Average Error: 12.1 → 12.1
Time: 9.5s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.4986631122414473 \cdot 10^{-284} \lor \neg \left(b \le 2.39488469224657437 \cdot 10^{-241}\right):\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -1.4986631122414473 \cdot 10^{-284} \lor \neg \left(b \le 2.39488469224657437 \cdot 10^{-241}\right):\\
\;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{\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{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - 0\right) + j \cdot \left(c \cdot t - i \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 r113774 = x;
        double r113775 = y;
        double r113776 = z;
        double r113777 = r113775 * r113776;
        double r113778 = t;
        double r113779 = a;
        double r113780 = r113778 * r113779;
        double r113781 = r113777 - r113780;
        double r113782 = r113774 * r113781;
        double r113783 = b;
        double r113784 = c;
        double r113785 = r113784 * r113776;
        double r113786 = i;
        double r113787 = r113786 * r113779;
        double r113788 = r113785 - r113787;
        double r113789 = r113783 * r113788;
        double r113790 = r113782 - r113789;
        double r113791 = j;
        double r113792 = r113784 * r113778;
        double r113793 = r113786 * r113775;
        double r113794 = r113792 - r113793;
        double r113795 = r113791 * r113794;
        double r113796 = r113790 + r113795;
        return r113796;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r113797 = b;
        double r113798 = -1.4986631122414473e-284;
        bool r113799 = r113797 <= r113798;
        double r113800 = 2.3948846922465744e-241;
        bool r113801 = r113797 <= r113800;
        double r113802 = !r113801;
        bool r113803 = r113799 || r113802;
        double r113804 = x;
        double r113805 = y;
        double r113806 = z;
        double r113807 = r113805 * r113806;
        double r113808 = t;
        double r113809 = a;
        double r113810 = r113808 * r113809;
        double r113811 = r113807 - r113810;
        double r113812 = r113804 * r113811;
        double r113813 = cbrt(r113812);
        double r113814 = r113813 * r113813;
        double r113815 = cbrt(r113811);
        double r113816 = r113815 * r113815;
        double r113817 = r113804 * r113816;
        double r113818 = r113817 * r113815;
        double r113819 = cbrt(r113818);
        double r113820 = r113814 * r113819;
        double r113821 = c;
        double r113822 = r113821 * r113806;
        double r113823 = i;
        double r113824 = r113823 * r113809;
        double r113825 = r113822 - r113824;
        double r113826 = r113797 * r113825;
        double r113827 = r113820 - r113826;
        double r113828 = j;
        double r113829 = r113821 * r113808;
        double r113830 = r113823 * r113805;
        double r113831 = r113829 - r113830;
        double r113832 = r113828 * r113831;
        double r113833 = r113827 + r113832;
        double r113834 = 0.0;
        double r113835 = r113812 - r113834;
        double r113836 = r113835 + r113832;
        double r113837 = r113803 ? r113833 : r113836;
        return r113837;
}

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 2 regimes

  2. if b < -1.4986631122414473e-284 or 2.3948846922465744e-241 < b

    1. Initial program 11.4

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

    3. Applied add-cube-cbrt11.7

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

    5. Applied add-cube-cbrt11.6

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

    6. Applied associate-*r*11.6

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

    if -1.4986631122414473e-284 < b < 2.3948846922465744e-241

    1. Initial program 18.3

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

    2. Taylor expanded around 0 16.5

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{0}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.4986631122414473 \cdot 10^{-284} \lor \neg \left(b \le 2.39488469224657437 \cdot 10^{-241}\right):\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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)))))