Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 11.9 → 11.0

Time: 15.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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}\;y \le -2.42765769235918329 \cdot 10^{50}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-\left(x \cdot a\right) \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le -8.0409641531815185 \cdot 10^{-61}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-a \cdot \left(i \cdot b\right)\right) + z \cdot \left(b \cdot c\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le -6.89944287855898492 \cdot 10^{-190}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \le 5.04520886396705384 \cdot 10^{-266}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-\left(x \cdot a\right) \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + i \cdot \left(\left(-a\right) \cdot b\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le 6.49469144586640412 \cdot 10^{-155}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-a \cdot \left(i \cdot b\right)\right) + z \cdot \left(b \cdot c\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le 2.44461552747405897 \cdot 10^{-97}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-\left(x \cdot a\right) \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\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 r110536 = x;
        double r110537 = y;
        double r110538 = z;
        double r110539 = r110537 * r110538;
        double r110540 = t;
        double r110541 = a;
        double r110542 = r110540 * r110541;
        double r110543 = r110539 - r110542;
        double r110544 = r110536 * r110543;
        double r110545 = b;
        double r110546 = c;
        double r110547 = r110546 * r110538;
        double r110548 = i;
        double r110549 = r110548 * r110541;
        double r110550 = r110547 - r110549;
        double r110551 = r110545 * r110550;
        double r110552 = r110544 - r110551;
        double r110553 = j;
        double r110554 = r110546 * r110540;
        double r110555 = r110548 * r110537;
        double r110556 = r110554 - r110555;
        double r110557 = r110553 * r110556;
        double r110558 = r110552 + r110557;
        return r110558;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r110559 = y;
        double r110560 = -2.4276576923591833e+50;
        bool r110561 = r110559 <= r110560;
        double r110562 = z;
        double r110563 = x;
        double r110564 = r110562 * r110563;
        double r110565 = r110559 * r110564;
        double r110566 = a;
        double r110567 = r110563 * r110566;
        double r110568 = t;
        double r110569 = r110567 * r110568;
        double r110570 = -r110569;
        double r110571 = r110565 + r110570;
        double r110572 = b;
        double r110573 = c;
        double r110574 = r110572 * r110573;
        double r110575 = r110562 * r110574;
        double r110576 = i;
        double r110577 = r110576 * r110566;
        double r110578 = -r110577;
        double r110579 = r110578 * r110572;
        double r110580 = r110575 + r110579;
        double r110581 = r110571 - r110580;
        double r110582 = j;
        double r110583 = r110573 * r110568;
        double r110584 = r110576 * r110559;
        double r110585 = r110583 - r110584;
        double r110586 = r110582 * r110585;
        double r110587 = r110581 + r110586;
        double r110588 = -8.040964153181518e-61;
        bool r110589 = r110559 <= r110588;
        double r110590 = r110559 * r110562;
        double r110591 = r110568 * r110566;
        double r110592 = r110590 - r110591;
        double r110593 = r110563 * r110592;
        double r110594 = r110576 * r110572;
        double r110595 = r110566 * r110594;
        double r110596 = -r110595;
        double r110597 = r110596 + r110575;
        double r110598 = r110593 - r110597;
        double r110599 = r110598 + r110586;
        double r110600 = -6.899442878558985e-190;
        bool r110601 = r110559 <= r110600;
        double r110602 = r110590 * r110563;
        double r110603 = r110563 * r110568;
        double r110604 = r110566 * r110603;
        double r110605 = -r110604;
        double r110606 = r110602 + r110605;
        double r110607 = r110606 - r110580;
        double r110608 = r110582 * r110573;
        double r110609 = r110568 * r110608;
        double r110610 = r110582 * r110559;
        double r110611 = r110576 * r110610;
        double r110612 = -r110611;
        double r110613 = r110609 + r110612;
        double r110614 = r110607 + r110613;
        double r110615 = 5.045208863967054e-266;
        bool r110616 = r110559 <= r110615;
        double r110617 = r110602 + r110570;
        double r110618 = -r110566;
        double r110619 = r110618 * r110572;
        double r110620 = r110576 * r110619;
        double r110621 = r110575 + r110620;
        double r110622 = r110617 - r110621;
        double r110623 = r110622 + r110586;
        double r110624 = 6.494691445866404e-155;
        bool r110625 = r110559 <= r110624;
        double r110626 = 2.444615527474059e-97;
        bool r110627 = r110559 <= r110626;
        double r110628 = r110627 ? r110614 : r110587;
        double r110629 = r110625 ? r110599 : r110628;
        double r110630 = r110616 ? r110623 : r110629;
        double r110631 = r110601 ? r110614 : r110630;
        double r110632 = r110589 ? r110599 : r110631;
        double r110633 = r110561 ? r110587 : r110632;
        return r110633;
}

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 4 regimes

2. if y < -2.4276576923591833e+50 or 2.444615527474059e-97 < y

   1. Initial program 15.5

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

   3. Applied sub-neg 15.5

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

   4. Applied distribute-lft-in 15.5

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

   5. Simplified 16.6

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

   6. Simplified 16.6

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

   8. Applied sub-neg 16.6

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

   9. Applied distribute-lft-in 16.6

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

   10. Simplified 16.6

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

   11. Simplified 16.6

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

   13. Applied associate-*r* 16.9

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

   14. Simplified 16.9

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

   16. Applied associate-*l* 13.1

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

   if -2.4276576923591833e+50 < y < -8.040964153181518e-61 or 5.045208863967054e-266 < y < 6.494691445866404e-155

   1. Initial program 9.1

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

   3. Applied sub-neg 9.1

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

   4. Applied distribute-lft-in 9.1

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

   5. Simplified 9.0

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

   6. Simplified 9.0

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

   8. Applied neg-mul-1 9.0

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

   9. Applied associate-*l* 9.0

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

   10. Simplified 9.1

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

   if -8.040964153181518e-61 < y < -6.899442878558985e-190 or 6.494691445866404e-155 < y < 2.444615527474059e-97

   1. Initial program 9.1

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

   3. Applied sub-neg 9.1

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

   4. Applied distribute-lft-in 9.1

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

   5. Simplified 9.5

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

   6. Simplified 9.5

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

   8. Applied sub-neg 9.5

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

   9. Applied distribute-lft-in 9.5

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

   10. Simplified 9.5

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

   11. Simplified 9.8

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

   13. Applied sub-neg 9.8

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

   14. Applied distribute-lft-in 9.8

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

   15. Simplified 10.6

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

   16. Simplified 10.7

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

   if -6.899442878558985e-190 < y < 5.045208863967054e-266

   1. Initial program 8.6

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

   3. Applied sub-neg 8.6

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

   4. Applied distribute-lft-in 8.6

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

   5. Simplified 8.9

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

   6. Simplified 8.9

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

   8. Applied sub-neg 8.9

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

   9. Applied distribute-lft-in 8.9

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

   10. Simplified 8.9

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

   11. Simplified 10.0

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

   13. Applied associate-*r* 9.0

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

   14. Simplified 9.0

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

   16. Applied distribute-rgt-neg-in 9.0

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

   17. Applied associate-*l* 8.3

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

4. Final simplification 11.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.42765769235918329 \cdot 10^{50}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-\left(x \cdot a\right) \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le -8.0409641531815185 \cdot 10^{-61}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-a \cdot \left(i \cdot b\right)\right) + z \cdot \left(b \cdot c\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le -6.89944287855898492 \cdot 10^{-190}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \le 5.04520886396705384 \cdot 10^{-266}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-\left(x \cdot a\right) \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + i \cdot \left(\left(-a\right) \cdot b\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le 6.49469144586640412 \cdot 10^{-155}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-a \cdot \left(i \cdot b\right)\right) + z \cdot \left(b \cdot c\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le 2.44461552747405897 \cdot 10^{-97}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-\left(x \cdot a\right) \cdot t\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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)))))