Average Error: 25.8 → 27.8
Time: 2.5m
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}\;x \le -2.1372002604629256 \cdot 10^{-63}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \cdot \sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)}\right) \cdot \sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y2 \cdot k - j \cdot y3\right) \cdot \left(\sqrt[3]{y4 \cdot y1 - y5 \cdot y0} \cdot \sqrt[3]{y4 \cdot y1 - y5 \cdot y0}\right)\right) \cdot \sqrt[3]{y4 \cdot y1 - y5 \cdot y0}\\ \mathbf{elif}\;x \le 4.480059003985887 \cdot 10^{-101}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(a \cdot \left(\left(y3 \cdot y1\right) \cdot z - y2 \cdot \left(x \cdot y1\right)\right) - z \cdot \left(c \cdot \left(y3 \cdot y0\right)\right)\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \mathbf{elif}\;x \le 3.2670001790969278 \cdot 10^{-74}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \mathbf{elif}\;x \le 7.531769519783287 \cdot 10^{+115}:\\ \;\;\;\;\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(\left(\left(y1 \cdot k\right) \cdot z\right) \cdot i - \left(\left(\left(b \cdot y0\right) \cdot z\right) \cdot k + \left(j \cdot \left(x \cdot y1\right)\right) \cdot i\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}\;x \le -2.1372002604629256 \cdot 10^{-63}:\\
\;\;\;\;\left(\left(\left(\sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \cdot \sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)}\right) \cdot \sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y2 \cdot k - j \cdot y3\right) \cdot \left(\sqrt[3]{y4 \cdot y1 - y5 \cdot y0} \cdot \sqrt[3]{y4 \cdot y1 - y5 \cdot y0}\right)\right) \cdot \sqrt[3]{y4 \cdot y1 - y5 \cdot y0}\\

\mathbf{elif}\;x \le 4.480059003985887 \cdot 10^{-101}:\\
\;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(a \cdot \left(\left(y3 \cdot y1\right) \cdot z - y2 \cdot \left(x \cdot y1\right)\right) - z \cdot \left(c \cdot \left(y3 \cdot y0\right)\right)\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\

\mathbf{elif}\;x \le 3.2670001790969278 \cdot 10^{-74}:\\
\;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\

\mathbf{elif}\;x \le 7.531769519783287 \cdot 10^{+115}:\\
\;\;\;\;\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\\

\mathbf{else}:\\
\;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(\left(\left(y1 \cdot k\right) \cdot z\right) \cdot i - \left(\left(\left(b \cdot y0\right) \cdot z\right) \cdot k + \left(j \cdot \left(x \cdot y1\right)\right) \cdot i\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 r7567460 = x;
        double r7567461 = y;
        double r7567462 = r7567460 * r7567461;
        double r7567463 = z;
        double r7567464 = t;
        double r7567465 = r7567463 * r7567464;
        double r7567466 = r7567462 - r7567465;
        double r7567467 = a;
        double r7567468 = b;
        double r7567469 = r7567467 * r7567468;
        double r7567470 = c;
        double r7567471 = i;
        double r7567472 = r7567470 * r7567471;
        double r7567473 = r7567469 - r7567472;
        double r7567474 = r7567466 * r7567473;
        double r7567475 = j;
        double r7567476 = r7567460 * r7567475;
        double r7567477 = k;
        double r7567478 = r7567463 * r7567477;
        double r7567479 = r7567476 - r7567478;
        double r7567480 = y0;
        double r7567481 = r7567480 * r7567468;
        double r7567482 = y1;
        double r7567483 = r7567482 * r7567471;
        double r7567484 = r7567481 - r7567483;
        double r7567485 = r7567479 * r7567484;
        double r7567486 = r7567474 - r7567485;
        double r7567487 = y2;
        double r7567488 = r7567460 * r7567487;
        double r7567489 = y3;
        double r7567490 = r7567463 * r7567489;
        double r7567491 = r7567488 - r7567490;
        double r7567492 = r7567480 * r7567470;
        double r7567493 = r7567482 * r7567467;
        double r7567494 = r7567492 - r7567493;
        double r7567495 = r7567491 * r7567494;
        double r7567496 = r7567486 + r7567495;
        double r7567497 = r7567464 * r7567475;
        double r7567498 = r7567461 * r7567477;
        double r7567499 = r7567497 - r7567498;
        double r7567500 = y4;
        double r7567501 = r7567500 * r7567468;
        double r7567502 = y5;
        double r7567503 = r7567502 * r7567471;
        double r7567504 = r7567501 - r7567503;
        double r7567505 = r7567499 * r7567504;
        double r7567506 = r7567496 + r7567505;
        double r7567507 = r7567464 * r7567487;
        double r7567508 = r7567461 * r7567489;
        double r7567509 = r7567507 - r7567508;
        double r7567510 = r7567500 * r7567470;
        double r7567511 = r7567502 * r7567467;
        double r7567512 = r7567510 - r7567511;
        double r7567513 = r7567509 * r7567512;
        double r7567514 = r7567506 - r7567513;
        double r7567515 = r7567477 * r7567487;
        double r7567516 = r7567475 * r7567489;
        double r7567517 = r7567515 - r7567516;
        double r7567518 = r7567500 * r7567482;
        double r7567519 = r7567502 * r7567480;
        double r7567520 = r7567518 - r7567519;
        double r7567521 = r7567517 * r7567520;
        double r7567522 = r7567514 + r7567521;
        return r7567522;
}
↓
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 r7567523 = x;
        double r7567524 = -2.1372002604629256e-63;
        bool r7567525 = r7567523 <= r7567524;
        double r7567526 = t;
        double r7567527 = j;
        double r7567528 = r7567526 * r7567527;
        double r7567529 = y;
        double r7567530 = k;
        double r7567531 = r7567529 * r7567530;
        double r7567532 = r7567528 - r7567531;
        double r7567533 = y4;
        double r7567534 = b;
        double r7567535 = r7567533 * r7567534;
        double r7567536 = i;
        double r7567537 = y5;
        double r7567538 = r7567536 * r7567537;
        double r7567539 = r7567535 - r7567538;
        double r7567540 = r7567532 * r7567539;
        double r7567541 = cbrt(r7567540);
        double r7567542 = r7567541 * r7567541;
        double r7567543 = r7567542 * r7567541;
        double r7567544 = c;
        double r7567545 = y0;
        double r7567546 = r7567544 * r7567545;
        double r7567547 = a;
        double r7567548 = y1;
        double r7567549 = r7567547 * r7567548;
        double r7567550 = r7567546 - r7567549;
        double r7567551 = y2;
        double r7567552 = r7567551 * r7567523;
        double r7567553 = y3;
        double r7567554 = z;
        double r7567555 = r7567553 * r7567554;
        double r7567556 = r7567552 - r7567555;
        double r7567557 = r7567550 * r7567556;
        double r7567558 = r7567547 * r7567534;
        double r7567559 = r7567536 * r7567544;
        double r7567560 = r7567558 - r7567559;
        double r7567561 = r7567529 * r7567523;
        double r7567562 = r7567554 * r7567526;
        double r7567563 = r7567561 - r7567562;
        double r7567564 = r7567560 * r7567563;
        double r7567565 = r7567523 * r7567527;
        double r7567566 = r7567554 * r7567530;
        double r7567567 = r7567565 - r7567566;
        double r7567568 = r7567534 * r7567545;
        double r7567569 = r7567536 * r7567548;
        double r7567570 = r7567568 - r7567569;
        double r7567571 = r7567567 * r7567570;
        double r7567572 = r7567564 - r7567571;
        double r7567573 = r7567557 + r7567572;
        double r7567574 = r7567543 + r7567573;
        double r7567575 = r7567526 * r7567551;
        double r7567576 = r7567529 * r7567553;
        double r7567577 = r7567575 - r7567576;
        double r7567578 = r7567533 * r7567544;
        double r7567579 = r7567537 * r7567547;
        double r7567580 = r7567578 - r7567579;
        double r7567581 = r7567577 * r7567580;
        double r7567582 = r7567574 - r7567581;
        double r7567583 = r7567551 * r7567530;
        double r7567584 = r7567527 * r7567553;
        double r7567585 = r7567583 - r7567584;
        double r7567586 = r7567533 * r7567548;
        double r7567587 = r7567537 * r7567545;
        double r7567588 = r7567586 - r7567587;
        double r7567589 = cbrt(r7567588);
        double r7567590 = r7567589 * r7567589;
        double r7567591 = r7567585 * r7567590;
        double r7567592 = r7567591 * r7567589;
        double r7567593 = r7567582 + r7567592;
        double r7567594 = 4.480059003985887e-101;
        bool r7567595 = r7567523 <= r7567594;
        double r7567596 = r7567585 * r7567588;
        double r7567597 = r7567553 * r7567548;
        double r7567598 = r7567597 * r7567554;
        double r7567599 = r7567523 * r7567548;
        double r7567600 = r7567551 * r7567599;
        double r7567601 = r7567598 - r7567600;
        double r7567602 = r7567547 * r7567601;
        double r7567603 = r7567553 * r7567545;
        double r7567604 = r7567544 * r7567603;
        double r7567605 = r7567554 * r7567604;
        double r7567606 = r7567602 - r7567605;
        double r7567607 = r7567606 + r7567572;
        double r7567608 = r7567540 + r7567607;
        double r7567609 = r7567608 - r7567581;
        double r7567610 = r7567596 + r7567609;
        double r7567611 = 3.2670001790969278e-74;
        bool r7567612 = r7567523 <= r7567611;
        double r7567613 = r7567564 + r7567557;
        double r7567614 = r7567540 + r7567613;
        double r7567615 = r7567614 - r7567581;
        double r7567616 = r7567596 + r7567615;
        double r7567617 = 7.531769519783287e+115;
        bool r7567618 = r7567523 <= r7567617;
        double r7567619 = r7567573 + r7567540;
        double r7567620 = r7567619 - r7567581;
        double r7567621 = r7567548 * r7567530;
        double r7567622 = r7567621 * r7567554;
        double r7567623 = r7567622 * r7567536;
        double r7567624 = r7567568 * r7567554;
        double r7567625 = r7567624 * r7567530;
        double r7567626 = r7567527 * r7567599;
        double r7567627 = r7567626 * r7567536;
        double r7567628 = r7567625 + r7567627;
        double r7567629 = r7567623 - r7567628;
        double r7567630 = r7567564 - r7567629;
        double r7567631 = r7567557 + r7567630;
        double r7567632 = r7567540 + r7567631;
        double r7567633 = r7567632 - r7567581;
        double r7567634 = r7567596 + r7567633;
        double r7567635 = r7567618 ? r7567620 : r7567634;
        double r7567636 = r7567612 ? r7567616 : r7567635;
        double r7567637 = r7567595 ? r7567610 : r7567636;
        double r7567638 = r7567525 ? r7567593 : r7567637;
        return r7567638;
}

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 5 regimes

  2. if x < -2.1372002604629256e-63

    1. Initial program 27.5

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

    3. Applied add-cube-cbrt27.6

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

    4. Applied associate-*r*27.6

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

    6. Applied add-cube-cbrt27.6

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

    if -2.1372002604629256e-63 < x < 4.480059003985887e-101

    1. Initial program 24.9

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

    2. Taylor expanded around -inf 27.2

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

    3. Simplified26.2

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

    if 4.480059003985887e-101 < x < 3.2670001790969278e-74

    1. Initial program 24.0

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

    2. Taylor expanded around 0 28.6

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

    if 3.2670001790969278e-74 < x < 7.531769519783287e+115

    1. Initial program 23.3

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

    2. Taylor expanded around 0 28.0

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

    if 7.531769519783287e+115 < x

    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 36.8

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

  4. Final simplification27.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.1372002604629256 \cdot 10^{-63}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \cdot \sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)}\right) \cdot \sqrt[3]{\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y2 \cdot k - j \cdot y3\right) \cdot \left(\sqrt[3]{y4 \cdot y1 - y5 \cdot y0} \cdot \sqrt[3]{y4 \cdot y1 - y5 \cdot y0}\right)\right) \cdot \sqrt[3]{y4 \cdot y1 - y5 \cdot y0}\\ \mathbf{elif}\;x \le 4.480059003985887 \cdot 10^{-101}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(a \cdot \left(\left(y3 \cdot y1\right) \cdot z - y2 \cdot \left(x \cdot y1\right)\right) - z \cdot \left(c \cdot \left(y3 \cdot y0\right)\right)\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \mathbf{elif}\;x \le 3.2670001790969278 \cdot 10^{-74}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\\ \mathbf{elif}\;x \le 7.531769519783287 \cdot 10^{+115}:\\ \;\;\;\;\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y2 \cdot k - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - i \cdot y5\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x - y3 \cdot z\right) + \left(\left(a \cdot b - i \cdot c\right) \cdot \left(y \cdot x - z \cdot t\right) - \left(\left(\left(y1 \cdot k\right) \cdot z\right) \cdot i - \left(\left(\left(b \cdot y0\right) \cdot z\right) \cdot k + \left(j \cdot \left(x \cdot y1\right)\right) \cdot i\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 2019144 
(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)))))