Average Error: 25.6 → 28.6
Time: 3.4m
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}\;z \le -2.7518514594683767 \cdot 10^{+140}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(\left(\left(\left(c \cdot i - a \cdot b\right) \cdot t\right) \cdot z - \left(x \cdot \left(y \cdot i\right)\right) \cdot c\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \le -1.1164309374417192 \cdot 10^{-225}:\\ \;\;\;\;\left(\left(\left(k \cdot \left(\left(y5 \cdot i - b \cdot y4\right) \cdot y\right) - \left(y5 \cdot j\right) \cdot \left(t \cdot i\right)\right) + \left(\left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;z \le 2.6912037617819743 \cdot 10^{-157}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\sqrt[3]{b \cdot y4 - y5 \cdot i} \cdot \left(\left(\sqrt[3]{b \cdot y4 - y5 \cdot i} \cdot \sqrt[3]{b \cdot y4 - y5 \cdot i}\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(\left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right) + \left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \le 4.6009040431505826 \cdot 10^{+29}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\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 r15125460 = x;
        double r15125461 = y;
        double r15125462 = r15125460 * r15125461;
        double r15125463 = z;
        double r15125464 = t;
        double r15125465 = r15125463 * r15125464;
        double r15125466 = r15125462 - r15125465;
        double r15125467 = a;
        double r15125468 = b;
        double r15125469 = r15125467 * r15125468;
        double r15125470 = c;
        double r15125471 = i;
        double r15125472 = r15125470 * r15125471;
        double r15125473 = r15125469 - r15125472;
        double r15125474 = r15125466 * r15125473;
        double r15125475 = j;
        double r15125476 = r15125460 * r15125475;
        double r15125477 = k;
        double r15125478 = r15125463 * r15125477;
        double r15125479 = r15125476 - r15125478;
        double r15125480 = y0;
        double r15125481 = r15125480 * r15125468;
        double r15125482 = y1;
        double r15125483 = r15125482 * r15125471;
        double r15125484 = r15125481 - r15125483;
        double r15125485 = r15125479 * r15125484;
        double r15125486 = r15125474 - r15125485;
        double r15125487 = y2;
        double r15125488 = r15125460 * r15125487;
        double r15125489 = y3;
        double r15125490 = r15125463 * r15125489;
        double r15125491 = r15125488 - r15125490;
        double r15125492 = r15125480 * r15125470;
        double r15125493 = r15125482 * r15125467;
        double r15125494 = r15125492 - r15125493;
        double r15125495 = r15125491 * r15125494;
        double r15125496 = r15125486 + r15125495;
        double r15125497 = r15125464 * r15125475;
        double r15125498 = r15125461 * r15125477;
        double r15125499 = r15125497 - r15125498;
        double r15125500 = y4;
        double r15125501 = r15125500 * r15125468;
        double r15125502 = y5;
        double r15125503 = r15125502 * r15125471;
        double r15125504 = r15125501 - r15125503;
        double r15125505 = r15125499 * r15125504;
        double r15125506 = r15125496 + r15125505;
        double r15125507 = r15125464 * r15125487;
        double r15125508 = r15125461 * r15125489;
        double r15125509 = r15125507 - r15125508;
        double r15125510 = r15125500 * r15125470;
        double r15125511 = r15125502 * r15125467;
        double r15125512 = r15125510 - r15125511;
        double r15125513 = r15125509 * r15125512;
        double r15125514 = r15125506 - r15125513;
        double r15125515 = r15125477 * r15125487;
        double r15125516 = r15125475 * r15125489;
        double r15125517 = r15125515 - r15125516;
        double r15125518 = r15125500 * r15125482;
        double r15125519 = r15125502 * r15125480;
        double r15125520 = r15125518 - r15125519;
        double r15125521 = r15125517 * r15125520;
        double r15125522 = r15125514 + r15125521;
        return r15125522;
}
↓
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 r15125523 = z;
        double r15125524 = -2.7518514594683767e+140;
        bool r15125525 = r15125523 <= r15125524;
        double r15125526 = k;
        double r15125527 = y2;
        double r15125528 = r15125526 * r15125527;
        double r15125529 = j;
        double r15125530 = y3;
        double r15125531 = r15125529 * r15125530;
        double r15125532 = r15125528 - r15125531;
        double r15125533 = y1;
        double r15125534 = y4;
        double r15125535 = r15125533 * r15125534;
        double r15125536 = y0;
        double r15125537 = y5;
        double r15125538 = r15125536 * r15125537;
        double r15125539 = r15125535 - r15125538;
        double r15125540 = r15125532 * r15125539;
        double r15125541 = b;
        double r15125542 = r15125541 * r15125534;
        double r15125543 = i;
        double r15125544 = r15125537 * r15125543;
        double r15125545 = r15125542 - r15125544;
        double r15125546 = t;
        double r15125547 = r15125546 * r15125529;
        double r15125548 = y;
        double r15125549 = r15125548 * r15125526;
        double r15125550 = r15125547 - r15125549;
        double r15125551 = r15125545 * r15125550;
        double r15125552 = c;
        double r15125553 = r15125552 * r15125543;
        double r15125554 = a;
        double r15125555 = r15125554 * r15125541;
        double r15125556 = r15125553 - r15125555;
        double r15125557 = r15125556 * r15125546;
        double r15125558 = r15125557 * r15125523;
        double r15125559 = x;
        double r15125560 = r15125548 * r15125543;
        double r15125561 = r15125559 * r15125560;
        double r15125562 = r15125561 * r15125552;
        double r15125563 = r15125558 - r15125562;
        double r15125564 = r15125559 * r15125529;
        double r15125565 = r15125526 * r15125523;
        double r15125566 = r15125564 - r15125565;
        double r15125567 = r15125541 * r15125536;
        double r15125568 = r15125533 * r15125543;
        double r15125569 = r15125567 - r15125568;
        double r15125570 = r15125566 * r15125569;
        double r15125571 = r15125563 - r15125570;
        double r15125572 = r15125527 * r15125559;
        double r15125573 = r15125523 * r15125530;
        double r15125574 = r15125572 - r15125573;
        double r15125575 = r15125552 * r15125536;
        double r15125576 = r15125533 * r15125554;
        double r15125577 = r15125575 - r15125576;
        double r15125578 = r15125574 * r15125577;
        double r15125579 = r15125571 + r15125578;
        double r15125580 = r15125551 + r15125579;
        double r15125581 = r15125552 * r15125534;
        double r15125582 = r15125537 * r15125554;
        double r15125583 = r15125581 - r15125582;
        double r15125584 = r15125546 * r15125527;
        double r15125585 = r15125548 * r15125530;
        double r15125586 = r15125584 - r15125585;
        double r15125587 = r15125583 * r15125586;
        double r15125588 = r15125580 - r15125587;
        double r15125589 = r15125540 + r15125588;
        double r15125590 = -1.1164309374417192e-225;
        bool r15125591 = r15125523 <= r15125590;
        double r15125592 = r15125544 - r15125542;
        double r15125593 = r15125592 * r15125548;
        double r15125594 = r15125526 * r15125593;
        double r15125595 = r15125537 * r15125529;
        double r15125596 = r15125546 * r15125543;
        double r15125597 = r15125595 * r15125596;
        double r15125598 = r15125594 - r15125597;
        double r15125599 = r15125548 * r15125559;
        double r15125600 = r15125546 * r15125523;
        double r15125601 = r15125599 - r15125600;
        double r15125602 = r15125555 - r15125553;
        double r15125603 = r15125601 * r15125602;
        double r15125604 = r15125603 - r15125570;
        double r15125605 = r15125604 + r15125578;
        double r15125606 = r15125598 + r15125605;
        double r15125607 = r15125606 - r15125587;
        double r15125608 = r15125607 + r15125540;
        double r15125609 = 2.6912037617819743e-157;
        bool r15125610 = r15125523 <= r15125609;
        double r15125611 = cbrt(r15125545);
        double r15125612 = r15125611 * r15125611;
        double r15125613 = r15125612 * r15125550;
        double r15125614 = r15125611 * r15125613;
        double r15125615 = r15125578 + r15125603;
        double r15125616 = r15125614 + r15125615;
        double r15125617 = r15125616 - r15125587;
        double r15125618 = r15125540 + r15125617;
        double r15125619 = 4.6009040431505826e+29;
        bool r15125620 = r15125523 <= r15125619;
        double r15125621 = r15125605 - r15125587;
        double r15125622 = r15125540 + r15125621;
        double r15125623 = r15125551 + r15125604;
        double r15125624 = r15125623 - r15125587;
        double r15125625 = r15125540 + r15125624;
        double r15125626 = r15125620 ? r15125622 : r15125625;
        double r15125627 = r15125610 ? r15125618 : r15125626;
        double r15125628 = r15125591 ? r15125608 : r15125627;
        double r15125629 = r15125525 ? r15125589 : r15125628;
        return r15125629;
}


\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}\;z \le -2.7518514594683767 \cdot 10^{+140}:\\
\;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(\left(\left(\left(c \cdot i - a \cdot b\right) \cdot t\right) \cdot z - \left(x \cdot \left(y \cdot i\right)\right) \cdot c\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\

\mathbf{elif}\;z \le -1.1164309374417192 \cdot 10^{-225}:\\
\;\;\;\;\left(\left(\left(k \cdot \left(\left(y5 \cdot i - b \cdot y4\right) \cdot y\right) - \left(y5 \cdot j\right) \cdot \left(t \cdot i\right)\right) + \left(\left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\

\mathbf{elif}\;z \le 2.6912037617819743 \cdot 10^{-157}:\\
\;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\sqrt[3]{b \cdot y4 - y5 \cdot i} \cdot \left(\left(\sqrt[3]{b \cdot y4 - y5 \cdot i} \cdot \sqrt[3]{b \cdot y4 - y5 \cdot i}\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(\left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right) + \left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\

\mathbf{elif}\;z \le 4.6009040431505826 \cdot 10^{+29}:\\
\;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\

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

\end{array}

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

Derivation

  1. Split input into 5 regimes

  2. if z < -2.7518514594683767e+140

    1. Initial program 31.0

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

    2. Taylor expanded around inf 39.7

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

    3. Simplified27.6

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

    if -2.7518514594683767e+140 < z < -1.1164309374417192e-225

    1. Initial program 24.1

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

    2. Taylor expanded around inf 26.6

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

    3. Simplified26.5

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

    if -1.1164309374417192e-225 < z < 2.6912037617819743e-157

    1. Initial program 26.0

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

    3. Applied add-cube-cbrt26.1

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

    4. Applied associate-*r*26.1

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

    5. Taylor expanded around 0 28.3

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

    if 2.6912037617819743e-157 < z < 4.6009040431505826e+29

    1. Initial program 23.6

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

    2. Taylor expanded around 0 29.3

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

    if 4.6009040431505826e+29 < z

    1. Initial program 28.4

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

    2. Taylor expanded around 0 33.9

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \color{blue}{0}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  3. Recombined 5 regimes into one program.

  4. Final simplification28.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.7518514594683767 \cdot 10^{+140}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(\left(\left(\left(c \cdot i - a \cdot b\right) \cdot t\right) \cdot z - \left(x \cdot \left(y \cdot i\right)\right) \cdot c\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \le -1.1164309374417192 \cdot 10^{-225}:\\ \;\;\;\;\left(\left(\left(k \cdot \left(\left(y5 \cdot i - b \cdot y4\right) \cdot y\right) - \left(y5 \cdot j\right) \cdot \left(t \cdot i\right)\right) + \left(\left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;z \le 2.6912037617819743 \cdot 10^{-157}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\sqrt[3]{b \cdot y4 - y5 \cdot i} \cdot \left(\left(\sqrt[3]{b \cdot y4 - y5 \cdot i} \cdot \sqrt[3]{b \cdot y4 - y5 \cdot i}\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(\left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right) + \left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \le 4.6009040431505826 \cdot 10^{+29}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right) + \left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(b \cdot y4 - y5 \cdot i\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(\left(y \cdot x - t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - k \cdot z\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)\right) - \left(c \cdot y4 - y5 \cdot a\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019101 
(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)))))