Linear.Matrix:det44 from linear-1.19.1.3

Average Error: 27.0 → 28.1

Time: 1.5m

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;j \le -5.423307827391987656847104322360977276686 \cdot 10^{-206} \lor \neg \left(j \le 6.591415557374126792319668655786595642762 \cdot 10^{-241}\right):\\ \;\;\;\;\left(\left(\left(\left(\left(\sqrt[3]{x \cdot y - z \cdot t} \cdot \sqrt[3]{x \cdot y - z \cdot t}\right) \cdot \left(\sqrt[3]{x \cdot y - z \cdot t} \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y4 \cdot y1\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-y5\right) \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y4 \cdot y1\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-y5\right) \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \end{array}\]

C

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 r131456 = x;
        double r131457 = y;
        double r131458 = r131456 * r131457;
        double r131459 = z;
        double r131460 = t;
        double r131461 = r131459 * r131460;
        double r131462 = r131458 - r131461;
        double r131463 = a;
        double r131464 = b;
        double r131465 = r131463 * r131464;
        double r131466 = c;
        double r131467 = i;
        double r131468 = r131466 * r131467;
        double r131469 = r131465 - r131468;
        double r131470 = r131462 * r131469;
        double r131471 = j;
        double r131472 = r131456 * r131471;
        double r131473 = k;
        double r131474 = r131459 * r131473;
        double r131475 = r131472 - r131474;
        double r131476 = y0;
        double r131477 = r131476 * r131464;
        double r131478 = y1;
        double r131479 = r131478 * r131467;
        double r131480 = r131477 - r131479;
        double r131481 = r131475 * r131480;
        double r131482 = r131470 - r131481;
        double r131483 = y2;
        double r131484 = r131456 * r131483;
        double r131485 = y3;
        double r131486 = r131459 * r131485;
        double r131487 = r131484 - r131486;
        double r131488 = r131476 * r131466;
        double r131489 = r131478 * r131463;
        double r131490 = r131488 - r131489;
        double r131491 = r131487 * r131490;
        double r131492 = r131482 + r131491;
        double r131493 = r131460 * r131471;
        double r131494 = r131457 * r131473;
        double r131495 = r131493 - r131494;
        double r131496 = y4;
        double r131497 = r131496 * r131464;
        double r131498 = y5;
        double r131499 = r131498 * r131467;
        double r131500 = r131497 - r131499;
        double r131501 = r131495 * r131500;
        double r131502 = r131492 + r131501;
        double r131503 = r131460 * r131483;
        double r131504 = r131457 * r131485;
        double r131505 = r131503 - r131504;
        double r131506 = r131496 * r131466;
        double r131507 = r131498 * r131463;
        double r131508 = r131506 - r131507;
        double r131509 = r131505 * r131508;
        double r131510 = r131502 - r131509;
        double r131511 = r131473 * r131483;
        double r131512 = r131471 * r131485;
        double r131513 = r131511 - r131512;
        double r131514 = r131496 * r131478;
        double r131515 = r131498 * r131476;
        double r131516 = r131514 - r131515;
        double r131517 = r131513 * r131516;
        double r131518 = r131510 + r131517;
        return r131518;
}

↓

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 r131519 = j;
        double r131520 = -5.423307827391988e-206;
        bool r131521 = r131519 <= r131520;
        double r131522 = 6.591415557374127e-241;
        bool r131523 = r131519 <= r131522;
        double r131524 = !r131523;
        bool r131525 = r131521 || r131524;
        double r131526 = x;
        double r131527 = y;
        double r131528 = r131526 * r131527;
        double r131529 = z;
        double r131530 = t;
        double r131531 = r131529 * r131530;
        double r131532 = r131528 - r131531;
        double r131533 = cbrt(r131532);
        double r131534 = r131533 * r131533;
        double r131535 = a;
        double r131536 = b;
        double r131537 = r131535 * r131536;
        double r131538 = c;
        double r131539 = i;
        double r131540 = r131538 * r131539;
        double r131541 = r131537 - r131540;
        double r131542 = r131533 * r131541;
        double r131543 = r131534 * r131542;
        double r131544 = r131526 * r131519;
        double r131545 = k;
        double r131546 = r131529 * r131545;
        double r131547 = r131544 - r131546;
        double r131548 = y0;
        double r131549 = r131548 * r131536;
        double r131550 = y1;
        double r131551 = r131550 * r131539;
        double r131552 = r131549 - r131551;
        double r131553 = r131547 * r131552;
        double r131554 = r131543 - r131553;
        double r131555 = y2;
        double r131556 = r131526 * r131555;
        double r131557 = y3;
        double r131558 = r131529 * r131557;
        double r131559 = r131556 - r131558;
        double r131560 = r131548 * r131538;
        double r131561 = r131550 * r131535;
        double r131562 = r131560 - r131561;
        double r131563 = r131559 * r131562;
        double r131564 = r131554 + r131563;
        double r131565 = r131530 * r131519;
        double r131566 = r131527 * r131545;
        double r131567 = r131565 - r131566;
        double r131568 = y4;
        double r131569 = r131568 * r131536;
        double r131570 = y5;
        double r131571 = r131570 * r131539;
        double r131572 = r131569 - r131571;
        double r131573 = r131567 * r131572;
        double r131574 = r131564 + r131573;
        double r131575 = r131530 * r131555;
        double r131576 = r131527 * r131557;
        double r131577 = r131575 - r131576;
        double r131578 = r131568 * r131538;
        double r131579 = r131570 * r131535;
        double r131580 = r131578 - r131579;
        double r131581 = r131577 * r131580;
        double r131582 = r131574 - r131581;
        double r131583 = r131568 * r131550;
        double r131584 = r131545 * r131555;
        double r131585 = r131519 * r131557;
        double r131586 = r131584 - r131585;
        double r131587 = r131583 * r131586;
        double r131588 = -r131570;
        double r131589 = r131548 * r131586;
        double r131590 = r131588 * r131589;
        double r131591 = r131587 + r131590;
        double r131592 = r131582 + r131591;
        double r131593 = r131532 * r131541;
        double r131594 = r131593 + r131563;
        double r131595 = r131594 + r131573;
        double r131596 = r131595 - r131581;
        double r131597 = r131596 + r131591;
        double r131598 = r131525 ? r131592 : r131597;
        return r131598;
}

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 2 regimes

2. if j < -5.423307827391988e-206 or 6.591415557374127e-241 < j

   1. Initial program 26.9

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

   3. Applied sub-neg 26.9

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

   4. Applied distribute-lft-in 26.9

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

   5. Simplified 26.9

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

   6. Simplified 26.9

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

   8. Applied distribute-lft-neg-in 26.9

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

   9. Applied associate-*l* 27.6

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

   11. Applied add-cube-cbrt 27.7

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

   12. Applied associate-*l* 27.7

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

   if -5.423307827391988e-206 < j < 6.591415557374127e-241

   1. Initial program 27.3

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

   3. Applied sub-neg 27.3

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

   4. Applied distribute-lft-in 27.3

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

   5. Simplified 27.3

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

   6. Simplified 27.3

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

   8. Applied distribute-lft-neg-in 27.3

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

   9. Applied associate-*l* 27.0

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

   10. Taylor expanded around 0 29.6

       \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \color{blue}{0}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y4 \cdot y1\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-y5\right) \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification 28.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -5.423307827391987656847104322360977276686 \cdot 10^{-206} \lor \neg \left(j \le 6.591415557374126792319668655786595642762 \cdot 10^{-241}\right):\\ \;\;\;\;\left(\left(\left(\left(\left(\sqrt[3]{x \cdot y - z \cdot t} \cdot \sqrt[3]{x \cdot y - z \cdot t}\right) \cdot \left(\sqrt[3]{x \cdot y - z \cdot t} \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y4 \cdot y1\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-y5\right) \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(\left(y4 \cdot y1\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-y5\right) \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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"
  :precision binary64
  (+ (- (+ (+ (- (* (- (* 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)))))