Average Error: 12.4 → 9.3
Time: 7.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -28270.9569472437033:\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 1080895057447519360:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\left(j \cdot c\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(j \cdot \left(-i\right)\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\ \end{array}\]
\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}\;j \le -28270.9569472437033:\\
\;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{elif}\;j \le 1080895057447519360:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\left(j \cdot c\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(j \cdot \left(-i\right)\right) \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\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 r92840 = x;
        double r92841 = y;
        double r92842 = z;
        double r92843 = r92841 * r92842;
        double r92844 = t;
        double r92845 = a;
        double r92846 = r92844 * r92845;
        double r92847 = r92843 - r92846;
        double r92848 = r92840 * r92847;
        double r92849 = b;
        double r92850 = c;
        double r92851 = r92850 * r92842;
        double r92852 = i;
        double r92853 = r92852 * r92845;
        double r92854 = r92851 - r92853;
        double r92855 = r92849 * r92854;
        double r92856 = r92848 - r92855;
        double r92857 = j;
        double r92858 = r92850 * r92844;
        double r92859 = r92852 * r92841;
        double r92860 = r92858 - r92859;
        double r92861 = r92857 * r92860;
        double r92862 = r92856 + r92861;
        return r92862;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r92863 = j;
        double r92864 = -28270.956947243703;
        bool r92865 = r92863 <= r92864;
        double r92866 = x;
        double r92867 = y;
        double r92868 = z;
        double r92869 = r92867 * r92868;
        double r92870 = t;
        double r92871 = a;
        double r92872 = r92870 * r92871;
        double r92873 = r92869 - r92872;
        double r92874 = cbrt(r92873);
        double r92875 = r92874 * r92874;
        double r92876 = r92866 * r92875;
        double r92877 = r92876 * r92874;
        double r92878 = b;
        double r92879 = c;
        double r92880 = r92879 * r92868;
        double r92881 = i;
        double r92882 = r92881 * r92871;
        double r92883 = r92880 - r92882;
        double r92884 = r92878 * r92883;
        double r92885 = r92877 - r92884;
        double r92886 = r92879 * r92870;
        double r92887 = r92881 * r92867;
        double r92888 = r92886 - r92887;
        double r92889 = r92863 * r92888;
        double r92890 = r92885 + r92889;
        double r92891 = 1.0808950574475194e+18;
        bool r92892 = r92863 <= r92891;
        double r92893 = r92866 * r92873;
        double r92894 = r92893 - r92884;
        double r92895 = r92863 * r92879;
        double r92896 = cbrt(r92870);
        double r92897 = r92896 * r92896;
        double r92898 = r92895 * r92897;
        double r92899 = r92898 * r92896;
        double r92900 = -r92881;
        double r92901 = r92863 * r92900;
        double r92902 = r92901 * r92867;
        double r92903 = r92899 + r92902;
        double r92904 = r92894 + r92903;
        double r92905 = cbrt(r92866);
        double r92906 = r92905 * r92905;
        double r92907 = r92905 * r92873;
        double r92908 = r92906 * r92907;
        double r92909 = r92908 - r92884;
        double r92910 = r92863 * r92886;
        double r92911 = -r92887;
        double r92912 = r92863 * r92911;
        double r92913 = r92910 + r92912;
        double r92914 = r92909 + r92913;
        double r92915 = r92892 ? r92904 : r92914;
        double r92916 = r92865 ? r92890 : r92915;
        return r92916;
}

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

Derivation

  1. Split input into 3 regimes

  2. if j < -28270.956947243703

    1. Initial program 7.6

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt7.8

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

    4. Applied associate-*r*7.8

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

    if -28270.956947243703 < j < 1.0808950574475194e+18

    1. Initial program 15.1

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied sub-neg15.1

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

    4. Applied distribute-lft-in15.1

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

    6. Applied associate-*r*12.5

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

    8. Applied distribute-lft-neg-in12.5

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

    9. Applied associate-*r*10.0

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

    11. Applied add-cube-cbrt10.1

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

    12. Applied associate-*r*10.1

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

    if 1.0808950574475194e+18 < j

    1. Initial program 7.7

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied sub-neg7.7

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

    4. Applied distribute-lft-in7.7

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

    6. Applied add-cube-cbrt8.0

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

    7. Applied associate-*l*8.0

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

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -28270.9569472437033:\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 1080895057447519360:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\left(j \cdot c\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + \left(j \cdot \left(-i\right)\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020059 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))