Average Error: 26.8 → 28.9
Time: 2.9m
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}\;c \le -5.42423195281810071178944798742094235422 \cdot 10^{-5}:\\ \;\;\;\;\left(\left(\left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(\sqrt[3]{j \cdot x - z \cdot k} \cdot \sqrt[3]{j \cdot x - z \cdot k}\right) \cdot \left(\left(y0 \cdot b - y1 \cdot i\right) \cdot \sqrt[3]{j \cdot x - z \cdot k}\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\\ \mathbf{elif}\;c \le -1.063843804848684809768563552980133772853 \cdot 10^{-208}:\\ \;\;\;\;\left(\left(\left(\left(a \cdot \left(\left(z \cdot y1\right) \cdot y3\right) - \left(\left(\left(y1 \cdot y2\right) \cdot x\right) \cdot a + \left(\left(y3 \cdot c\right) \cdot z\right) \cdot y0\right)\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{elif}\;c \le 1.213882826940811552324221651193040372757 \cdot 10^{-284}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(\left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(k \cdot \left(i \cdot \left(y5 \cdot y\right)\right) - \left(\left(y4 \cdot \left(b \cdot y\right)\right) \cdot k + t \cdot \left(\left(j \cdot y5\right) \cdot i\right)\right)\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\\ \mathbf{elif}\;c \le 4.317409275790695709030528357537462504805 \cdot 10^{-16}:\\ \;\;\;\;\left(\left(\left(\left(a \cdot \left(\left(z \cdot y1\right) \cdot y3\right) - \left(\left(\left(y1 \cdot y2\right) \cdot x\right) \cdot a + \left(\left(y3 \cdot c\right) \cdot z\right) \cdot y0\right)\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(\sqrt[3]{j \cdot x - z \cdot k} \cdot \sqrt[3]{j \cdot x - z \cdot k}\right) \cdot \left(\left(y0 \cdot b - y1 \cdot i\right) \cdot \sqrt[3]{j \cdot x - z \cdot k}\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\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}\;c \le -5.42423195281810071178944798742094235422 \cdot 10^{-5}:\\
\;\;\;\;\left(\left(\left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(\sqrt[3]{j \cdot x - z \cdot k} \cdot \sqrt[3]{j \cdot x - z \cdot k}\right) \cdot \left(\left(y0 \cdot b - y1 \cdot i\right) \cdot \sqrt[3]{j \cdot x - z \cdot k}\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\\

\mathbf{elif}\;c \le -1.063843804848684809768563552980133772853 \cdot 10^{-208}:\\
\;\;\;\;\left(\left(\left(\left(a \cdot \left(\left(z \cdot y1\right) \cdot y3\right) - \left(\left(\left(y1 \cdot y2\right) \cdot x\right) \cdot a + \left(\left(y3 \cdot c\right) \cdot z\right) \cdot y0\right)\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\

\mathbf{elif}\;c \le 1.213882826940811552324221651193040372757 \cdot 10^{-284}:\\
\;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(\left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(k \cdot \left(i \cdot \left(y5 \cdot y\right)\right) - \left(\left(y4 \cdot \left(b \cdot y\right)\right) \cdot k + t \cdot \left(\left(j \cdot y5\right) \cdot i\right)\right)\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\\

\mathbf{elif}\;c \le 4.317409275790695709030528357537462504805 \cdot 10^{-16}:\\
\;\;\;\;\left(\left(\left(\left(a \cdot \left(\left(z \cdot y1\right) \cdot y3\right) - \left(\left(\left(y1 \cdot y2\right) \cdot x\right) \cdot a + \left(\left(y3 \cdot c\right) \cdot z\right) \cdot y0\right)\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(\sqrt[3]{j \cdot x - z \cdot k} \cdot \sqrt[3]{j \cdot x - z \cdot k}\right) \cdot \left(\left(y0 \cdot b - y1 \cdot i\right) \cdot \sqrt[3]{j \cdot x - z \cdot k}\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\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 r4698986 = x;
        double r4698987 = y;
        double r4698988 = r4698986 * r4698987;
        double r4698989 = z;
        double r4698990 = t;
        double r4698991 = r4698989 * r4698990;
        double r4698992 = r4698988 - r4698991;
        double r4698993 = a;
        double r4698994 = b;
        double r4698995 = r4698993 * r4698994;
        double r4698996 = c;
        double r4698997 = i;
        double r4698998 = r4698996 * r4698997;
        double r4698999 = r4698995 - r4698998;
        double r4699000 = r4698992 * r4698999;
        double r4699001 = j;
        double r4699002 = r4698986 * r4699001;
        double r4699003 = k;
        double r4699004 = r4698989 * r4699003;
        double r4699005 = r4699002 - r4699004;
        double r4699006 = y0;
        double r4699007 = r4699006 * r4698994;
        double r4699008 = y1;
        double r4699009 = r4699008 * r4698997;
        double r4699010 = r4699007 - r4699009;
        double r4699011 = r4699005 * r4699010;
        double r4699012 = r4699000 - r4699011;
        double r4699013 = y2;
        double r4699014 = r4698986 * r4699013;
        double r4699015 = y3;
        double r4699016 = r4698989 * r4699015;
        double r4699017 = r4699014 - r4699016;
        double r4699018 = r4699006 * r4698996;
        double r4699019 = r4699008 * r4698993;
        double r4699020 = r4699018 - r4699019;
        double r4699021 = r4699017 * r4699020;
        double r4699022 = r4699012 + r4699021;
        double r4699023 = r4698990 * r4699001;
        double r4699024 = r4698987 * r4699003;
        double r4699025 = r4699023 - r4699024;
        double r4699026 = y4;
        double r4699027 = r4699026 * r4698994;
        double r4699028 = y5;
        double r4699029 = r4699028 * r4698997;
        double r4699030 = r4699027 - r4699029;
        double r4699031 = r4699025 * r4699030;
        double r4699032 = r4699022 + r4699031;
        double r4699033 = r4698990 * r4699013;
        double r4699034 = r4698987 * r4699015;
        double r4699035 = r4699033 - r4699034;
        double r4699036 = r4699026 * r4698996;
        double r4699037 = r4699028 * r4698993;
        double r4699038 = r4699036 - r4699037;
        double r4699039 = r4699035 * r4699038;
        double r4699040 = r4699032 - r4699039;
        double r4699041 = r4699003 * r4699013;
        double r4699042 = r4699001 * r4699015;
        double r4699043 = r4699041 - r4699042;
        double r4699044 = r4699026 * r4699008;
        double r4699045 = r4699028 * r4699006;
        double r4699046 = r4699044 - r4699045;
        double r4699047 = r4699043 * r4699046;
        double r4699048 = r4699040 + r4699047;
        return r4699048;
}
↓
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 r4699049 = c;
        double r4699050 = -5.424231952818101e-05;
        bool r4699051 = r4699049 <= r4699050;
        double r4699052 = b;
        double r4699053 = a;
        double r4699054 = r4699052 * r4699053;
        double r4699055 = i;
        double r4699056 = r4699049 * r4699055;
        double r4699057 = r4699054 - r4699056;
        double r4699058 = y;
        double r4699059 = x;
        double r4699060 = r4699058 * r4699059;
        double r4699061 = t;
        double r4699062 = z;
        double r4699063 = r4699061 * r4699062;
        double r4699064 = r4699060 - r4699063;
        double r4699065 = r4699057 * r4699064;
        double r4699066 = j;
        double r4699067 = r4699066 * r4699059;
        double r4699068 = k;
        double r4699069 = r4699062 * r4699068;
        double r4699070 = r4699067 - r4699069;
        double r4699071 = cbrt(r4699070);
        double r4699072 = r4699071 * r4699071;
        double r4699073 = y0;
        double r4699074 = r4699073 * r4699052;
        double r4699075 = y1;
        double r4699076 = r4699075 * r4699055;
        double r4699077 = r4699074 - r4699076;
        double r4699078 = r4699077 * r4699071;
        double r4699079 = r4699072 * r4699078;
        double r4699080 = r4699065 - r4699079;
        double r4699081 = y2;
        double r4699082 = r4699081 * r4699059;
        double r4699083 = y3;
        double r4699084 = r4699062 * r4699083;
        double r4699085 = r4699082 - r4699084;
        double r4699086 = r4699073 * r4699049;
        double r4699087 = r4699053 * r4699075;
        double r4699088 = r4699086 - r4699087;
        double r4699089 = r4699085 * r4699088;
        double r4699090 = r4699080 + r4699089;
        double r4699091 = y4;
        double r4699092 = r4699052 * r4699091;
        double r4699093 = y5;
        double r4699094 = r4699093 * r4699055;
        double r4699095 = r4699092 - r4699094;
        double r4699096 = r4699066 * r4699061;
        double r4699097 = r4699068 * r4699058;
        double r4699098 = r4699096 - r4699097;
        double r4699099 = r4699095 * r4699098;
        double r4699100 = r4699090 + r4699099;
        double r4699101 = r4699091 * r4699049;
        double r4699102 = r4699093 * r4699053;
        double r4699103 = r4699101 - r4699102;
        double r4699104 = r4699081 * r4699061;
        double r4699105 = r4699083 * r4699058;
        double r4699106 = r4699104 - r4699105;
        double r4699107 = r4699103 * r4699106;
        double r4699108 = r4699100 - r4699107;
        double r4699109 = -1.0638438048486848e-208;
        bool r4699110 = r4699049 <= r4699109;
        double r4699111 = r4699062 * r4699075;
        double r4699112 = r4699111 * r4699083;
        double r4699113 = r4699053 * r4699112;
        double r4699114 = r4699075 * r4699081;
        double r4699115 = r4699114 * r4699059;
        double r4699116 = r4699115 * r4699053;
        double r4699117 = r4699083 * r4699049;
        double r4699118 = r4699117 * r4699062;
        double r4699119 = r4699118 * r4699073;
        double r4699120 = r4699116 + r4699119;
        double r4699121 = r4699113 - r4699120;
        double r4699122 = r4699077 * r4699070;
        double r4699123 = r4699065 - r4699122;
        double r4699124 = r4699121 + r4699123;
        double r4699125 = r4699124 + r4699099;
        double r4699126 = r4699125 - r4699107;
        double r4699127 = r4699068 * r4699081;
        double r4699128 = r4699083 * r4699066;
        double r4699129 = r4699127 - r4699128;
        double r4699130 = r4699075 * r4699091;
        double r4699131 = r4699093 * r4699073;
        double r4699132 = r4699130 - r4699131;
        double r4699133 = r4699129 * r4699132;
        double r4699134 = r4699126 + r4699133;
        double r4699135 = 1.2138828269408116e-284;
        bool r4699136 = r4699049 <= r4699135;
        double r4699137 = r4699089 + r4699123;
        double r4699138 = r4699093 * r4699058;
        double r4699139 = r4699055 * r4699138;
        double r4699140 = r4699068 * r4699139;
        double r4699141 = r4699052 * r4699058;
        double r4699142 = r4699091 * r4699141;
        double r4699143 = r4699142 * r4699068;
        double r4699144 = r4699066 * r4699093;
        double r4699145 = r4699144 * r4699055;
        double r4699146 = r4699061 * r4699145;
        double r4699147 = r4699143 + r4699146;
        double r4699148 = r4699140 - r4699147;
        double r4699149 = r4699137 + r4699148;
        double r4699150 = r4699149 - r4699107;
        double r4699151 = r4699133 + r4699150;
        double r4699152 = 4.3174092757906957e-16;
        bool r4699153 = r4699049 <= r4699152;
        double r4699154 = r4699153 ? r4699134 : r4699108;
        double r4699155 = r4699136 ? r4699151 : r4699154;
        double r4699156 = r4699110 ? r4699134 : r4699155;
        double r4699157 = r4699051 ? r4699108 : r4699156;
        return r4699157;
}

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 c < -5.424231952818101e-05 or 4.3174092757906957e-16 < c

    1. Initial program 27.6

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

    3. Applied add-cube-cbrt27.7

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

    4. Applied associate-*l*27.7

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

    5. Taylor expanded around 0 30.8

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \sqrt[3]{x \cdot j - z \cdot k}\right) \cdot \left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \color{blue}{0}\]

    if -5.424231952818101e-05 < c < -1.0638438048486848e-208 or 1.2138828269408116e-284 < c < 4.3174092757906957e-16

    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 27.1

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

    if -1.0638438048486848e-208 < c < 1.2138828269408116e-284

    1. Initial program 26.9

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

    2. Taylor expanded around inf 29.8

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

  4. Final simplification28.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;c \le -5.42423195281810071178944798742094235422 \cdot 10^{-5}:\\ \;\;\;\;\left(\left(\left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(\sqrt[3]{j \cdot x - z \cdot k} \cdot \sqrt[3]{j \cdot x - z \cdot k}\right) \cdot \left(\left(y0 \cdot b - y1 \cdot i\right) \cdot \sqrt[3]{j \cdot x - z \cdot k}\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\\ \mathbf{elif}\;c \le -1.063843804848684809768563552980133772853 \cdot 10^{-208}:\\ \;\;\;\;\left(\left(\left(\left(a \cdot \left(\left(z \cdot y1\right) \cdot y3\right) - \left(\left(\left(y1 \cdot y2\right) \cdot x\right) \cdot a + \left(\left(y3 \cdot c\right) \cdot z\right) \cdot y0\right)\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{elif}\;c \le 1.213882826940811552324221651193040372757 \cdot 10^{-284}:\\ \;\;\;\;\left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) + \left(\left(\left(\left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(k \cdot \left(i \cdot \left(y5 \cdot y\right)\right) - \left(\left(y4 \cdot \left(b \cdot y\right)\right) \cdot k + t \cdot \left(\left(j \cdot y5\right) \cdot i\right)\right)\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\\ \mathbf{elif}\;c \le 4.317409275790695709030528357537462504805 \cdot 10^{-16}:\\ \;\;\;\;\left(\left(\left(\left(a \cdot \left(\left(z \cdot y1\right) \cdot y3\right) - \left(\left(\left(y1 \cdot y2\right) \cdot x\right) \cdot a + \left(\left(y3 \cdot c\right) \cdot z\right) \cdot y0\right)\right) + \left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - z \cdot k\right)\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right) + \left(k \cdot y2 - y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(b \cdot a - c \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) - \left(\sqrt[3]{j \cdot x - z \cdot k} \cdot \sqrt[3]{j \cdot x - z \cdot k}\right) \cdot \left(\left(y0 \cdot b - y1 \cdot i\right) \cdot \sqrt[3]{j \cdot x - z \cdot k}\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(y0 \cdot c - a \cdot y1\right)\right) + \left(b \cdot y4 - y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(y4 \cdot c - y5 \cdot a\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(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)))))