Average Error: 26.6 → 27.7
Time: 1.3m
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}\;y \le -3.068136913593689871171353580308452333931 \cdot 10^{57}:\\ \;\;\;\;\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) + 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)\\ \mathbf{elif}\;y \le \frac{254462235520565}{3.31961245510479436680992629095292892081 \cdot 10^{181}}:\\ \;\;\;\;\left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\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(\sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)}\right) \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\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}\;y \le -3.068136913593689871171353580308452333931 \cdot 10^{57}:\\
\;\;\;\;\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) + 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)\\

\mathbf{elif}\;y \le \frac{254462235520565}{3.31961245510479436680992629095292892081 \cdot 10^{181}}:\\
\;\;\;\;\left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\

\mathbf{else}:\\
\;\;\;\;\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(\sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)}\right) \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\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 r128005 = x;
        double r128006 = y;
        double r128007 = r128005 * r128006;
        double r128008 = z;
        double r128009 = t;
        double r128010 = r128008 * r128009;
        double r128011 = r128007 - r128010;
        double r128012 = a;
        double r128013 = b;
        double r128014 = r128012 * r128013;
        double r128015 = c;
        double r128016 = i;
        double r128017 = r128015 * r128016;
        double r128018 = r128014 - r128017;
        double r128019 = r128011 * r128018;
        double r128020 = j;
        double r128021 = r128005 * r128020;
        double r128022 = k;
        double r128023 = r128008 * r128022;
        double r128024 = r128021 - r128023;
        double r128025 = y0;
        double r128026 = r128025 * r128013;
        double r128027 = y1;
        double r128028 = r128027 * r128016;
        double r128029 = r128026 - r128028;
        double r128030 = r128024 * r128029;
        double r128031 = r128019 - r128030;
        double r128032 = y2;
        double r128033 = r128005 * r128032;
        double r128034 = y3;
        double r128035 = r128008 * r128034;
        double r128036 = r128033 - r128035;
        double r128037 = r128025 * r128015;
        double r128038 = r128027 * r128012;
        double r128039 = r128037 - r128038;
        double r128040 = r128036 * r128039;
        double r128041 = r128031 + r128040;
        double r128042 = r128009 * r128020;
        double r128043 = r128006 * r128022;
        double r128044 = r128042 - r128043;
        double r128045 = y4;
        double r128046 = r128045 * r128013;
        double r128047 = y5;
        double r128048 = r128047 * r128016;
        double r128049 = r128046 - r128048;
        double r128050 = r128044 * r128049;
        double r128051 = r128041 + r128050;
        double r128052 = r128009 * r128032;
        double r128053 = r128006 * r128034;
        double r128054 = r128052 - r128053;
        double r128055 = r128045 * r128015;
        double r128056 = r128047 * r128012;
        double r128057 = r128055 - r128056;
        double r128058 = r128054 * r128057;
        double r128059 = r128051 - r128058;
        double r128060 = r128022 * r128032;
        double r128061 = r128020 * r128034;
        double r128062 = r128060 - r128061;
        double r128063 = r128045 * r128027;
        double r128064 = r128047 * r128025;
        double r128065 = r128063 - r128064;
        double r128066 = r128062 * r128065;
        double r128067 = r128059 + r128066;
        return r128067;
}
↓
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 r128068 = y;
        double r128069 = -3.06813691359369e+57;
        bool r128070 = r128068 <= r128069;
        double r128071 = x;
        double r128072 = r128071 * r128068;
        double r128073 = z;
        double r128074 = t;
        double r128075 = r128073 * r128074;
        double r128076 = r128072 - r128075;
        double r128077 = a;
        double r128078 = b;
        double r128079 = r128077 * r128078;
        double r128080 = c;
        double r128081 = i;
        double r128082 = r128080 * r128081;
        double r128083 = r128079 - r128082;
        double r128084 = r128076 * r128083;
        double r128085 = j;
        double r128086 = r128071 * r128085;
        double r128087 = k;
        double r128088 = r128073 * r128087;
        double r128089 = r128086 - r128088;
        double r128090 = y0;
        double r128091 = r128090 * r128078;
        double r128092 = y1;
        double r128093 = r128092 * r128081;
        double r128094 = r128091 - r128093;
        double r128095 = r128089 * r128094;
        double r128096 = r128084 - r128095;
        double r128097 = 0.0;
        double r128098 = r128096 + r128097;
        double r128099 = r128074 * r128085;
        double r128100 = r128068 * r128087;
        double r128101 = r128099 - r128100;
        double r128102 = y4;
        double r128103 = r128102 * r128078;
        double r128104 = y5;
        double r128105 = r128104 * r128081;
        double r128106 = r128103 - r128105;
        double r128107 = r128101 * r128106;
        double r128108 = r128098 + r128107;
        double r128109 = y2;
        double r128110 = r128074 * r128109;
        double r128111 = y3;
        double r128112 = r128068 * r128111;
        double r128113 = r128110 - r128112;
        double r128114 = r128102 * r128080;
        double r128115 = r128104 * r128077;
        double r128116 = r128114 - r128115;
        double r128117 = r128113 * r128116;
        double r128118 = r128108 - r128117;
        double r128119 = r128087 * r128109;
        double r128120 = r128085 * r128111;
        double r128121 = r128119 - r128120;
        double r128122 = r128102 * r128092;
        double r128123 = r128104 * r128090;
        double r128124 = r128122 - r128123;
        double r128125 = r128121 * r128124;
        double r128126 = r128118 + r128125;
        double r128127 = 254462235520565.0;
        double r128128 = 3.3196124551047944e+181;
        double r128129 = r128127 / r128128;
        bool r128130 = r128068 <= r128129;
        double r128131 = r128073 * r128080;
        double r128132 = r128081 * r128131;
        double r128133 = r128074 * r128132;
        double r128134 = r128068 * r128071;
        double r128135 = r128080 * r128134;
        double r128136 = r128081 * r128135;
        double r128137 = r128073 * r128078;
        double r128138 = r128074 * r128137;
        double r128139 = r128077 * r128138;
        double r128140 = r128136 + r128139;
        double r128141 = r128133 - r128140;
        double r128142 = r128141 - r128095;
        double r128143 = r128071 * r128109;
        double r128144 = r128073 * r128111;
        double r128145 = r128143 - r128144;
        double r128146 = r128090 * r128080;
        double r128147 = r128092 * r128077;
        double r128148 = r128146 - r128147;
        double r128149 = r128145 * r128148;
        double r128150 = r128142 + r128149;
        double r128151 = r128150 + r128107;
        double r128152 = r128151 - r128117;
        double r128153 = r128152 + r128125;
        double r128154 = r128096 + r128149;
        double r128155 = r128154 + r128107;
        double r128156 = r128155 - r128117;
        double r128157 = cbrt(r128125);
        double r128158 = r128157 * r128157;
        double r128159 = r128158 * r128157;
        double r128160 = r128156 + r128159;
        double r128161 = r128130 ? r128153 : r128160;
        double r128162 = r128070 ? r128126 : r128161;
        return r128162;
}

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 y < -3.06813691359369e+57

    1. Initial program 29.7

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

    2. Taylor expanded around 0 32.3

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

    if -3.06813691359369e+57 < y < 7.665419953743729e-168

    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 27.6

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

    if 7.665419953743729e-168 < y

    1. Initial program 26.1

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

    3. Applied add-cube-cbrt26.2

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

  4. Final simplification27.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.068136913593689871171353580308452333931 \cdot 10^{57}:\\ \;\;\;\;\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) + 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)\\ \mathbf{elif}\;y \le \frac{254462235520565}{3.31961245510479436680992629095292892081 \cdot 10^{181}}:\\ \;\;\;\;\left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\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(\sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)}\right) \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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"
  :precision binary64
  (+ (- (+ (+ (- (* (- (* 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)))))