * r3935790;
        double r3935792 = a;
        double r3935793 = r3935760 * r3935792;
        double r3935794 = r3935791 - r3935793;
        double r3935795 = x;
        double r3935796 = r3935759 * r3935795;
        double r3935797 = z;
        double r3935798 = r3935767 * r3935797;
        double r3935799 = r3935796 - r3935798;
        double r3935800 = r3935794 * r3935799;
        double r3935801 = r3935795 * r3935786;
        double r3935802 = r3935784 * r3935797;
        double r3935803 = r3935801 - r3935802;
        double r3935804 = r3935792 * r3935779;
        double r3935805 = r3935781 * r3935790;
        double r3935806 = r3935804 - r3935805;
        double r3935807 = r3935803 * r3935806;
        double r3935808 = r3935775 * r3935779;
        double r3935809 = r3935781 * r3935760;
        double r3935810 = r3935808 - r3935809;
        double r3935811 = r3935795 * r3935766;
        double r3935812 = r3935797 * r3935762;
        double r3935813 = r3935811 - r3935812;
        double r3935814 = r3935810 * r3935813;
        double r3935815 = r3935807 - r3935814;
        double r3935816 = r3935800 + r3935815;
        double r3935817 = r3935789 + r3935816;
        double r3935818 = r3935759 * r3935784;
        double r3935819 = r3935767 * r3935786;
        double r3935820 = r3935818 - r3935819;
        double r3935821 = r3935790 * r3935761;
        double r3935822 = r3935756 * r3935792;
        double r3935823 = r3935821 - r3935822;
        double r3935824 = r3935820 * r3935823;
        double r3935825 = r3935817 - r3935824;
        double r3935826 = r3935778 + r3935825;
        double r3935827 = 1.522479190400549e-296;
        bool r3935828 = r3935756 <= r3935827;
        double r3935829 = r3935786 * r3935756;
        double r3935830 = r3935829 * r3935767;
        double r3935831 = r3935830 * r3935792;
        double r3935832 = r3935784 * r3935756;
        double r3935833 = r3935832 * r3935759;
        double r3935834 = r3935833 * r3935792;
        double r3935835 = r3935786 * r3935790;
        double r3935836 = r3935761 * r3935835;
        double r3935837 = r3935836 * r3935767;
        double r3935838 = r3935834 + r3935837;
        double r3935839 = r3935831 - r3935838;
        double r3935840 = r3935817 - r3935839;
        double r3935841 = r3935775 * r3935756;
        double r3935842 = r3935769 - r3935841;
        double r3935843 = r3935773 * r3935842;
        double r3935844 = r3935840 + r3935843;
        double r3935845 = 1.1351536813200046e-198;
        bool r3935846 = r3935756 <= r3935845;
        double r3935847 = cbrt(r3935824);
        double r3935848 = r3935847 * r3935847;
        double r3935849 = r3935847 * r3935848;
        double r3935850 = r3935817 - r3935849;
        double r3935851 = r3935843 + r3935850;
        double r3935852 = r3935790 * r3935797;
        double r3935853 = r3935781 * r3935852;
        double r3935854 = r3935784 * r3935853;
        double r3935855 = r3935779 * r3935797;
        double r3935856 = r3935784 * r3935855;
        double r3935857 = r3935792 * r3935856;
        double r3935858 = r3935835 * r3935795;
        double r3935859 = r3935858 * r3935781;
        double r3935860 = r3935857 + r3935859;
        double r3935861 = r3935854 - r3935860;
        double r3935862 = r3935861 - r3935814;
        double r3935863 = r3935862 + r3935800;
        double r3935864 = r3935863 + r3935789;
        double r3935865 = r3935864 - r3935824;
        double r3935866 = r3935843 + r3935865;
        double r3935867 = r3935846 ? r3935851 : r3935866;
        double r3935868 = r3935828 ? r3935844 : r3935867;
        double r3935869 = r3935758 ? r3935826 : r3935868;
        return r3935869;
}

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

Bits error versus y0

Bits error versus y1

Bits error versus y2

Bits error versus y3

Bits error versus y4

Bits error versus y5

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if y5 < -8.103181025477281e-243

    1. Initial program 25.4

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
    2. Using strategy rm

    3. Applied sub-neg25.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \color{blue}{\left(y4 \cdot y1 + \left(-y5 \cdot y0\right)\right)}\]

    4. Applied distribute-lft-in25.5

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y5 \cdot y0\right)\right)}\]

    5. Taylor expanded around inf 27.1

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot \left(y4 \cdot k\right)\right) - j \cdot \left(y3 \cdot \left(y1 \cdot y4\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y5 \cdot y0\right)\right)\]

    6. Simplified26.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\color{blue}{\left(y2 \cdot \left(\left(k \cdot y4\right) \cdot y1\right) - \left(j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y5 \cdot y0\right)\right)\]

    if -8.103181025477281e-243 < y5 < 1.522479190400549e-296

    1. Initial program 25.9

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    2. Taylor expanded around -inf 26.6

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \color{blue}{\left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y3 \cdot \left(y4 \cdot \left(c \cdot y\right)\right) + a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\right)\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if 1.522479190400549e-296 < y5 < 1.1351536813200046e-198

    1. Initial program 25.6

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt25.7

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \color{blue}{\left(\sqrt[3]{\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)}}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if 1.1351536813200046e-198 < y5

    1. Initial program 24.3

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    2. Taylor expanded around -inf 26.8

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(a \cdot \left(t \cdot \left(b \cdot z\right)\right) + i \cdot \left(x \cdot \left(c \cdot y\right)\right)\right)\right)} - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification26.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \le -8.103181025477281 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(y2 \cdot \left(y1 \cdot \left(y4 \cdot k\right)\right) - \left(j \cdot y3\right) \cdot \left(y4 \cdot y1\right)\right) + \left(y2 \cdot k - j \cdot y3\right) \cdot \left(\left(-y5\right) \cdot y0\right)\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\\ \mathbf{elif}\;y5 \le 1.522479190400549 \cdot 10^{-296}:\\ \;\;\;\;\left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \left(\left(\left(y \cdot y5\right) \cdot y3\right) \cdot a - \left(\left(\left(t \cdot y5\right) \cdot y2\right) \cdot a + \left(y4 \cdot \left(y \cdot c\right)\right) \cdot y3\right)\right)\right) + \left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\\ \mathbf{elif}\;y5 \le 1.1351536813200046 \cdot 10^{-198}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - i \cdot c\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\right) - \sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)} \cdot \left(\sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)} \cdot \sqrt[3]{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(c \cdot z\right)\right) - \left(a \cdot \left(t \cdot \left(b \cdot z\right)\right) + \left(\left(y \cdot c\right) \cdot x\right) \cdot i\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\right) + \left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019134 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))