Average Error: 25.9 → 28.2
Time: 3.2m
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}\;y4 \le -4.3196630416306697 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(i \cdot \left(c \cdot z\right) - \left(b \cdot z\right) \cdot a\right) \cdot t - \left(\left(y \cdot x\right) \cdot c\right) \cdot i\right)\right) - \left(b \cdot y0 - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y4 \le -2.148753223607781 \cdot 10^{-224}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y4 \le 4.835416382576044 \cdot 10^{-96}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(\left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(j, x, \left(\left(-k\right) \cdot z\right)\right) + \left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(\left(-k\right), z, \left(z \cdot k\right)\right)\right)\right) - \left(\left(y \cdot \left(y3 \cdot y5\right)\right) \cdot a - \mathsf{fma}\left(\left(a \cdot y2\right), \left(y5 \cdot t\right), \left(y3 \cdot \left(\left(y4 \cdot c\right) \cdot y\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(z \cdot \left(c \cdot i\right) - \left(a \cdot b\right) \cdot z\right) \cdot t - x \cdot \left(\left(c \cdot i\right) \cdot y\right)\right)\right) - \left(\left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(j, x, \left(\left(-k\right) \cdot z\right)\right) + \left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(\left(-k\right), z, \left(z \cdot k\right)\right)\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\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}\;y4 \le -4.3196630416306697 \cdot 10^{-10}:\\
\;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(i \cdot \left(c \cdot z\right) - \left(b \cdot z\right) \cdot a\right) \cdot t - \left(\left(y \cdot x\right) \cdot c\right) \cdot i\right)\right) - \left(b \cdot y0 - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\

\mathbf{elif}\;y4 \le -2.148753223607781 \cdot 10^{-224}:\\
\;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\

\mathbf{elif}\;y4 \le 4.835416382576044 \cdot 10^{-96}:\\
\;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(\left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(j, x, \left(\left(-k\right) \cdot z\right)\right) + \left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(\left(-k\right), z, \left(z \cdot k\right)\right)\right)\right) - \left(\left(y \cdot \left(y3 \cdot y5\right)\right) \cdot a - \mathsf{fma}\left(\left(a \cdot y2\right), \left(y5 \cdot t\right), \left(y3 \cdot \left(\left(y4 \cdot c\right) \cdot y\right)\right)\right)\right)\right)\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(z \cdot \left(c \cdot i\right) - \left(a \cdot b\right) \cdot z\right) \cdot t - x \cdot \left(\left(c \cdot i\right) \cdot y\right)\right)\right) - \left(\left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(j, x, \left(\left(-k\right) \cdot z\right)\right) + \left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(\left(-k\right), z, \left(z \cdot k\right)\right)\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\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 r3772737 = x;
        double r3772738 = y;
        double r3772739 = r3772737 * r3772738;
        double r3772740 = z;
        double r3772741 = t;
        double r3772742 = r3772740 * r3772741;
        double r3772743 = r3772739 - r3772742;
        double r3772744 = a;
        double r3772745 = b;
        double r3772746 = r3772744 * r3772745;
        double r3772747 = c;
        double r3772748 = i;
        double r3772749 = r3772747 * r3772748;
        double r3772750 = r3772746 - r3772749;
        double r3772751 = r3772743 * r3772750;
        double r3772752 = j;
        double r3772753 = r3772737 * r3772752;
        double r3772754 = k;
        double r3772755 = r3772740 * r3772754;
        double r3772756 = r3772753 - r3772755;
        double r3772757 = y0;
        double r3772758 = r3772757 * r3772745;
        double r3772759 = y1;
        double r3772760 = r3772759 * r3772748;
        double r3772761 = r3772758 - r3772760;
        double r3772762 = r3772756 * r3772761;
        double r3772763 = r3772751 - r3772762;
        double r3772764 = y2;
        double r3772765 = r3772737 * r3772764;
        double r3772766 = y3;
        double r3772767 = r3772740 * r3772766;
        double r3772768 = r3772765 - r3772767;
        double r3772769 = r3772757 * r3772747;
        double r3772770 = r3772759 * r3772744;
        double r3772771 = r3772769 - r3772770;
        double r3772772 = r3772768 * r3772771;
        double r3772773 = r3772763 + r3772772;
        double r3772774 = r3772741 * r3772752;
        double r3772775 = r3772738 * r3772754;
        double r3772776 = r3772774 - r3772775;
        double r3772777 = y4;
        double r3772778 = r3772777 * r3772745;
        double r3772779 = y5;
        double r3772780 = r3772779 * r3772748;
        double r3772781 = r3772778 - r3772780;
        double r3772782 = r3772776 * r3772781;
        double r3772783 = r3772773 + r3772782;
        double r3772784 = r3772741 * r3772764;
        double r3772785 = r3772738 * r3772766;
        double r3772786 = r3772784 - r3772785;
        double r3772787 = r3772777 * r3772747;
        double r3772788 = r3772779 * r3772744;
        double r3772789 = r3772787 - r3772788;
        double r3772790 = r3772786 * r3772789;
        double r3772791 = r3772783 - r3772790;
        double r3772792 = r3772754 * r3772764;
        double r3772793 = r3772752 * r3772766;
        double r3772794 = r3772792 - r3772793;
        double r3772795 = r3772777 * r3772759;
        double r3772796 = r3772779 * r3772757;
        double r3772797 = r3772795 - r3772796;
        double r3772798 = r3772794 * r3772797;
        double r3772799 = r3772791 + r3772798;
        return r3772799;
}
↓
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 r3772800 = y4;
        double r3772801 = -4.3196630416306697e-10;
        bool r3772802 = r3772800 <= r3772801;
        double r3772803 = y1;
        double r3772804 = r3772803 * r3772800;
        double r3772805 = y0;
        double r3772806 = y5;
        double r3772807 = r3772805 * r3772806;
        double r3772808 = r3772804 - r3772807;
        double r3772809 = y2;
        double r3772810 = k;
        double r3772811 = r3772809 * r3772810;
        double r3772812 = y3;
        double r3772813 = j;
        double r3772814 = r3772812 * r3772813;
        double r3772815 = r3772811 - r3772814;
        double r3772816 = b;
        double r3772817 = r3772800 * r3772816;
        double r3772818 = i;
        double r3772819 = r3772818 * r3772806;
        double r3772820 = r3772817 - r3772819;
        double r3772821 = t;
        double r3772822 = r3772813 * r3772821;
        double r3772823 = y;
        double r3772824 = r3772810 * r3772823;
        double r3772825 = r3772822 - r3772824;
        double r3772826 = c;
        double r3772827 = r3772826 * r3772805;
        double r3772828 = a;
        double r3772829 = r3772828 * r3772803;
        double r3772830 = r3772827 - r3772829;
        double r3772831 = x;
        double r3772832 = r3772831 * r3772809;
        double r3772833 = z;
        double r3772834 = r3772833 * r3772812;
        double r3772835 = r3772832 - r3772834;
        double r3772836 = r3772826 * r3772833;
        double r3772837 = r3772818 * r3772836;
        double r3772838 = r3772816 * r3772833;
        double r3772839 = r3772838 * r3772828;
        double r3772840 = r3772837 - r3772839;
        double r3772841 = r3772840 * r3772821;
        double r3772842 = r3772823 * r3772831;
        double r3772843 = r3772842 * r3772826;
        double r3772844 = r3772843 * r3772818;
        double r3772845 = r3772841 - r3772844;
        double r3772846 = fma(r3772830, r3772835, r3772845);
        double r3772847 = r3772816 * r3772805;
        double r3772848 = r3772803 * r3772818;
        double r3772849 = r3772847 - r3772848;
        double r3772850 = r3772813 * r3772831;
        double r3772851 = r3772833 * r3772810;
        double r3772852 = r3772850 - r3772851;
        double r3772853 = r3772849 * r3772852;
        double r3772854 = r3772846 - r3772853;
        double r3772855 = r3772800 * r3772826;
        double r3772856 = r3772828 * r3772806;
        double r3772857 = r3772855 - r3772856;
        double r3772858 = r3772821 * r3772809;
        double r3772859 = r3772823 * r3772812;
        double r3772860 = r3772858 - r3772859;
        double r3772861 = r3772857 * r3772860;
        double r3772862 = r3772854 - r3772861;
        double r3772863 = fma(r3772820, r3772825, r3772862);
        double r3772864 = fma(r3772808, r3772815, r3772863);
        double r3772865 = -2.148753223607781e-224;
        bool r3772866 = r3772800 <= r3772865;
        double r3772867 = r3772821 * r3772833;
        double r3772868 = r3772842 - r3772867;
        double r3772869 = r3772828 * r3772816;
        double r3772870 = r3772826 * r3772818;
        double r3772871 = r3772869 - r3772870;
        double r3772872 = r3772868 * r3772871;
        double r3772873 = fma(r3772830, r3772835, r3772872);
        double r3772874 = r3772873 - r3772861;
        double r3772875 = fma(r3772820, r3772825, r3772874);
        double r3772876 = fma(r3772808, r3772815, r3772875);
        double r3772877 = 4.835416382576044e-96;
        bool r3772878 = r3772800 <= r3772877;
        double r3772879 = -r3772810;
        double r3772880 = r3772879 * r3772833;
        double r3772881 = fma(r3772813, r3772831, r3772880);
        double r3772882 = r3772849 * r3772881;
        double r3772883 = fma(r3772879, r3772833, r3772851);
        double r3772884 = r3772849 * r3772883;
        double r3772885 = r3772882 + r3772884;
        double r3772886 = r3772873 - r3772885;
        double r3772887 = r3772812 * r3772806;
        double r3772888 = r3772823 * r3772887;
        double r3772889 = r3772888 * r3772828;
        double r3772890 = r3772828 * r3772809;
        double r3772891 = r3772806 * r3772821;
        double r3772892 = r3772855 * r3772823;
        double r3772893 = r3772812 * r3772892;
        double r3772894 = fma(r3772890, r3772891, r3772893);
        double r3772895 = r3772889 - r3772894;
        double r3772896 = r3772886 - r3772895;
        double r3772897 = fma(r3772820, r3772825, r3772896);
        double r3772898 = fma(r3772808, r3772815, r3772897);
        double r3772899 = r3772833 * r3772870;
        double r3772900 = r3772869 * r3772833;
        double r3772901 = r3772899 - r3772900;
        double r3772902 = r3772901 * r3772821;
        double r3772903 = r3772870 * r3772823;
        double r3772904 = r3772831 * r3772903;
        double r3772905 = r3772902 - r3772904;
        double r3772906 = fma(r3772830, r3772835, r3772905);
        double r3772907 = r3772906 - r3772885;
        double r3772908 = r3772907 - r3772861;
        double r3772909 = fma(r3772820, r3772825, r3772908);
        double r3772910 = fma(r3772808, r3772815, r3772909);
        double r3772911 = r3772878 ? r3772898 : r3772910;
        double r3772912 = r3772866 ? r3772876 : r3772911;
        double r3772913 = r3772802 ? r3772864 : r3772912;
        return r3772913;
}

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

Derivation

  1. Split input into 4 regimes

  2. if y4 < -4.3196630416306697e-10

    1. Initial program 27.5

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

    2. Simplified27.5

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

    3. Taylor expanded around -inf 28.9

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

    4. Simplified28.9

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

    if -4.3196630416306697e-10 < y4 < -2.148753223607781e-224

    1. Initial program 24.9

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

    2. Simplified24.9

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

    3. Taylor expanded around 0 29.9

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

    if -2.148753223607781e-224 < y4 < 4.835416382576044e-96

    1. Initial program 25.0

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

    2. Simplified25.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y4 \cdot y1 - y0 \cdot y5\right), \left(y2 \cdot k - j \cdot y3\right), \left(\mathsf{fma}\left(\left(b \cdot y4 - y5 \cdot i\right), \left(t \cdot j - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(y0 \cdot c - y1 \cdot a\right), \left(y2 \cdot x - z \cdot y3\right), \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right)\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right)}\]
    3. Using strategy rm

    4. Applied prod-diff25.0

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

    5. Applied distribute-lft-in25.0

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

    6. Taylor expanded around inf 27.9

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

    7. Simplified26.5

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

    if 4.835416382576044e-96 < y4

    1. Initial program 26.8

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

    2. Simplified26.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y4 \cdot y1 - y0 \cdot y5\right), \left(y2 \cdot k - j \cdot y3\right), \left(\mathsf{fma}\left(\left(b \cdot y4 - y5 \cdot i\right), \left(t \cdot j - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(y0 \cdot c - y1 \cdot a\right), \left(y2 \cdot x - z \cdot y3\right), \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right)\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right)}\]
    3. Using strategy rm

    4. Applied prod-diff26.8

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

    5. Applied distribute-lft-in26.9

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

    6. Taylor expanded around inf 29.0

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

    7. Simplified28.4

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

  4. Final simplification28.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \le -4.3196630416306697 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(i \cdot \left(c \cdot z\right) - \left(b \cdot z\right) \cdot a\right) \cdot t - \left(\left(y \cdot x\right) \cdot c\right) \cdot i\right)\right) - \left(b \cdot y0 - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y4 \le -2.148753223607781 \cdot 10^{-224}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y4 \le 4.835416382576044 \cdot 10^{-96}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(\left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(j, x, \left(\left(-k\right) \cdot z\right)\right) + \left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(\left(-k\right), z, \left(z \cdot k\right)\right)\right)\right) - \left(\left(y \cdot \left(y3 \cdot y5\right)\right) \cdot a - \mathsf{fma}\left(\left(a \cdot y2\right), \left(y5 \cdot t\right), \left(y3 \cdot \left(\left(y4 \cdot c\right) \cdot y\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y1 \cdot y4 - y0 \cdot y5\right), \left(y2 \cdot k - y3 \cdot j\right), \left(\mathsf{fma}\left(\left(y4 \cdot b - i \cdot y5\right), \left(j \cdot t - k \cdot y\right), \left(\left(\mathsf{fma}\left(\left(c \cdot y0 - a \cdot y1\right), \left(x \cdot y2 - z \cdot y3\right), \left(\left(z \cdot \left(c \cdot i\right) - \left(a \cdot b\right) \cdot z\right) \cdot t - x \cdot \left(\left(c \cdot i\right) \cdot y\right)\right)\right) - \left(\left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(j, x, \left(\left(-k\right) \cdot z\right)\right) + \left(b \cdot y0 - y1 \cdot i\right) \cdot \mathsf{fma}\left(\left(-k\right), z, \left(z \cdot k\right)\right)\right)\right) - \left(y4 \cdot c - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(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)))))