Average Error: 26.3 → 26.7
Time: 2.0m
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 -3.5330856269526526 \cdot 10^{+70}:\\ \;\;\;\;\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(\left(\left(y2 \cdot k - j \cdot y3\right) \cdot y0\right) \cdot \left(-y5\right) + \left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right) \cdot y4\right)\\ \mathbf{elif}\;y5 \le -1.3464225199830876 \cdot 10^{-99}:\\ \;\;\;\;\left(y4 \cdot y1 - y0 \cdot y5\right) \cdot \left(y2 \cdot k - j \cdot y3\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(\left(\left(y \cdot y5\right) \cdot y3\right) \cdot a - \left(a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) + y3 \cdot \left(y4 \cdot \left(y \cdot c\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y5 \le 9.64053022884884 \cdot 10^{-169}:\\ \;\;\;\;\left(\left(\left(\left(\left(y5 \cdot k\right) \cdot y\right) \cdot i - \left(k \cdot \left(\left(b \cdot y4\right) \cdot y\right) + t \cdot \left(\left(y5 \cdot j\right) \cdot i\right)\right)\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot \left(y2 \cdot k - j \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(\left(\left(y2 \cdot k - j \cdot y3\right) \cdot y0\right) \cdot \left(-y5\right) + \left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right) \cdot y4\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 -3.5330856269526526 \cdot 10^{+70}:\\
\;\;\;\;\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(\left(\left(y2 \cdot k - j \cdot y3\right) \cdot y0\right) \cdot \left(-y5\right) + \left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right) \cdot y4\right)\\

\mathbf{elif}\;y5 \le -1.3464225199830876 \cdot 10^{-99}:\\
\;\;\;\;\left(y4 \cdot y1 - y0 \cdot y5\right) \cdot \left(y2 \cdot k - j \cdot y3\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(\left(\left(y \cdot y5\right) \cdot y3\right) \cdot a - \left(a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) + y3 \cdot \left(y4 \cdot \left(y \cdot c\right)\right)\right)\right)\right)\\

\mathbf{elif}\;y5 \le 9.64053022884884 \cdot 10^{-169}:\\
\;\;\;\;\left(\left(\left(\left(\left(y5 \cdot k\right) \cdot y\right) \cdot i - \left(k \cdot \left(\left(b \cdot y4\right) \cdot y\right) + t \cdot \left(\left(y5 \cdot j\right) \cdot i\right)\right)\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot \left(y2 \cdot k - j \cdot y3\right)\\

\mathbf{else}:\\
\;\;\;\;\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(\left(\left(y2 \cdot k - j \cdot y3\right) \cdot y0\right) \cdot \left(-y5\right) + \left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right) \cdot y4\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 r3365023 = x;
        double r3365024 = y;
        double r3365025 = r3365023 * r3365024;
        double r3365026 = z;
        double r3365027 = t;
        double r3365028 = r3365026 * r3365027;
        double r3365029 = r3365025 - r3365028;
        double r3365030 = a;
        double r3365031 = b;
        double r3365032 = r3365030 * r3365031;
        double r3365033 = c;
        double r3365034 = i;
        double r3365035 = r3365033 * r3365034;
        double r3365036 = r3365032 - r3365035;
        double r3365037 = r3365029 * r3365036;
        double r3365038 = j;
        double r3365039 = r3365023 * r3365038;
        double r3365040 = k;
        double r3365041 = r3365026 * r3365040;
        double r3365042 = r3365039 - r3365041;
        double r3365043 = y0;
        double r3365044 = r3365043 * r3365031;
        double r3365045 = y1;
        double r3365046 = r3365045 * r3365034;
        double r3365047 = r3365044 - r3365046;
        double r3365048 = r3365042 * r3365047;
        double r3365049 = r3365037 - r3365048;
        double r3365050 = y2;
        double r3365051 = r3365023 * r3365050;
        double r3365052 = y3;
        double r3365053 = r3365026 * r3365052;
        double r3365054 = r3365051 - r3365053;
        double r3365055 = r3365043 * r3365033;
        double r3365056 = r3365045 * r3365030;
        double r3365057 = r3365055 - r3365056;
        double r3365058 = r3365054 * r3365057;
        double r3365059 = r3365049 + r3365058;
        double r3365060 = r3365027 * r3365038;
        double r3365061 = r3365024 * r3365040;
        double r3365062 = r3365060 - r3365061;
        double r3365063 = y4;
        double r3365064 = r3365063 * r3365031;
        double r3365065 = y5;
        double r3365066 = r3365065 * r3365034;
        double r3365067 = r3365064 - r3365066;
        double r3365068 = r3365062 * r3365067;
        double r3365069 = r3365059 + r3365068;
        double r3365070 = r3365027 * r3365050;
        double r3365071 = r3365024 * r3365052;
        double r3365072 = r3365070 - r3365071;
        double r3365073 = r3365063 * r3365033;
        double r3365074 = r3365065 * r3365030;
        double r3365075 = r3365073 - r3365074;
        double r3365076 = r3365072 * r3365075;
        double r3365077 = r3365069 - r3365076;
        double r3365078 = r3365040 * r3365050;
        double r3365079 = r3365038 * r3365052;
        double r3365080 = r3365078 - r3365079;
        double r3365081 = r3365063 * r3365045;
        double r3365082 = r3365065 * r3365043;
        double r3365083 = r3365081 - r3365082;
        double r3365084 = r3365080 * r3365083;
        double r3365085 = r3365077 + r3365084;
        return r3365085;
}
↓
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 r3365086 = y5;
        double r3365087 = -3.5330856269526526e+70;
        bool r3365088 = r3365086 <= r3365087;
        double r3365089 = b;
        double r3365090 = y4;
        double r3365091 = r3365089 * r3365090;
        double r3365092 = i;
        double r3365093 = r3365086 * r3365092;
        double r3365094 = r3365091 - r3365093;
        double r3365095 = t;
        double r3365096 = j;
        double r3365097 = r3365095 * r3365096;
        double r3365098 = y;
        double r3365099 = k;
        double r3365100 = r3365098 * r3365099;
        double r3365101 = r3365097 - r3365100;
        double r3365102 = r3365094 * r3365101;
        double r3365103 = y0;
        double r3365104 = c;
        double r3365105 = r3365103 * r3365104;
        double r3365106 = y1;
        double r3365107 = a;
        double r3365108 = r3365106 * r3365107;
        double r3365109 = r3365105 - r3365108;
        double r3365110 = y2;
        double r3365111 = x;
        double r3365112 = r3365110 * r3365111;
        double r3365113 = y3;
        double r3365114 = z;
        double r3365115 = r3365113 * r3365114;
        double r3365116 = r3365112 - r3365115;
        double r3365117 = r3365109 * r3365116;
        double r3365118 = r3365111 * r3365098;
        double r3365119 = r3365095 * r3365114;
        double r3365120 = r3365118 - r3365119;
        double r3365121 = r3365107 * r3365089;
        double r3365122 = r3365092 * r3365104;
        double r3365123 = r3365121 - r3365122;
        double r3365124 = r3365120 * r3365123;
        double r3365125 = r3365103 * r3365089;
        double r3365126 = r3365092 * r3365106;
        double r3365127 = r3365125 - r3365126;
        double r3365128 = r3365111 * r3365096;
        double r3365129 = r3365114 * r3365099;
        double r3365130 = r3365128 - r3365129;
        double r3365131 = r3365127 * r3365130;
        double r3365132 = r3365124 - r3365131;
        double r3365133 = r3365117 + r3365132;
        double r3365134 = r3365102 + r3365133;
        double r3365135 = r3365104 * r3365090;
        double r3365136 = r3365086 * r3365107;
        double r3365137 = r3365135 - r3365136;
        double r3365138 = r3365110 * r3365095;
        double r3365139 = r3365113 * r3365098;
        double r3365140 = r3365138 - r3365139;
        double r3365141 = cbrt(r3365140);
        double r3365142 = r3365137 * r3365141;
        double r3365143 = r3365141 * r3365141;
        double r3365144 = r3365142 * r3365143;
        double r3365145 = r3365134 - r3365144;
        double r3365146 = r3365110 * r3365099;
        double r3365147 = r3365096 * r3365113;
        double r3365148 = r3365146 - r3365147;
        double r3365149 = r3365148 * r3365103;
        double r3365150 = -r3365086;
        double r3365151 = r3365149 * r3365150;
        double r3365152 = r3365106 * r3365148;
        double r3365153 = r3365152 * r3365090;
        double r3365154 = r3365151 + r3365153;
        double r3365155 = r3365145 + r3365154;
        double r3365156 = -1.3464225199830876e-99;
        bool r3365157 = r3365086 <= r3365156;
        double r3365158 = r3365090 * r3365106;
        double r3365159 = r3365103 * r3365086;
        double r3365160 = r3365158 - r3365159;
        double r3365161 = r3365160 * r3365148;
        double r3365162 = r3365098 * r3365086;
        double r3365163 = r3365162 * r3365113;
        double r3365164 = r3365163 * r3365107;
        double r3365165 = r3365095 * r3365086;
        double r3365166 = r3365110 * r3365165;
        double r3365167 = r3365107 * r3365166;
        double r3365168 = r3365098 * r3365104;
        double r3365169 = r3365090 * r3365168;
        double r3365170 = r3365113 * r3365169;
        double r3365171 = r3365167 + r3365170;
        double r3365172 = r3365164 - r3365171;
        double r3365173 = r3365134 - r3365172;
        double r3365174 = r3365161 + r3365173;
        double r3365175 = 9.64053022884884e-169;
        bool r3365176 = r3365086 <= r3365175;
        double r3365177 = r3365086 * r3365099;
        double r3365178 = r3365177 * r3365098;
        double r3365179 = r3365178 * r3365092;
        double r3365180 = r3365091 * r3365098;
        double r3365181 = r3365099 * r3365180;
        double r3365182 = r3365086 * r3365096;
        double r3365183 = r3365182 * r3365092;
        double r3365184 = r3365095 * r3365183;
        double r3365185 = r3365181 + r3365184;
        double r3365186 = r3365179 - r3365185;
        double r3365187 = r3365186 + r3365133;
        double r3365188 = r3365187 - r3365144;
        double r3365189 = r3365188 + r3365161;
        double r3365190 = r3365176 ? r3365189 : r3365155;
        double r3365191 = r3365157 ? r3365174 : r3365190;
        double r3365192 = r3365088 ? r3365155 : r3365191;
        return r3365192;
}

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 3 regimes

  2. if y5 < -3.5330856269526526e+70 or 9.64053022884884e-169 < y5

    1. Initial program 27.4

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

    3. Applied add-cube-cbrt27.5

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

    4. Applied associate-*l*27.5

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

    6. Applied sub-neg27.5

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

    7. Applied distribute-rgt-in27.5

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

    8. Taylor expanded around -inf 29.4

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

    9. Simplified27.9

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

    11. Applied distribute-lft-neg-in27.9

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

    12. Applied associate-*l*26.5

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

    if -3.5330856269526526e+70 < y5 < -1.3464225199830876e-99

    1. Initial program 24.1

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

    2. Taylor expanded around -inf 25.9

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

    if -1.3464225199830876e-99 < y5 < 9.64053022884884e-169

    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. Using strategy rm

    3. Applied add-cube-cbrt26.0

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

    4. Applied associate-*l*26.0

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

    5. Taylor expanded around inf 27.3

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

  4. Final simplification26.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \le -3.5330856269526526 \cdot 10^{+70}:\\ \;\;\;\;\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(\left(\left(y2 \cdot k - j \cdot y3\right) \cdot y0\right) \cdot \left(-y5\right) + \left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right) \cdot y4\right)\\ \mathbf{elif}\;y5 \le -1.3464225199830876 \cdot 10^{-99}:\\ \;\;\;\;\left(y4 \cdot y1 - y0 \cdot y5\right) \cdot \left(y2 \cdot k - j \cdot y3\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(\left(\left(y \cdot y5\right) \cdot y3\right) \cdot a - \left(a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) + y3 \cdot \left(y4 \cdot \left(y \cdot c\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y5 \le 9.64053022884884 \cdot 10^{-169}:\\ \;\;\;\;\left(\left(\left(\left(\left(y5 \cdot k\right) \cdot y\right) \cdot i - \left(k \cdot \left(\left(b \cdot y4\right) \cdot y\right) + t \cdot \left(\left(y5 \cdot j\right) \cdot i\right)\right)\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot \left(y2 \cdot k - j \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;\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(c \cdot y4 - y5 \cdot a\right) \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right) \cdot \left(\sqrt[3]{y2 \cdot t - y3 \cdot y} \cdot \sqrt[3]{y2 \cdot t - y3 \cdot y}\right)\right) + \left(\left(\left(y2 \cdot k - j \cdot y3\right) \cdot y0\right) \cdot \left(-y5\right) + \left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right) \cdot y4\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019132 
(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)))))