Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.5 → 12.8

Time: 12.9s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -2.90881967942563483 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;i \le -3.32669010728924322 \cdot 10^{-237}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;i \le 2.12326389170847901 \cdot 10^{-217}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + j \cdot \left(-y \cdot i\right)\right)\\ \mathbf{elif}\;i \le 9.09088801127753167 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;i \le 1.71178825962153685 \cdot 10^{37}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot i - c \cdot z, b, \mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-y \cdot i\right) \cdot j\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r804568 = x;
        double r804569 = y;
        double r804570 = z;
        double r804571 = r804569 * r804570;
        double r804572 = t;
        double r804573 = a;
        double r804574 = r804572 * r804573;
        double r804575 = r804571 - r804574;
        double r804576 = r804568 * r804575;
        double r804577 = b;
        double r804578 = c;
        double r804579 = r804578 * r804570;
        double r804580 = i;
        double r804581 = r804572 * r804580;
        double r804582 = r804579 - r804581;
        double r804583 = r804577 * r804582;
        double r804584 = r804576 - r804583;
        double r804585 = j;
        double r804586 = r804578 * r804573;
        double r804587 = r804569 * r804580;
        double r804588 = r804586 - r804587;
        double r804589 = r804585 * r804588;
        double r804590 = r804584 + r804589;
        return r804590;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r804591 = i;
        double r804592 = -2.908819679425635e-25;
        bool r804593 = r804591 <= r804592;
        double r804594 = x;
        double r804595 = y;
        double r804596 = z;
        double r804597 = r804595 * r804596;
        double r804598 = t;
        double r804599 = a;
        double r804600 = r804598 * r804599;
        double r804601 = r804597 - r804600;
        double r804602 = r804594 * r804601;
        double r804603 = b;
        double r804604 = r804596 * r804603;
        double r804605 = c;
        double r804606 = r804604 * r804605;
        double r804607 = -r804598;
        double r804608 = r804591 * r804603;
        double r804609 = r804607 * r804608;
        double r804610 = r804606 + r804609;
        double r804611 = r804602 - r804610;
        double r804612 = r804605 * r804599;
        double r804613 = j;
        double r804614 = r804612 * r804613;
        double r804615 = r804595 * r804591;
        double r804616 = -r804615;
        double r804617 = r804616 * r804613;
        double r804618 = r804614 + r804617;
        double r804619 = r804611 + r804618;
        double r804620 = -3.326690107289243e-237;
        bool r804621 = r804591 <= r804620;
        double r804622 = r804597 * r804594;
        double r804623 = r804594 * r804598;
        double r804624 = r804599 * r804623;
        double r804625 = -r804624;
        double r804626 = r804622 + r804625;
        double r804627 = r804603 * r804605;
        double r804628 = r804596 * r804627;
        double r804629 = r804628 + r804609;
        double r804630 = r804626 - r804629;
        double r804631 = r804630 + r804618;
        double r804632 = 2.123263891708479e-217;
        bool r804633 = r804591 <= r804632;
        double r804634 = r804605 * r804596;
        double r804635 = r804598 * r804591;
        double r804636 = r804634 - r804635;
        double r804637 = r804603 * r804636;
        double r804638 = r804602 - r804637;
        double r804639 = r804613 * r804605;
        double r804640 = r804599 * r804639;
        double r804641 = r804613 * r804616;
        double r804642 = r804640 + r804641;
        double r804643 = r804638 + r804642;
        double r804644 = 9.090888011277532e-91;
        bool r804645 = r804591 <= r804644;
        double r804646 = 1.7117882596215369e+37;
        bool r804647 = r804591 <= r804646;
        double r804648 = r804635 - r804634;
        double r804649 = r804612 - r804615;
        double r804650 = fma(r804613, r804649, r804602);
        double r804651 = fma(r804648, r804603, r804650);
        double r804652 = r804602 - r804629;
        double r804653 = r804599 * r804613;
        double r804654 = r804605 * r804653;
        double r804655 = r804654 + r804617;
        double r804656 = r804652 + r804655;
        double r804657 = r804647 ? r804651 : r804656;
        double r804658 = r804645 ? r804631 : r804657;
        double r804659 = r804633 ? r804643 : r804658;
        double r804660 = r804621 ? r804631 : r804659;
        double r804661 = r804593 ? r804619 : r804660;
        return r804661;
}

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

Target

Original	12.5
Target	20.3
Herbie	12.8

\[\begin{array}{l} \mathbf{if}\;x \lt -1.46969429677770502 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

1. Split input into 5 regimes

2. if i < -2.908819679425635e-25

   1. Initial program 14.9

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

   3. Applied sub-neg 14.9

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

   4. Applied distribute-lft-in 14.9

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

   5. Simplified 15.1

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

   6. Simplified 15.1

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

   8. Applied distribute-lft-neg-in 15.1

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

   9. Applied associate-*l* 15.4

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

   11. Applied sub-neg 15.4

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

   12. Applied distribute-lft-in 15.4

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

   13. Simplified 15.4

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

   14. Simplified 15.4

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

   16. Applied associate-*r* 15.4

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

   if -2.908819679425635e-25 < i < -3.326690107289243e-237 or 2.123263891708479e-217 < i < 9.090888011277532e-91

   1. Initial program 10.2

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

   3. Applied sub-neg 10.2

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

   4. Applied distribute-lft-in 10.2

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

   5. Simplified 11.4

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

   6. Simplified 11.4

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

   8. Applied distribute-lft-neg-in 11.4

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

   9. Applied associate-*l* 11.1

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

   11. Applied sub-neg 11.1

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

   12. Applied distribute-lft-in 11.1

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

   13. Simplified 11.1

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

   14. Simplified 11.1

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

   16. Applied sub-neg 11.1

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

   17. Applied distribute-lft-in 11.1

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

   18. Simplified 11.1

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

   19. Simplified 11.2

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

   if -3.326690107289243e-237 < i < 2.123263891708479e-217

   1. Initial program 9.6

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

   3. Applied sub-neg 9.6

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

   4. Applied distribute-lft-in 9.6

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

   5. Simplified 9.9

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

   if 9.090888011277532e-91 < i < 1.7117882596215369e+37

   1. Initial program 9.9

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

   2. Simplified 9.9

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

   if 1.7117882596215369e+37 < i

   1. Initial program 18.8

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

   3. Applied sub-neg 18.8

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

   4. Applied distribute-lft-in 18.8

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

   5. Simplified 18.4

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

   6. Simplified 18.4

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

   8. Applied distribute-lft-neg-in 18.4

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

   9. Applied associate-*l* 17.4

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

   11. Applied sub-neg 17.4

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

   12. Applied distribute-lft-in 17.4

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

   13. Simplified 17.4

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

   14. Simplified 17.4

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

   16. Applied associate-*l* 17.5

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

4. Final simplification 12.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -2.90881967942563483 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;i \le -3.32669010728924322 \cdot 10^{-237}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;i \le 2.12326389170847901 \cdot 10^{-217}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + j \cdot \left(-y \cdot i\right)\right)\\ \mathbf{elif}\;i \le 9.09088801127753167 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;i \le 1.71178825962153685 \cdot 10^{37}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot i - c \cdot z, b, \mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t\right) \cdot \left(i \cdot b\right)\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-y \cdot i\right) \cdot j\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))