Average Error: 12.3 → 9.8
Time: 25.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -5.40768492793686555941761981699772927749 \cdot 10^{-39}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right)\right) + \left(a \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -1.310708033188256852286497632350011018004 \cdot 10^{-167}:\\ \;\;\;\;\left(\left(j \cdot \left(-y \cdot i\right) + \left(j \cdot c\right) \cdot t\right) + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;b \le -5.939141620508838471044724084871683968029 \cdot 10^{-276}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - \left(t \cdot x\right) \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\right) + \left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \sqrt[3]{\left(i \cdot b\right) \cdot a}\right) - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;b \le 2.248851513589900759233480267753595172809 \cdot 10^{-207}:\\ \;\;\;\;\left(\left(j \cdot \left(-y \cdot i\right) + \left(j \cdot c\right) \cdot t\right) + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;b \le 1.659927328976305946610149570336434936816 \cdot 10^{118}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z\right) - \sqrt[3]{a} \cdot \left(t \cdot \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot x\right)\right)\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i - c \cdot z\right) \cdot b + \left(\left(\left(j \cdot c\right) \cdot t + y \cdot \left(\left(-i\right) \cdot j\right)\right) + \left(y \cdot z - t \cdot a\right) \cdot x\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)
↓
\begin{array}{l}
\mathbf{if}\;b \le -5.40768492793686555941761981699772927749 \cdot 10^{-39}:\\
\;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right)\right) + \left(a \cdot i - c \cdot z\right) \cdot b\\

\mathbf{elif}\;b \le -1.310708033188256852286497632350011018004 \cdot 10^{-167}:\\
\;\;\;\;\left(\left(j \cdot \left(-y \cdot i\right) + \left(j \cdot c\right) \cdot t\right) + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\

\mathbf{elif}\;b \le -5.939141620508838471044724084871683968029 \cdot 10^{-276}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - \left(t \cdot x\right) \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\right) + \left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \sqrt[3]{\left(i \cdot b\right) \cdot a}\right) - \left(b \cdot z\right) \cdot c\right)\\

\mathbf{elif}\;b \le 2.248851513589900759233480267753595172809 \cdot 10^{-207}:\\
\;\;\;\;\left(\left(j \cdot \left(-y \cdot i\right) + \left(j \cdot c\right) \cdot t\right) + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\

\mathbf{elif}\;b \le 1.659927328976305946610149570336434936816 \cdot 10^{118}:\\
\;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z\right) - \sqrt[3]{a} \cdot \left(t \cdot \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot x\right)\right)\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\

\mathbf{else}:\\
\;\;\;\;\left(a \cdot i - c \cdot z\right) \cdot b + \left(\left(\left(j \cdot c\right) \cdot t + y \cdot \left(\left(-i\right) \cdot j\right)\right) + \left(y \cdot z - t \cdot a\right) \cdot x\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r426810 = x;
        double r426811 = y;
        double r426812 = z;
        double r426813 = r426811 * r426812;
        double r426814 = t;
        double r426815 = a;
        double r426816 = r426814 * r426815;
        double r426817 = r426813 - r426816;
        double r426818 = r426810 * r426817;
        double r426819 = b;
        double r426820 = c;
        double r426821 = r426820 * r426812;
        double r426822 = i;
        double r426823 = r426822 * r426815;
        double r426824 = r426821 - r426823;
        double r426825 = r426819 * r426824;
        double r426826 = r426818 - r426825;
        double r426827 = j;
        double r426828 = r426820 * r426814;
        double r426829 = r426822 * r426811;
        double r426830 = r426828 - r426829;
        double r426831 = r426827 * r426830;
        double r426832 = r426826 + r426831;
        return r426832;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r426833 = b;
        double r426834 = -5.4076849279368656e-39;
        bool r426835 = r426833 <= r426834;
        double r426836 = j;
        double r426837 = t;
        double r426838 = c;
        double r426839 = r426837 * r426838;
        double r426840 = y;
        double r426841 = i;
        double r426842 = r426840 * r426841;
        double r426843 = r426839 - r426842;
        double r426844 = r426836 * r426843;
        double r426845 = x;
        double r426846 = z;
        double r426847 = r426845 * r426846;
        double r426848 = r426840 * r426847;
        double r426849 = a;
        double r426850 = r426845 * r426849;
        double r426851 = r426837 * r426850;
        double r426852 = r426848 - r426851;
        double r426853 = r426844 + r426852;
        double r426854 = r426849 * r426841;
        double r426855 = r426838 * r426846;
        double r426856 = r426854 - r426855;
        double r426857 = r426856 * r426833;
        double r426858 = r426853 + r426857;
        double r426859 = -1.3107080331882569e-167;
        bool r426860 = r426833 <= r426859;
        double r426861 = -r426842;
        double r426862 = r426836 * r426861;
        double r426863 = r426836 * r426838;
        double r426864 = r426863 * r426837;
        double r426865 = r426862 + r426864;
        double r426866 = r426837 * r426845;
        double r426867 = r426866 * r426849;
        double r426868 = r426848 - r426867;
        double r426869 = r426865 + r426868;
        double r426870 = r426841 * r426833;
        double r426871 = r426870 * r426849;
        double r426872 = r426833 * r426846;
        double r426873 = r426872 * r426838;
        double r426874 = r426871 - r426873;
        double r426875 = r426869 + r426874;
        double r426876 = -5.9391416205088385e-276;
        bool r426877 = r426833 <= r426876;
        double r426878 = r426840 * r426846;
        double r426879 = r426845 * r426878;
        double r426880 = r426879 - r426867;
        double r426881 = r426880 + r426844;
        double r426882 = cbrt(r426871);
        double r426883 = r426882 * r426882;
        double r426884 = r426882 * r426883;
        double r426885 = r426884 - r426873;
        double r426886 = r426881 + r426885;
        double r426887 = 2.2488515135899008e-207;
        bool r426888 = r426833 <= r426887;
        double r426889 = 1.659927328976306e+118;
        bool r426890 = r426833 <= r426889;
        double r426891 = cbrt(r426849);
        double r426892 = r426891 * r426891;
        double r426893 = r426892 * r426845;
        double r426894 = r426837 * r426893;
        double r426895 = r426891 * r426894;
        double r426896 = r426879 - r426895;
        double r426897 = r426844 + r426896;
        double r426898 = r426897 + r426874;
        double r426899 = -r426841;
        double r426900 = r426899 * r426836;
        double r426901 = r426840 * r426900;
        double r426902 = r426864 + r426901;
        double r426903 = r426837 * r426849;
        double r426904 = r426878 - r426903;
        double r426905 = r426904 * r426845;
        double r426906 = r426902 + r426905;
        double r426907 = r426857 + r426906;
        double r426908 = r426890 ? r426898 : r426907;
        double r426909 = r426888 ? r426875 : r426908;
        double r426910 = r426877 ? r426886 : r426909;
        double r426911 = r426860 ? r426875 : r426910;
        double r426912 = r426835 ? r426858 : r426911;
        return r426912;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.3
Target16.0
Herbie9.8
\[\begin{array}{l} \mathbf{if}\;t \lt -8.12097891919591218149793027759825150959 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.712553818218485141757938537793350881052 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.633533346031583686060259351057142920433 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.053588855745548710002760210539645467715 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if b < -5.4076849279368656e-39

    1. Initial program 8.0

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Simplified8.0

      \[\leadsto \color{blue}{\left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)}\]

    3. Taylor expanded around inf 9.4

      \[\leadsto \left(a \cdot i - z \cdot c\right) \cdot b + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    4. Simplified8.2

      \[\leadsto \left(a \cdot i - z \cdot c\right) \cdot b + \left(\color{blue}{\left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    if -5.4076849279368656e-39 < b < -1.3107080331882569e-167 or -5.9391416205088385e-276 < b < 2.2488515135899008e-207

    1. Initial program 15.8

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Simplified15.8

      \[\leadsto \color{blue}{\left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)}\]

    3. Taylor expanded around inf 10.5

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b\right) - z \cdot \left(b \cdot c\right)\right)} + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    4. Simplified10.4

      \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right)} + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    5. Taylor expanded around inf 10.2

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    6. Simplified10.2

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]
    7. Using strategy rm

    8. Applied sub-neg10.2

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + j \cdot \color{blue}{\left(t \cdot c + \left(-i \cdot y\right)\right)}\right)\]

    9. Applied distribute-lft-in10.2

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + \color{blue}{\left(j \cdot \left(t \cdot c\right) + j \cdot \left(-i \cdot y\right)\right)}\right)\]

    10. Simplified10.9

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + \left(\color{blue}{\left(j \cdot c\right) \cdot t} + j \cdot \left(-i \cdot y\right)\right)\right)\]

    11. Simplified10.9

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + \left(\left(j \cdot c\right) \cdot t + \color{blue}{\left(y \cdot i\right) \cdot \left(-j\right)}\right)\right)\]
    12. Using strategy rm

    13. Applied associate-*r*10.5

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(\color{blue}{\left(x \cdot z\right) \cdot y} - \left(x \cdot t\right) \cdot a\right) + \left(\left(j \cdot c\right) \cdot t + \left(y \cdot i\right) \cdot \left(-j\right)\right)\right)\]

    if -1.3107080331882569e-167 < b < -5.9391416205088385e-276

    1. Initial program 17.3

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Simplified17.3

      \[\leadsto \color{blue}{\left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)}\]

    3. Taylor expanded around inf 10.9

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b\right) - z \cdot \left(b \cdot c\right)\right)} + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    4. Simplified11.0

      \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right)} + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    5. Taylor expanded around inf 10.0

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    6. Simplified10.0

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]
    7. Using strategy rm

    8. Applied add-cube-cbrt10.1

      \[\leadsto \left(\color{blue}{\left(\sqrt[3]{a \cdot \left(b \cdot i\right)} \cdot \sqrt[3]{a \cdot \left(b \cdot i\right)}\right) \cdot \sqrt[3]{a \cdot \left(b \cdot i\right)}} - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    9. Simplified10.1

      \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \sqrt[3]{\left(i \cdot b\right) \cdot a}\right)} \cdot \sqrt[3]{a \cdot \left(b \cdot i\right)} - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    10. Simplified10.1

      \[\leadsto \left(\left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \sqrt[3]{\left(i \cdot b\right) \cdot a}\right) \cdot \color{blue}{\sqrt[3]{\left(i \cdot b\right) \cdot a}} - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right) + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    if 2.2488515135899008e-207 < b < 1.659927328976306e+118

    1. Initial program 12.9

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Simplified12.9

      \[\leadsto \color{blue}{\left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)}\]

    3. Taylor expanded around inf 11.2

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b\right) - z \cdot \left(b \cdot c\right)\right)} + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    4. Simplified11.3

      \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right)} + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    5. Taylor expanded around inf 11.2

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    6. Simplified11.2

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot a\right)} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]
    7. Using strategy rm

    8. Applied add-cube-cbrt11.4

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \left(x \cdot t\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)}\right) + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    9. Applied associate-*r*11.4

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \color{blue}{\left(\left(x \cdot t\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}}\right) + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    10. Simplified11.3

      \[\leadsto \left(a \cdot \left(b \cdot i\right) - \left(z \cdot b\right) \cdot c\right) + \left(\left(x \cdot \left(z \cdot y\right) - \color{blue}{\left(\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot x\right) \cdot t\right)} \cdot \sqrt[3]{a}\right) + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]

    if 1.659927328976306e+118 < b

    1. Initial program 6.0

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Simplified6.0

      \[\leadsto \color{blue}{\left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \left(t \cdot c - i \cdot y\right)\right)}\]
    3. Using strategy rm

    4. Applied sub-neg6.0

      \[\leadsto \left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + j \cdot \color{blue}{\left(t \cdot c + \left(-i \cdot y\right)\right)}\right)\]

    5. Applied distribute-lft-in6.0

      \[\leadsto \left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + \color{blue}{\left(j \cdot \left(t \cdot c\right) + j \cdot \left(-i \cdot y\right)\right)}\right)\]

    6. Simplified6.5

      \[\leadsto \left(a \cdot i - z \cdot c\right) \cdot b + \left(\left(z \cdot y - t \cdot a\right) \cdot x + \left(\color{blue}{t \cdot \left(j \cdot c\right)} + j \cdot \left(-i \cdot y\right)\right)\right)\]

    7. Simplified6.6

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -5.40768492793686555941761981699772927749 \cdot 10^{-39}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right)\right) + \left(a \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -1.310708033188256852286497632350011018004 \cdot 10^{-167}:\\ \;\;\;\;\left(\left(j \cdot \left(-y \cdot i\right) + \left(j \cdot c\right) \cdot t\right) + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;b \le -5.939141620508838471044724084871683968029 \cdot 10^{-276}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - \left(t \cdot x\right) \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\right) + \left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \left(\sqrt[3]{\left(i \cdot b\right) \cdot a} \cdot \sqrt[3]{\left(i \cdot b\right) \cdot a}\right) - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;b \le 2.248851513589900759233480267753595172809 \cdot 10^{-207}:\\ \;\;\;\;\left(\left(j \cdot \left(-y \cdot i\right) + \left(j \cdot c\right) \cdot t\right) + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;b \le 1.659927328976305946610149570336434936816 \cdot 10^{118}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z\right) - \sqrt[3]{a} \cdot \left(t \cdot \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot x\right)\right)\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i - c \cdot z\right) \cdot b + \left(\left(\left(j \cdot c\right) \cdot t + y \cdot \left(\left(-i\right) \cdot j\right)\right) + \left(y \cdot z - t \cdot a\right) \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))