Average Error: 25.3 → 26.0
Time: 1.7m
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}\;y2 \le -1.1377816797716678 \cdot 10^{+87}:\\ \;\;\;\;\left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(\left(b \cdot a - c \cdot i\right) \cdot \sqrt[3]{x \cdot y - t \cdot z}\right) \cdot \left(\sqrt[3]{x \cdot y - t \cdot z} \cdot \sqrt[3]{x \cdot y - t \cdot z}\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)\\ \mathbf{elif}\;y2 \le -4.558806736300179 \cdot 10^{-116}:\\ \;\;\;\;\left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(\left(\left(\left(c \cdot z\right) \cdot i\right) \cdot t - \left(\left(\left(b \cdot z\right) \cdot t\right) \cdot a + \left(\left(y \cdot c\right) \cdot x\right) \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)\\ \mathbf{elif}\;y2 \le 7.734092366103082 \cdot 10^{-74}:\\ \;\;\;\;\left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(\left(\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right)\right) - \left(\left(\left(t \cdot y2 - y \cdot y3\right) \cdot a\right) \cdot \left(-y5\right) + \left(y4 \cdot c\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right) - \left(\left(z \cdot \left(y1 \cdot k\right)\right) \cdot i - \left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot i + k \cdot \left(z \cdot \left(y0 \cdot b\right)\right)\right)\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\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}\;y2 \le -1.1377816797716678 \cdot 10^{+87}:\\
\;\;\;\;\left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(\left(b \cdot a - c \cdot i\right) \cdot \sqrt[3]{x \cdot y - t \cdot z}\right) \cdot \left(\sqrt[3]{x \cdot y - t \cdot z} \cdot \sqrt[3]{x \cdot y - t \cdot z}\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)\\

\mathbf{elif}\;y2 \le -4.558806736300179 \cdot 10^{-116}:\\
\;\;\;\;\left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(\left(\left(\left(c \cdot z\right) \cdot i\right) \cdot t - \left(\left(\left(b \cdot z\right) \cdot t\right) \cdot a + \left(\left(y \cdot c\right) \cdot x\right) \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)\\

\mathbf{elif}\;y2 \le 7.734092366103082 \cdot 10^{-74}:\\
\;\;\;\;\left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(\left(\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right)\right) - \left(\left(\left(t \cdot y2 - y \cdot y3\right) \cdot a\right) \cdot \left(-y5\right) + \left(y4 \cdot c\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right) - \left(\left(z \cdot \left(y1 \cdot k\right)\right) \cdot i - \left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot i + k \cdot \left(z \cdot \left(y0 \cdot b\right)\right)\right)\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\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 k, double y0, double y1, double y2, double y3, double y4, double y5) {
        double r2761555 = x;
        double r2761556 = y;
        double r2761557 = r2761555 * r2761556;
        double r2761558 = z;
        double r2761559 = t;
        double r2761560 = r2761558 * r2761559;
        double r2761561 = r2761557 - r2761560;
        double r2761562 = a;
        double r2761563 = b;
        double r2761564 = r2761562 * r2761563;
        double r2761565 = c;
        double r2761566 = i;
        double r2761567 = r2761565 * r2761566;
        double r2761568 = r2761564 - r2761567;
        double r2761569 = r2761561 * r2761568;
        double r2761570 = j;
        double r2761571 = r2761555 * r2761570;
        double r2761572 = k;
        double r2761573 = r2761558 * r2761572;
        double r2761574 = r2761571 - r2761573;
        double r2761575 = y0;
        double r2761576 = r2761575 * r2761563;
        double r2761577 = y1;
        double r2761578 = r2761577 * r2761566;
        double r2761579 = r2761576 - r2761578;
        double r2761580 = r2761574 * r2761579;
        double r2761581 = r2761569 - r2761580;
        double r2761582 = y2;
        double r2761583 = r2761555 * r2761582;
        double r2761584 = y3;
        double r2761585 = r2761558 * r2761584;
        double r2761586 = r2761583 - r2761585;
        double r2761587 = r2761575 * r2761565;
        double r2761588 = r2761577 * r2761562;
        double r2761589 = r2761587 - r2761588;
        double r2761590 = r2761586 * r2761589;
        double r2761591 = r2761581 + r2761590;
        double r2761592 = r2761559 * r2761570;
        double r2761593 = r2761556 * r2761572;
        double r2761594 = r2761592 - r2761593;
        double r2761595 = y4;
        double r2761596 = r2761595 * r2761563;
        double r2761597 = y5;
        double r2761598 = r2761597 * r2761566;
        double r2761599 = r2761596 - r2761598;
        double r2761600 = r2761594 * r2761599;
        double r2761601 = r2761591 + r2761600;
        double r2761602 = r2761559 * r2761582;
        double r2761603 = r2761556 * r2761584;
        double r2761604 = r2761602 - r2761603;
        double r2761605 = r2761595 * r2761565;
        double r2761606 = r2761597 * r2761562;
        double r2761607 = r2761605 - r2761606;
        double r2761608 = r2761604 * r2761607;
        double r2761609 = r2761601 - r2761608;
        double r2761610 = r2761572 * r2761582;
        double r2761611 = r2761570 * r2761584;
        double r2761612 = r2761610 - r2761611;
        double r2761613 = r2761595 * r2761577;
        double r2761614 = r2761597 * r2761575;
        double r2761615 = r2761613 - r2761614;
        double r2761616 = r2761612 * r2761615;
        double r2761617 = r2761609 + r2761616;
        return r2761617;
}
↓
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 r2761618 = y2;
        double r2761619 = -1.1377816797716678e+87;
        bool r2761620 = r2761618 <= r2761619;
        double r2761621 = j;
        double r2761622 = t;
        double r2761623 = r2761621 * r2761622;
        double r2761624 = y;
        double r2761625 = k;
        double r2761626 = r2761624 * r2761625;
        double r2761627 = r2761623 - r2761626;
        double r2761628 = b;
        double r2761629 = y4;
        double r2761630 = r2761628 * r2761629;
        double r2761631 = y5;
        double r2761632 = i;
        double r2761633 = r2761631 * r2761632;
        double r2761634 = r2761630 - r2761633;
        double r2761635 = r2761627 * r2761634;
        double r2761636 = a;
        double r2761637 = r2761628 * r2761636;
        double r2761638 = c;
        double r2761639 = r2761638 * r2761632;
        double r2761640 = r2761637 - r2761639;
        double r2761641 = x;
        double r2761642 = r2761641 * r2761624;
        double r2761643 = z;
        double r2761644 = r2761622 * r2761643;
        double r2761645 = r2761642 - r2761644;
        double r2761646 = cbrt(r2761645);
        double r2761647 = r2761640 * r2761646;
        double r2761648 = r2761646 * r2761646;
        double r2761649 = r2761647 * r2761648;
        double r2761650 = y0;
        double r2761651 = r2761638 * r2761650;
        double r2761652 = y1;
        double r2761653 = r2761652 * r2761636;
        double r2761654 = r2761651 - r2761653;
        double r2761655 = r2761641 * r2761618;
        double r2761656 = y3;
        double r2761657 = r2761643 * r2761656;
        double r2761658 = r2761655 - r2761657;
        double r2761659 = r2761654 * r2761658;
        double r2761660 = r2761649 + r2761659;
        double r2761661 = r2761635 + r2761660;
        double r2761662 = r2761622 * r2761618;
        double r2761663 = r2761624 * r2761656;
        double r2761664 = r2761662 - r2761663;
        double r2761665 = r2761629 * r2761638;
        double r2761666 = r2761631 * r2761636;
        double r2761667 = r2761665 - r2761666;
        double r2761668 = r2761664 * r2761667;
        double r2761669 = r2761661 - r2761668;
        double r2761670 = r2761652 * r2761629;
        double r2761671 = r2761631 * r2761650;
        double r2761672 = r2761670 - r2761671;
        double r2761673 = r2761625 * r2761618;
        double r2761674 = r2761656 * r2761621;
        double r2761675 = r2761673 - r2761674;
        double r2761676 = r2761672 * r2761675;
        double r2761677 = r2761669 + r2761676;
        double r2761678 = -4.558806736300179e-116;
        bool r2761679 = r2761618 <= r2761678;
        double r2761680 = r2761638 * r2761643;
        double r2761681 = r2761680 * r2761632;
        double r2761682 = r2761681 * r2761622;
        double r2761683 = r2761628 * r2761643;
        double r2761684 = r2761683 * r2761622;
        double r2761685 = r2761684 * r2761636;
        double r2761686 = r2761624 * r2761638;
        double r2761687 = r2761686 * r2761641;
        double r2761688 = r2761687 * r2761632;
        double r2761689 = r2761685 + r2761688;
        double r2761690 = r2761682 - r2761689;
        double r2761691 = r2761650 * r2761628;
        double r2761692 = r2761652 * r2761632;
        double r2761693 = r2761691 - r2761692;
        double r2761694 = r2761621 * r2761641;
        double r2761695 = r2761625 * r2761643;
        double r2761696 = r2761694 - r2761695;
        double r2761697 = r2761693 * r2761696;
        double r2761698 = r2761690 - r2761697;
        double r2761699 = r2761698 + r2761659;
        double r2761700 = r2761635 + r2761699;
        double r2761701 = r2761700 - r2761668;
        double r2761702 = r2761701 + r2761676;
        double r2761703 = 7.734092366103082e-74;
        bool r2761704 = r2761618 <= r2761703;
        double r2761705 = r2761645 * r2761640;
        double r2761706 = r2761705 - r2761697;
        double r2761707 = r2761659 + r2761706;
        double r2761708 = r2761707 + r2761635;
        double r2761709 = r2761664 * r2761636;
        double r2761710 = -r2761631;
        double r2761711 = r2761709 * r2761710;
        double r2761712 = r2761665 * r2761664;
        double r2761713 = r2761711 + r2761712;
        double r2761714 = r2761708 - r2761713;
        double r2761715 = r2761676 + r2761714;
        double r2761716 = r2761652 * r2761625;
        double r2761717 = r2761643 * r2761716;
        double r2761718 = r2761717 * r2761632;
        double r2761719 = r2761641 * r2761652;
        double r2761720 = r2761621 * r2761719;
        double r2761721 = r2761720 * r2761632;
        double r2761722 = r2761643 * r2761691;
        double r2761723 = r2761625 * r2761722;
        double r2761724 = r2761721 + r2761723;
        double r2761725 = r2761718 - r2761724;
        double r2761726 = r2761705 - r2761725;
        double r2761727 = r2761659 + r2761726;
        double r2761728 = r2761635 + r2761727;
        double r2761729 = r2761728 - r2761668;
        double r2761730 = r2761676 + r2761729;
        double r2761731 = r2761704 ? r2761715 : r2761730;
        double r2761732 = r2761679 ? r2761702 : r2761731;
        double r2761733 = r2761620 ? r2761677 : r2761732;
        return r2761733;
}

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 4 regimes

  2. if y2 < -1.1377816797716678e+87

    1. Initial program 29.0

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

    3. Applied add-cube-cbrt29.1

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

    4. Applied associate-*l*29.1

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

    5. Taylor expanded around 0 31.2

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

    if -1.1377816797716678e+87 < y2 < -4.558806736300179e-116

    1. Initial program 22.2

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

    2. Taylor expanded around inf 24.3

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

    if -4.558806736300179e-116 < y2 < 7.734092366103082e-74

    1. Initial program 25.1

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

    3. Applied sub-neg25.1

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

    4. Applied distribute-rgt-in25.1

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

    6. Applied distribute-lft-neg-in25.1

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

    7. Applied associate-*l*24.6

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

    if 7.734092366103082e-74 < y2

    1. Initial program 26.7

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

    2. Taylor expanded around inf 28.0

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \color{blue}{\left(i \cdot \left(z \cdot \left(y1 \cdot k\right)\right) - \left(k \cdot \left(z \cdot \left(b \cdot y0\right)\right) + i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification26.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \le -1.1377816797716678 \cdot 10^{+87}:\\ \;\;\;\;\left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(\left(b \cdot a - c \cdot i\right) \cdot \sqrt[3]{x \cdot y - t \cdot z}\right) \cdot \left(\sqrt[3]{x \cdot y - t \cdot z} \cdot \sqrt[3]{x \cdot y - t \cdot z}\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)\\ \mathbf{elif}\;y2 \le -4.558806736300179 \cdot 10^{-116}:\\ \;\;\;\;\left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(\left(\left(\left(c \cdot z\right) \cdot i\right) \cdot t - \left(\left(\left(b \cdot z\right) \cdot t\right) \cdot a + \left(\left(y \cdot c\right) \cdot x\right) \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)\\ \mathbf{elif}\;y2 \le 7.734092366103082 \cdot 10^{-74}:\\ \;\;\;\;\left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(\left(\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right)\right) - \left(\left(\left(t \cdot y2 - y \cdot y3\right) \cdot a\right) \cdot \left(-y5\right) + \left(y4 \cdot c\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y4 - y5 \cdot y0\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(\left(\left(j \cdot t - y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right) + \left(\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(\left(x \cdot y - t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right) - \left(\left(z \cdot \left(y1 \cdot k\right)\right) \cdot i - \left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot i + k \cdot \left(z \cdot \left(y0 \cdot b\right)\right)\right)\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(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)))))