Average Error: 27.1 → 28.6
Time: 1.7m
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}\;y3 \le -3.595776988237863373771750623877926458958 \cdot 10^{-185}:\\ \;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(\left(\sqrt[3]{y4 \cdot c - y5 \cdot a} \cdot \sqrt[3]{y4 \cdot c - y5 \cdot a}\right) \cdot \left(y2 \cdot t - y \cdot y3\right)\right) \cdot \sqrt[3]{y4 \cdot c - y5 \cdot a}\right)\\ \mathbf{elif}\;y3 \le 8.418886350060508995884021700772650744265 \cdot 10^{-139}:\\ \;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(\left(\left(\left(y3 \cdot y1\right) \cdot z - \left(y1 \cdot y2\right) \cdot x\right) \cdot a - z \cdot \left(c \cdot \left(y0 \cdot y3\right)\right)\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \mathbf{elif}\;y3 \le 547616716379274825875150864384:\\ \;\;\;\;\left(\left(\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(a \cdot \left(\left(y \cdot y5\right) \cdot y3\right) - \left(a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right) + \left(y4 \cdot \left(y \cdot c\right)\right) \cdot y3\right)\right)\right) + \left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;y3 \le 5.178775168900364758784354220649389195172 \cdot 10^{174}:\\ \;\;\;\;\left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\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) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\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(i \cdot \left(z \cdot \left(y1 \cdot k\right)\right) - \left(i \cdot \left(\left(x \cdot y1\right) \cdot j\right) + \left(\left(y0 \cdot b\right) \cdot z\right) \cdot k\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \end{array}\]
\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)
↓
\begin{array}{l}
\mathbf{if}\;y3 \le -3.595776988237863373771750623877926458958 \cdot 10^{-185}:\\
\;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(\left(\sqrt[3]{y4 \cdot c - y5 \cdot a} \cdot \sqrt[3]{y4 \cdot c - y5 \cdot a}\right) \cdot \left(y2 \cdot t - y \cdot y3\right)\right) \cdot \sqrt[3]{y4 \cdot c - y5 \cdot a}\right)\\

\mathbf{elif}\;y3 \le 8.418886350060508995884021700772650744265 \cdot 10^{-139}:\\
\;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(\left(\left(\left(y3 \cdot y1\right) \cdot z - \left(y1 \cdot y2\right) \cdot x\right) \cdot a - z \cdot \left(c \cdot \left(y0 \cdot y3\right)\right)\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\

\mathbf{elif}\;y3 \le 547616716379274825875150864384:\\
\;\;\;\;\left(\left(\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(a \cdot \left(\left(y \cdot y5\right) \cdot y3\right) - \left(a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right) + \left(y4 \cdot \left(y \cdot c\right)\right) \cdot y3\right)\right)\right) + \left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\

\mathbf{elif}\;y3 \le 5.178775168900364758784354220649389195172 \cdot 10^{174}:\\
\;\;\;\;\left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\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) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
        double r4826059 = x;
        double r4826060 = y;
        double r4826061 = r4826059 * r4826060;
        double r4826062 = z;
        double r4826063 = t;
        double r4826064 = r4826062 * r4826063;
        double r4826065 = r4826061 - r4826064;
        double r4826066 = a;
        double r4826067 = b;
        double r4826068 = r4826066 * r4826067;
        double r4826069 = c;
        double r4826070 = i;
        double r4826071 = r4826069 * r4826070;
        double r4826072 = r4826068 - r4826071;
        double r4826073 = r4826065 * r4826072;
        double r4826074 = j;
        double r4826075 = r4826059 * r4826074;
        double r4826076 = k;
        double r4826077 = r4826062 * r4826076;
        double r4826078 = r4826075 - r4826077;
        double r4826079 = y0;
        double r4826080 = r4826079 * r4826067;
        double r4826081 = y1;
        double r4826082 = r4826081 * r4826070;
        double r4826083 = r4826080 - r4826082;
        double r4826084 = r4826078 * r4826083;
        double r4826085 = r4826073 - r4826084;
        double r4826086 = y2;
        double r4826087 = r4826059 * r4826086;
        double r4826088 = y3;
        double r4826089 = r4826062 * r4826088;
        double r4826090 = r4826087 - r4826089;
        double r4826091 = r4826079 * r4826069;
        double r4826092 = r4826081 * r4826066;
        double r4826093 = r4826091 - r4826092;
        double r4826094 = r4826090 * r4826093;
        double r4826095 = r4826085 + r4826094;
        double r4826096 = r4826063 * r4826074;
        double r4826097 = r4826060 * r4826076;
        double r4826098 = r4826096 - r4826097;
        double r4826099 = y4;
        double r4826100 = r4826099 * r4826067;
        double r4826101 = y5;
        double r4826102 = r4826101 * r4826070;
        double r4826103 = r4826100 - r4826102;
        double r4826104 = r4826098 * r4826103;
        double r4826105 = r4826095 + r4826104;
        double r4826106 = r4826063 * r4826086;
        double r4826107 = r4826060 * r4826088;
        double r4826108 = r4826106 - r4826107;
        double r4826109 = r4826099 * r4826069;
        double r4826110 = r4826101 * r4826066;
        double r4826111 = r4826109 - r4826110;
        double r4826112 = r4826108 * r4826111;
        double r4826113 = r4826105 - r4826112;
        double r4826114 = r4826076 * r4826086;
        double r4826115 = r4826074 * r4826088;
        double r4826116 = r4826114 - r4826115;
        double r4826117 = r4826099 * r4826081;
        double r4826118 = r4826101 * r4826079;
        double r4826119 = r4826117 - r4826118;
        double r4826120 = r4826116 * r4826119;
        double r4826121 = r4826113 + r4826120;
        return r4826121;
}
↓
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 r4826122 = y3;
        double r4826123 = -3.5957769882378634e-185;
        bool r4826124 = r4826122 <= r4826123;
        double r4826125 = y2;
        double r4826126 = k;
        double r4826127 = r4826125 * r4826126;
        double r4826128 = j;
        double r4826129 = r4826122 * r4826128;
        double r4826130 = r4826127 - r4826129;
        double r4826131 = y1;
        double r4826132 = y4;
        double r4826133 = r4826131 * r4826132;
        double r4826134 = y0;
        double r4826135 = y5;
        double r4826136 = r4826134 * r4826135;
        double r4826137 = r4826133 - r4826136;
        double r4826138 = r4826130 * r4826137;
        double r4826139 = c;
        double r4826140 = r4826134 * r4826139;
        double r4826141 = a;
        double r4826142 = r4826131 * r4826141;
        double r4826143 = r4826140 - r4826142;
        double r4826144 = x;
        double r4826145 = r4826125 * r4826144;
        double r4826146 = z;
        double r4826147 = r4826122 * r4826146;
        double r4826148 = r4826145 - r4826147;
        double r4826149 = r4826143 * r4826148;
        double r4826150 = y;
        double r4826151 = r4826144 * r4826150;
        double r4826152 = t;
        double r4826153 = r4826152 * r4826146;
        double r4826154 = r4826151 - r4826153;
        double r4826155 = b;
        double r4826156 = r4826141 * r4826155;
        double r4826157 = i;
        double r4826158 = r4826157 * r4826139;
        double r4826159 = r4826156 - r4826158;
        double r4826160 = r4826154 * r4826159;
        double r4826161 = r4826134 * r4826155;
        double r4826162 = r4826157 * r4826131;
        double r4826163 = r4826161 - r4826162;
        double r4826164 = r4826144 * r4826128;
        double r4826165 = r4826146 * r4826126;
        double r4826166 = r4826164 - r4826165;
        double r4826167 = r4826163 * r4826166;
        double r4826168 = r4826160 - r4826167;
        double r4826169 = r4826149 + r4826168;
        double r4826170 = r4826152 * r4826128;
        double r4826171 = r4826150 * r4826126;
        double r4826172 = r4826170 - r4826171;
        double r4826173 = r4826132 * r4826155;
        double r4826174 = r4826157 * r4826135;
        double r4826175 = r4826173 - r4826174;
        double r4826176 = r4826172 * r4826175;
        double r4826177 = r4826169 + r4826176;
        double r4826178 = r4826132 * r4826139;
        double r4826179 = r4826135 * r4826141;
        double r4826180 = r4826178 - r4826179;
        double r4826181 = cbrt(r4826180);
        double r4826182 = r4826181 * r4826181;
        double r4826183 = r4826125 * r4826152;
        double r4826184 = r4826150 * r4826122;
        double r4826185 = r4826183 - r4826184;
        double r4826186 = r4826182 * r4826185;
        double r4826187 = r4826186 * r4826181;
        double r4826188 = r4826177 - r4826187;
        double r4826189 = r4826138 + r4826188;
        double r4826190 = 8.418886350060509e-139;
        bool r4826191 = r4826122 <= r4826190;
        double r4826192 = r4826122 * r4826131;
        double r4826193 = r4826192 * r4826146;
        double r4826194 = r4826131 * r4826125;
        double r4826195 = r4826194 * r4826144;
        double r4826196 = r4826193 - r4826195;
        double r4826197 = r4826196 * r4826141;
        double r4826198 = r4826134 * r4826122;
        double r4826199 = r4826139 * r4826198;
        double r4826200 = r4826146 * r4826199;
        double r4826201 = r4826197 - r4826200;
        double r4826202 = r4826201 + r4826168;
        double r4826203 = r4826202 + r4826176;
        double r4826204 = r4826185 * r4826180;
        double r4826205 = r4826203 - r4826204;
        double r4826206 = r4826138 + r4826205;
        double r4826207 = 5.476167163792748e+29;
        bool r4826208 = r4826122 <= r4826207;
        double r4826209 = r4826150 * r4826135;
        double r4826210 = r4826209 * r4826122;
        double r4826211 = r4826141 * r4826210;
        double r4826212 = r4826135 * r4826152;
        double r4826213 = r4826125 * r4826212;
        double r4826214 = r4826141 * r4826213;
        double r4826215 = r4826150 * r4826139;
        double r4826216 = r4826132 * r4826215;
        double r4826217 = r4826216 * r4826122;
        double r4826218 = r4826214 + r4826217;
        double r4826219 = r4826211 - r4826218;
        double r4826220 = r4826177 - r4826219;
        double r4826221 = r4826220 + r4826138;
        double r4826222 = 5.178775168900365e+174;
        bool r4826223 = r4826122 <= r4826222;
        double r4826224 = r4826176 + r4826168;
        double r4826225 = r4826224 - r4826204;
        double r4826226 = r4826225 + r4826138;
        double r4826227 = r4826131 * r4826126;
        double r4826228 = r4826146 * r4826227;
        double r4826229 = r4826157 * r4826228;
        double r4826230 = r4826144 * r4826131;
        double r4826231 = r4826230 * r4826128;
        double r4826232 = r4826157 * r4826231;
        double r4826233 = r4826161 * r4826146;
        double r4826234 = r4826233 * r4826126;
        double r4826235 = r4826232 + r4826234;
        double r4826236 = r4826229 - r4826235;
        double r4826237 = r4826160 - r4826236;
        double r4826238 = r4826149 + r4826237;
        double r4826239 = r4826238 + r4826176;
        double r4826240 = r4826239 - r4826204;
        double r4826241 = r4826138 + r4826240;
        double r4826242 = r4826223 ? r4826226 : r4826241;
        double r4826243 = r4826208 ? r4826221 : r4826242;
        double r4826244 = r4826191 ? r4826206 : r4826243;
        double r4826245 = r4826124 ? r4826189 : r4826244;
        return r4826245;
}

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 5 regimes

  2. if y3 < -3.5957769882378634e-185

    1. Initial program 27.2

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

    3. Applied add-cube-cbrt27.3

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

    4. Applied associate-*r*27.3

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

    if -3.5957769882378634e-185 < y3 < 8.418886350060509e-139

    1. Initial program 26.2

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

    2. Taylor expanded around inf 28.5

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

    3. Simplified27.1

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

    if 8.418886350060509e-139 < y3 < 5.476167163792748e+29

    1. Initial program 26.3

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

    2. Taylor expanded around inf 29.4

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

    if 5.476167163792748e+29 < y3 < 5.178775168900365e+174

    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 0 32.6

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

    if 5.178775168900365e+174 < y3

    1. Initial program 34.8

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

    2. Taylor expanded around inf 36.2

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \color{blue}{\left(i \cdot \left(z \cdot \left(y1 \cdot k\right)\right) - \left(k \cdot \left(z \cdot \left(b \cdot y0\right)\right) + i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  3. Recombined 5 regimes into one program.

  4. Final simplification28.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \le -3.595776988237863373771750623877926458958 \cdot 10^{-185}:\\ \;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(\left(\sqrt[3]{y4 \cdot c - y5 \cdot a} \cdot \sqrt[3]{y4 \cdot c - y5 \cdot a}\right) \cdot \left(y2 \cdot t - y \cdot y3\right)\right) \cdot \sqrt[3]{y4 \cdot c - y5 \cdot a}\right)\\ \mathbf{elif}\;y3 \le 8.418886350060508995884021700772650744265 \cdot 10^{-139}:\\ \;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(\left(\left(\left(y3 \cdot y1\right) \cdot z - \left(y1 \cdot y2\right) \cdot x\right) \cdot a - z \cdot \left(c \cdot \left(y0 \cdot y3\right)\right)\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \mathbf{elif}\;y3 \le 547616716379274825875150864384:\\ \;\;\;\;\left(\left(\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) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(a \cdot \left(\left(y \cdot y5\right) \cdot y3\right) - \left(a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right) + \left(y4 \cdot \left(y \cdot c\right)\right) \cdot y3\right)\right)\right) + \left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;y3 \le 5.178775168900364758784354220649389195172 \cdot 10^{174}:\\ \;\;\;\;\left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\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) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y2 \cdot k - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\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(i \cdot \left(z \cdot \left(y1 \cdot k\right)\right) - \left(i \cdot \left(\left(x \cdot y1\right) \cdot j\right) + \left(\left(y0 \cdot b\right) \cdot z\right) \cdot k\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y2 \cdot t - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))))