Average Error: 25.9 → 28.6
Time: 2.2m
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}\;j \le -1.2392061038984322 \cdot 10^{-67}:\\ \;\;\;\;\left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(\left(\left(z \cdot c\right) \cdot i\right) \cdot t - \left(a \cdot \left(\left(z \cdot b\right) \cdot t\right) + i \cdot \left(x \cdot \left(c \cdot y\right)\right)\right)\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{elif}\;j \le -5.352512555925856 \cdot 10^{-226}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(\left(k \cdot y1\right) \cdot z\right) \cdot i - \left(k \cdot \left(z \cdot \left(y0 \cdot b\right)\right) + i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)\right)\right)\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \le -2.5398560045115965 \cdot 10^{-283}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \le 3.3378824399859848 \cdot 10^{-108}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(\left(\left(z \cdot y1\right) \cdot y3 - \left(y1 \cdot x\right) \cdot y2\right) \cdot a - z \cdot \left(\left(y3 \cdot y0\right) \cdot c\right)\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \le 2.425694207841494 \cdot 10^{-60}:\\ \;\;\;\;\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(a \cdot \left(y3 \cdot \left(y5 \cdot y\right)\right) - \left(\left(\left(c \cdot y\right) \cdot y4\right) \cdot y3 + a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\right)\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}\;j \le -1.2392061038984322 \cdot 10^{-67}:\\
\;\;\;\;\left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(\left(\left(z \cdot c\right) \cdot i\right) \cdot t - \left(a \cdot \left(\left(z \cdot b\right) \cdot t\right) + i \cdot \left(x \cdot \left(c \cdot y\right)\right)\right)\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\

\mathbf{elif}\;j \le -5.352512555925856 \cdot 10^{-226}:\\
\;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(\left(k \cdot y1\right) \cdot z\right) \cdot i - \left(k \cdot \left(z \cdot \left(y0 \cdot b\right)\right) + i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)\right)\right)\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\

\mathbf{elif}\;j \le -2.5398560045115965 \cdot 10^{-283}:\\
\;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\

\mathbf{elif}\;j \le 3.3378824399859848 \cdot 10^{-108}:\\
\;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(\left(\left(z \cdot y1\right) \cdot y3 - \left(y1 \cdot x\right) \cdot y2\right) \cdot a - z \cdot \left(\left(y3 \cdot y0\right) \cdot c\right)\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\

\mathbf{elif}\;j \le 2.425694207841494 \cdot 10^{-60}:\\
\;\;\;\;\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\

\mathbf{else}:\\
\;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(a \cdot \left(y3 \cdot \left(y5 \cdot y\right)\right) - \left(\left(\left(c \cdot y\right) \cdot y4\right) \cdot y3 + a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\right)\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 r4951691 = x;
        double r4951692 = y;
        double r4951693 = r4951691 * r4951692;
        double r4951694 = z;
        double r4951695 = t;
        double r4951696 = r4951694 * r4951695;
        double r4951697 = r4951693 - r4951696;
        double r4951698 = a;
        double r4951699 = b;
        double r4951700 = r4951698 * r4951699;
        double r4951701 = c;
        double r4951702 = i;
        double r4951703 = r4951701 * r4951702;
        double r4951704 = r4951700 - r4951703;
        double r4951705 = r4951697 * r4951704;
        double r4951706 = j;
        double r4951707 = r4951691 * r4951706;
        double r4951708 = k;
        double r4951709 = r4951694 * r4951708;
        double r4951710 = r4951707 - r4951709;
        double r4951711 = y0;
        double r4951712 = r4951711 * r4951699;
        double r4951713 = y1;
        double r4951714 = r4951713 * r4951702;
        double r4951715 = r4951712 - r4951714;
        double r4951716 = r4951710 * r4951715;
        double r4951717 = r4951705 - r4951716;
        double r4951718 = y2;
        double r4951719 = r4951691 * r4951718;
        double r4951720 = y3;
        double r4951721 = r4951694 * r4951720;
        double r4951722 = r4951719 - r4951721;
        double r4951723 = r4951711 * r4951701;
        double r4951724 = r4951713 * r4951698;
        double r4951725 = r4951723 - r4951724;
        double r4951726 = r4951722 * r4951725;
        double r4951727 = r4951717 + r4951726;
        double r4951728 = r4951695 * r4951706;
        double r4951729 = r4951692 * r4951708;
        double r4951730 = r4951728 - r4951729;
        double r4951731 = y4;
        double r4951732 = r4951731 * r4951699;
        double r4951733 = y5;
        double r4951734 = r4951733 * r4951702;
        double r4951735 = r4951732 - r4951734;
        double r4951736 = r4951730 * r4951735;
        double r4951737 = r4951727 + r4951736;
        double r4951738 = r4951695 * r4951718;
        double r4951739 = r4951692 * r4951720;
        double r4951740 = r4951738 - r4951739;
        double r4951741 = r4951731 * r4951701;
        double r4951742 = r4951733 * r4951698;
        double r4951743 = r4951741 - r4951742;
        double r4951744 = r4951740 * r4951743;
        double r4951745 = r4951737 - r4951744;
        double r4951746 = r4951708 * r4951718;
        double r4951747 = r4951706 * r4951720;
        double r4951748 = r4951746 - r4951747;
        double r4951749 = r4951731 * r4951713;
        double r4951750 = r4951733 * r4951711;
        double r4951751 = r4951749 - r4951750;
        double r4951752 = r4951748 * r4951751;
        double r4951753 = r4951745 + r4951752;
        return r4951753;
}
↓
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 r4951754 = j;
        double r4951755 = -1.2392061038984322e-67;
        bool r4951756 = r4951754 <= r4951755;
        double r4951757 = c;
        double r4951758 = y0;
        double r4951759 = r4951757 * r4951758;
        double r4951760 = a;
        double r4951761 = y1;
        double r4951762 = r4951760 * r4951761;
        double r4951763 = r4951759 - r4951762;
        double r4951764 = y2;
        double r4951765 = x;
        double r4951766 = r4951764 * r4951765;
        double r4951767 = y3;
        double r4951768 = z;
        double r4951769 = r4951767 * r4951768;
        double r4951770 = r4951766 - r4951769;
        double r4951771 = r4951763 * r4951770;
        double r4951772 = r4951768 * r4951757;
        double r4951773 = i;
        double r4951774 = r4951772 * r4951773;
        double r4951775 = t;
        double r4951776 = r4951774 * r4951775;
        double r4951777 = b;
        double r4951778 = r4951768 * r4951777;
        double r4951779 = r4951778 * r4951775;
        double r4951780 = r4951760 * r4951779;
        double r4951781 = y;
        double r4951782 = r4951757 * r4951781;
        double r4951783 = r4951765 * r4951782;
        double r4951784 = r4951773 * r4951783;
        double r4951785 = r4951780 + r4951784;
        double r4951786 = r4951776 - r4951785;
        double r4951787 = r4951765 * r4951754;
        double r4951788 = k;
        double r4951789 = r4951788 * r4951768;
        double r4951790 = r4951787 - r4951789;
        double r4951791 = r4951758 * r4951777;
        double r4951792 = r4951761 * r4951773;
        double r4951793 = r4951791 - r4951792;
        double r4951794 = r4951790 * r4951793;
        double r4951795 = r4951786 - r4951794;
        double r4951796 = r4951771 + r4951795;
        double r4951797 = y4;
        double r4951798 = r4951777 * r4951797;
        double r4951799 = y5;
        double r4951800 = r4951773 * r4951799;
        double r4951801 = r4951798 - r4951800;
        double r4951802 = r4951775 * r4951754;
        double r4951803 = r4951781 * r4951788;
        double r4951804 = r4951802 - r4951803;
        double r4951805 = r4951801 * r4951804;
        double r4951806 = r4951796 + r4951805;
        double r4951807 = r4951757 * r4951797;
        double r4951808 = r4951760 * r4951799;
        double r4951809 = r4951807 - r4951808;
        double r4951810 = r4951775 * r4951764;
        double r4951811 = r4951781 * r4951767;
        double r4951812 = r4951810 - r4951811;
        double r4951813 = r4951809 * r4951812;
        double r4951814 = r4951806 - r4951813;
        double r4951815 = r4951788 * r4951764;
        double r4951816 = r4951767 * r4951754;
        double r4951817 = r4951815 - r4951816;
        double r4951818 = r4951761 * r4951797;
        double r4951819 = r4951799 * r4951758;
        double r4951820 = r4951818 - r4951819;
        double r4951821 = r4951817 * r4951820;
        double r4951822 = r4951814 + r4951821;
        double r4951823 = -5.352512555925856e-226;
        bool r4951824 = r4951754 <= r4951823;
        double r4951825 = r4951765 * r4951781;
        double r4951826 = r4951775 * r4951768;
        double r4951827 = r4951825 - r4951826;
        double r4951828 = r4951760 * r4951777;
        double r4951829 = r4951757 * r4951773;
        double r4951830 = r4951828 - r4951829;
        double r4951831 = r4951827 * r4951830;
        double r4951832 = r4951788 * r4951761;
        double r4951833 = r4951832 * r4951768;
        double r4951834 = r4951833 * r4951773;
        double r4951835 = r4951768 * r4951791;
        double r4951836 = r4951788 * r4951835;
        double r4951837 = r4951761 * r4951765;
        double r4951838 = r4951754 * r4951837;
        double r4951839 = r4951773 * r4951838;
        double r4951840 = r4951836 + r4951839;
        double r4951841 = r4951834 - r4951840;
        double r4951842 = r4951831 - r4951841;
        double r4951843 = r4951771 + r4951842;
        double r4951844 = r4951805 + r4951843;
        double r4951845 = r4951844 - r4951813;
        double r4951846 = r4951821 + r4951845;
        double r4951847 = -2.5398560045115965e-283;
        bool r4951848 = r4951754 <= r4951847;
        double r4951849 = r4951831 + r4951771;
        double r4951850 = r4951805 + r4951849;
        double r4951851 = r4951850 - r4951813;
        double r4951852 = r4951821 + r4951851;
        double r4951853 = 3.3378824399859848e-108;
        bool r4951854 = r4951754 <= r4951853;
        double r4951855 = r4951768 * r4951761;
        double r4951856 = r4951855 * r4951767;
        double r4951857 = r4951837 * r4951764;
        double r4951858 = r4951856 - r4951857;
        double r4951859 = r4951858 * r4951760;
        double r4951860 = r4951767 * r4951758;
        double r4951861 = r4951860 * r4951757;
        double r4951862 = r4951768 * r4951861;
        double r4951863 = r4951859 - r4951862;
        double r4951864 = r4951831 - r4951794;
        double r4951865 = r4951863 + r4951864;
        double r4951866 = r4951805 + r4951865;
        double r4951867 = r4951866 - r4951813;
        double r4951868 = r4951821 + r4951867;
        double r4951869 = 2.425694207841494e-60;
        bool r4951870 = r4951754 <= r4951869;
        double r4951871 = r4951771 + r4951864;
        double r4951872 = r4951871 + r4951805;
        double r4951873 = r4951872 + r4951821;
        double r4951874 = r4951799 * r4951781;
        double r4951875 = r4951767 * r4951874;
        double r4951876 = r4951760 * r4951875;
        double r4951877 = r4951782 * r4951797;
        double r4951878 = r4951877 * r4951767;
        double r4951879 = r4951775 * r4951799;
        double r4951880 = r4951764 * r4951879;
        double r4951881 = r4951760 * r4951880;
        double r4951882 = r4951878 + r4951881;
        double r4951883 = r4951876 - r4951882;
        double r4951884 = r4951872 - r4951883;
        double r4951885 = r4951821 + r4951884;
        double r4951886 = r4951870 ? r4951873 : r4951885;
        double r4951887 = r4951854 ? r4951868 : r4951886;
        double r4951888 = r4951848 ? r4951852 : r4951887;
        double r4951889 = r4951824 ? r4951846 : r4951888;
        double r4951890 = r4951756 ? r4951822 : r4951889;
        return r4951890;
}

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 6 regimes

  2. if j < -1.2392061038984322e-67

    1. Initial program 26.7

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

    2. Taylor expanded around -inf 28.5

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

    if -1.2392061038984322e-67 < j < -5.352512555925856e-226

    1. Initial program 24.4

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

    2. Taylor expanded around inf 26.8

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

    if -5.352512555925856e-226 < j < -2.5398560045115965e-283

    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. Taylor expanded around 0 29.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \color{blue}{0}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if -2.5398560045115965e-283 < j < 3.3378824399859848e-108

    1. Initial program 25.8

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

    2. Taylor expanded around inf 29.6

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

    3. Simplified29.6

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

    if 3.3378824399859848e-108 < j < 2.425694207841494e-60

    1. Initial program 25.8

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

    2. Taylor expanded around 0 31.6

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \color{blue}{0}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if 2.425694207841494e-60 < j

    1. Initial program 26.5

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

    2. Taylor expanded around inf 28.3

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \color{blue}{\left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y3 \cdot \left(y4 \cdot \left(c \cdot y\right)\right) + a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\right)\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  3. Recombined 6 regimes into one program.

  4. Final simplification28.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -1.2392061038984322 \cdot 10^{-67}:\\ \;\;\;\;\left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(\left(\left(z \cdot c\right) \cdot i\right) \cdot t - \left(a \cdot \left(\left(z \cdot b\right) \cdot t\right) + i \cdot \left(x \cdot \left(c \cdot y\right)\right)\right)\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{elif}\;j \le -5.352512555925856 \cdot 10^{-226}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(\left(k \cdot y1\right) \cdot z\right) \cdot i - \left(k \cdot \left(z \cdot \left(y0 \cdot b\right)\right) + i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)\right)\right)\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \le -2.5398560045115965 \cdot 10^{-283}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \le 3.3378824399859848 \cdot 10^{-108}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(\left(\left(z \cdot y1\right) \cdot y3 - \left(y1 \cdot x\right) \cdot y2\right) \cdot a - z \cdot \left(\left(y3 \cdot y0\right) \cdot c\right)\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \le 2.425694207841494 \cdot 10^{-60}:\\ \;\;\;\;\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(a \cdot \left(y3 \cdot \left(y5 \cdot y\right)\right) - \left(\left(\left(c \cdot y\right) \cdot y4\right) \cdot y3 + a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(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)))))