Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.4 → 10.4

Time: 24.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.805708302932435031433559836574348051384 \cdot 10^{61}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{elif}\;b \le -2.141676771618829095111809513520822467409 \cdot 10^{-251}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{elif}\;b \le 6.065890939280876313546602514732864925099 \cdot 10^{-275}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(t \cdot \left(j \cdot c\right) + i \cdot \left(y \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \le 1.416033397586396513407339185362912266365 \cdot 10^{-196}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(b \cdot \left(-i\right)\right) \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;b \le 4.882729267856998925927266812009200535916 \cdot 10^{-49}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + y \cdot \left(-i \cdot j\right)\right)\\ \mathbf{elif}\;b \le 1.569269132260197617025510950717201955038 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{elif}\;b \le 1.522442645301260799179770546660228625058 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + j \cdot \left(-i \cdot y\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 r121491 = x;
        double r121492 = y;
        double r121493 = z;
        double r121494 = r121492 * r121493;
        double r121495 = t;
        double r121496 = a;
        double r121497 = r121495 * r121496;
        double r121498 = r121494 - r121497;
        double r121499 = r121491 * r121498;
        double r121500 = b;
        double r121501 = c;
        double r121502 = r121501 * r121493;
        double r121503 = i;
        double r121504 = r121503 * r121496;
        double r121505 = r121502 - r121504;
        double r121506 = r121500 * r121505;
        double r121507 = r121499 - r121506;
        double r121508 = j;
        double r121509 = r121501 * r121495;
        double r121510 = r121503 * r121492;
        double r121511 = r121509 - r121510;
        double r121512 = r121508 * r121511;
        double r121513 = r121507 + r121512;
        return r121513;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r121514 = b;
        double r121515 = -4.805708302932435e+61;
        bool r121516 = r121514 <= r121515;
        double r121517 = x;
        double r121518 = y;
        double r121519 = z;
        double r121520 = r121518 * r121519;
        double r121521 = t;
        double r121522 = a;
        double r121523 = r121521 * r121522;
        double r121524 = r121520 - r121523;
        double r121525 = r121517 * r121524;
        double r121526 = c;
        double r121527 = r121526 * r121519;
        double r121528 = i;
        double r121529 = r121528 * r121522;
        double r121530 = r121527 - r121529;
        double r121531 = r121514 * r121530;
        double r121532 = r121525 - r121531;
        double r121533 = j;
        double r121534 = r121533 * r121526;
        double r121535 = r121521 * r121534;
        double r121536 = r121528 * r121518;
        double r121537 = -r121536;
        double r121538 = r121533 * r121537;
        double r121539 = r121535 + r121538;
        double r121540 = r121532 + r121539;
        double r121541 = -2.141676771618829e-251;
        bool r121542 = r121514 <= r121541;
        double r121543 = r121519 * r121518;
        double r121544 = r121517 * r121543;
        double r121545 = r121517 * r121521;
        double r121546 = r121522 * r121545;
        double r121547 = r121544 - r121546;
        double r121548 = r121514 * r121526;
        double r121549 = r121519 * r121548;
        double r121550 = -r121529;
        double r121551 = r121514 * r121550;
        double r121552 = r121549 + r121551;
        double r121553 = r121547 - r121552;
        double r121554 = r121521 * r121533;
        double r121555 = r121554 * r121526;
        double r121556 = r121537 * r121533;
        double r121557 = r121555 + r121556;
        double r121558 = r121553 + r121557;
        double r121559 = 6.065890939280876e-275;
        bool r121560 = r121514 <= r121559;
        double r121561 = r121525 - r121552;
        double r121562 = -r121533;
        double r121563 = r121518 * r121562;
        double r121564 = r121528 * r121563;
        double r121565 = r121535 + r121564;
        double r121566 = r121561 + r121565;
        double r121567 = 1.4160333975863965e-196;
        bool r121568 = r121514 <= r121567;
        double r121569 = -r121528;
        double r121570 = r121514 * r121569;
        double r121571 = r121570 * r121522;
        double r121572 = r121549 + r121571;
        double r121573 = r121525 - r121572;
        double r121574 = r121526 * r121521;
        double r121575 = r121574 - r121536;
        double r121576 = r121533 * r121575;
        double r121577 = r121573 + r121576;
        double r121578 = 4.882729267856999e-49;
        bool r121579 = r121514 <= r121578;
        double r121580 = r121528 * r121533;
        double r121581 = -r121580;
        double r121582 = r121518 * r121581;
        double r121583 = r121555 + r121582;
        double r121584 = r121561 + r121583;
        double r121585 = 1.5692691322601976e-40;
        bool r121586 = r121514 <= r121585;
        double r121587 = -r121531;
        double r121588 = r121576 + r121587;
        double r121589 = 1.5224426453012608e-07;
        bool r121590 = r121514 <= r121589;
        double r121591 = r121590 ? r121558 : r121540;
        double r121592 = r121586 ? r121588 : r121591;
        double r121593 = r121579 ? r121584 : r121592;
        double r121594 = r121568 ? r121577 : r121593;
        double r121595 = r121560 ? r121566 : r121594;
        double r121596 = r121542 ? r121558 : r121595;
        double r121597 = r121516 ? r121540 : r121596;
        return r121597;
}

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

Derivation

1. Split input into 6 regimes

2. if b < -4.805708302932435e+61 or 1.5224426453012608e-07 < b

   1. Initial program 7.3

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

   3. Applied sub-neg 7.3

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

   4. Applied distribute-lft-in 7.3

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

   5. Simplified 7.8

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

   if -4.805708302932435e+61 < b < -2.141676771618829e-251 or 1.5692691322601976e-40 < b < 1.5224426453012608e-07

   1. Initial program 13.4

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

   3. Applied sub-neg 13.4

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

   4. Applied distribute-lft-in 13.4

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

   5. Simplified 11.7

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

   7. Applied sub-neg 11.7

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

   8. Applied distribute-lft-in 11.7

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

   9. Simplified 12.1

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

   10. Simplified 12.1

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

   12. Applied associate-*r* 10.9

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

   13. Taylor expanded around inf 10.8

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

   if -2.141676771618829e-251 < b < 6.065890939280876e-275

   1. Initial program 17.8

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

   3. Applied sub-neg 17.8

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

   4. Applied distribute-lft-in 17.8

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

   5. Simplified 13.7

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

   7. Applied sub-neg 13.7

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

   8. Applied distribute-lft-in 13.7

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

   9. Simplified 13.7

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

   10. Simplified 13.7

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

   12. Applied distribute-rgt-neg-in 13.7

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

   13. Applied associate-*l* 13.5

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

   14. Simplified 13.5

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

   if 6.065890939280876e-275 < b < 1.4160333975863965e-196

   1. Initial program 18.3

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

   3. Applied sub-neg 18.3

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

   4. Applied distribute-lft-in 18.3

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

   5. Simplified 14.6

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

   7. Applied distribute-lft-neg-in 14.6

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

   8. Applied associate-*r* 11.1

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

   if 1.4160333975863965e-196 < b < 4.882729267856999e-49

   1. Initial program 14.8

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

   3. Applied sub-neg 14.8

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

   4. Applied distribute-lft-in 14.8

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

   5. Simplified 12.7

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

   7. Applied sub-neg 12.7

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

   8. Applied distribute-lft-in 12.7

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

   9. Simplified 13.9

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

   10. Simplified 13.9

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

   12. Applied associate-*r* 12.7

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

   14. Applied pow1 12.7

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot y\right) \cdot \color{blue}{{j}^{1}}\right)\]

   15. Applied pow1 12.7

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \color{blue}{{\left(-i \cdot y\right)}^{1}} \cdot {j}^{1}\right)\]

   16. Applied pow-prod-down 12.7

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \color{blue}{{\left(\left(-i \cdot y\right) \cdot j\right)}^{1}}\right)\]

   17. Simplified 12.6

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + {\color{blue}{\left(\left(-i \cdot j\right) \cdot y\right)}}^{1}\right)\]

   if 4.882729267856999e-49 < b < 1.5692691322601976e-40

   1. Initial program 7.6

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

   2. Taylor expanded around 0 19.4

      \[\leadsto \left(\color{blue}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
3. Recombined 6 regimes into one program.

4. Final simplification 10.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.805708302932435031433559836574348051384 \cdot 10^{61}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{elif}\;b \le -2.141676771618829095111809513520822467409 \cdot 10^{-251}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{elif}\;b \le 6.065890939280876313546602514732864925099 \cdot 10^{-275}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(t \cdot \left(j \cdot c\right) + i \cdot \left(y \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \le 1.416033397586396513407339185362912266365 \cdot 10^{-196}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(b \cdot \left(-i\right)\right) \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;b \le 4.882729267856998925927266812009200535916 \cdot 10^{-49}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + y \cdot \left(-i \cdot j\right)\right)\\ \mathbf{elif}\;b \le 1.569269132260197617025510950717201955038 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{elif}\;b \le 1.522442645301260799179770546660228625058 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + j \cdot \left(-i \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))