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

Average Error: 12.4 → 9.7

Time: 25.9s

Precision: 64

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}\;b \le -3.725138153910988730936648146499484432334 \cdot 10^{76}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - \left(x \cdot a\right) \cdot t\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -6.544881131462384959170183205645892072607 \cdot 10^{-94}:\\ \;\;\;\;\left(\left(\left(-\left(y \cdot j\right) \cdot i\right) + c \cdot \left(j \cdot a\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(t \cdot b\right) \cdot i - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le -6.651701605731016043167399068212918503952 \cdot 10^{-134}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(i \cdot b\right)\right) - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le -2.965523078545726390551901853798335915023 \cdot 10^{-204}:\\ \;\;\;\;\left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right) + \left(\left(\left(y \cdot x\right) \cdot z - a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{elif}\;b \le 4.944497479843419684921438322625378474248 \cdot 10^{-214}:\\ \;\;\;\;\left(\left(\left(-\left(y \cdot j\right) \cdot i\right) + c \cdot \left(j \cdot a\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(t \cdot b\right) \cdot i - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le 2.700938591604041463230149378622378934965 \cdot 10^{-81}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(j \cdot c\right) \cdot a + y \cdot \left(i \cdot \left(-j\right)\right)\right)\right) + \left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le 1.75607632423487995539322255985778127624 \cdot 10^{80}:\\ \;\;\;\;\left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right) + \left(\left(\left(y \cdot x\right) \cdot z - a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{elif}\;b \le 2.149640478734169986509788916183067553901 \cdot 10^{89}:\\ \;\;\;\;\left(\left(\left(-\left(y \cdot j\right) \cdot i\right) + c \cdot \left(j \cdot a\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(t \cdot b\right) \cdot i - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le 5.591290094756511996649968865827829365135 \cdot 10^{130}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(j \cdot c\right) \cdot a + y \cdot \left(i \cdot \left(-j\right)\right)\right)\right) + \left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - \left(x \cdot a\right) \cdot t\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r638506 = x;
        double r638507 = y;
        double r638508 = z;
        double r638509 = r638507 * r638508;
        double r638510 = t;
        double r638511 = a;
        double r638512 = r638510 * r638511;
        double r638513 = r638509 - r638512;
        double r638514 = r638506 * r638513;
        double r638515 = b;
        double r638516 = c;
        double r638517 = r638516 * r638508;
        double r638518 = i;
        double r638519 = r638510 * r638518;
        double r638520 = r638517 - r638519;
        double r638521 = r638515 * r638520;
        double r638522 = r638514 - r638521;
        double r638523 = j;
        double r638524 = r638516 * r638511;
        double r638525 = r638507 * r638518;
        double r638526 = r638524 - r638525;
        double r638527 = r638523 * r638526;
        double r638528 = r638522 + r638527;
        return r638528;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r638529 = b;
        double r638530 = -3.725138153910989e+76;
        bool r638531 = r638529 <= r638530;
        double r638532 = j;
        double r638533 = a;
        double r638534 = c;
        double r638535 = r638533 * r638534;
        double r638536 = y;
        double r638537 = i;
        double r638538 = r638536 * r638537;
        double r638539 = r638535 - r638538;
        double r638540 = r638532 * r638539;
        double r638541 = x;
        double r638542 = z;
        double r638543 = r638541 * r638542;
        double r638544 = r638536 * r638543;
        double r638545 = r638541 * r638533;
        double r638546 = t;
        double r638547 = r638545 * r638546;
        double r638548 = r638544 - r638547;
        double r638549 = r638540 + r638548;
        double r638550 = r638546 * r638537;
        double r638551 = r638534 * r638542;
        double r638552 = r638550 - r638551;
        double r638553 = r638552 * r638529;
        double r638554 = r638549 + r638553;
        double r638555 = -6.544881131462385e-94;
        bool r638556 = r638529 <= r638555;
        double r638557 = r638536 * r638532;
        double r638558 = r638557 * r638537;
        double r638559 = -r638558;
        double r638560 = r638532 * r638533;
        double r638561 = r638534 * r638560;
        double r638562 = r638559 + r638561;
        double r638563 = r638536 * r638542;
        double r638564 = r638533 * r638546;
        double r638565 = r638563 - r638564;
        double r638566 = r638541 * r638565;
        double r638567 = r638562 + r638566;
        double r638568 = r638546 * r638529;
        double r638569 = r638568 * r638537;
        double r638570 = r638534 * r638529;
        double r638571 = r638542 * r638570;
        double r638572 = r638569 - r638571;
        double r638573 = r638567 + r638572;
        double r638574 = -6.651701605731016e-134;
        bool r638575 = r638529 <= r638574;
        double r638576 = r638540 + r638566;
        double r638577 = cbrt(r638546);
        double r638578 = r638577 * r638577;
        double r638579 = r638537 * r638529;
        double r638580 = r638578 * r638579;
        double r638581 = r638577 * r638580;
        double r638582 = r638581 - r638571;
        double r638583 = r638576 + r638582;
        double r638584 = -2.9655230785457264e-204;
        bool r638585 = r638529 <= r638584;
        double r638586 = r638546 * r638579;
        double r638587 = r638586 - r638571;
        double r638588 = r638536 * r638541;
        double r638589 = r638588 * r638542;
        double r638590 = r638546 * r638541;
        double r638591 = r638533 * r638590;
        double r638592 = r638589 - r638591;
        double r638593 = r638592 + r638540;
        double r638594 = r638587 + r638593;
        double r638595 = 4.94449747984342e-214;
        bool r638596 = r638529 <= r638595;
        double r638597 = 2.7009385916040415e-81;
        bool r638598 = r638529 <= r638597;
        double r638599 = r638532 * r638534;
        double r638600 = r638599 * r638533;
        double r638601 = -r638532;
        double r638602 = r638537 * r638601;
        double r638603 = r638536 * r638602;
        double r638604 = r638600 + r638603;
        double r638605 = r638566 + r638604;
        double r638606 = r638605 + r638587;
        double r638607 = 1.75607632423488e+80;
        bool r638608 = r638529 <= r638607;
        double r638609 = 2.14964047873417e+89;
        bool r638610 = r638529 <= r638609;
        double r638611 = 5.591290094756512e+130;
        bool r638612 = r638529 <= r638611;
        double r638613 = r638612 ? r638606 : r638554;
        double r638614 = r638610 ? r638573 : r638613;
        double r638615 = r638608 ? r638594 : r638614;
        double r638616 = r638598 ? r638606 : r638615;
        double r638617 = r638596 ? r638573 : r638616;
        double r638618 = r638585 ? r638594 : r638617;
        double r638619 = r638575 ? r638583 : r638618;
        double r638620 = r638556 ? r638573 : r638619;
        double r638621 = r638531 ? r638554 : r638620;
        return r638621;
}

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	12.4
Target	19.4
Herbie	9.7

\[\begin{array}{l} \mathbf{if}\;x \lt -1.469694296777705016266218530347997287942 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.21135273622268028942701600607048800714 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

1. Split input into 5 regimes

2. if b < -3.725138153910989e+76 or 5.591290094756512e+130 < b

   1. Initial program 7.4

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

   2. Simplified 7.4

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

   3. Taylor expanded around inf 7.2

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

   4. Simplified 8.1

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

   if -3.725138153910989e+76 < b < -6.544881131462385e-94 or -2.9655230785457264e-204 < b < 4.94449747984342e-214 or 1.75607632423488e+80 < b < 2.14964047873417e+89

   1. Initial program 15.0

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

   2. Simplified 15.0

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

   3. Taylor expanded around inf 10.5

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

   4. Simplified 10.5

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

   5. Taylor expanded around inf 10.5

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

   6. Simplified 10.5

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

   8. Applied sub-neg 10.5

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

   9. Applied distribute-lft-in 10.5

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

   10. Simplified 10.5

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

   11. Simplified 9.7

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

   if -6.544881131462385e-94 < b < -6.651701605731016e-134

   1. Initial program 13.4

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

   2. Simplified 13.4

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

   3. Taylor expanded around inf 9.3

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

   4. Simplified 9.3

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

   6. Applied add-cube-cbrt 9.4

      \[\leadsto \left(\left(i \cdot b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)} - z \cdot \left(b \cdot c\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(z \cdot y - t \cdot a\right) \cdot x\right)\]

   7. Applied associate-*r* 9.4

      \[\leadsto \left(\color{blue}{\left(\left(i \cdot b\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}} - z \cdot \left(b \cdot c\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(z \cdot y - t \cdot a\right) \cdot x\right)\]

   if -6.651701605731016e-134 < b < -2.9655230785457264e-204 or 2.7009385916040415e-81 < b < 1.75607632423488e+80

   1. Initial program 12.3

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

   2. Simplified 12.3

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

   3. Taylor expanded around inf 10.4

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

   4. Simplified 10.4

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

   5. Taylor expanded around inf 10.9

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

   6. Simplified 10.0

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

   if 4.94449747984342e-214 < b < 2.7009385916040415e-81 or 2.14964047873417e+89 < b < 5.591290094756512e+130

   1. Initial program 13.5

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

   2. Simplified 13.5

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

   3. Taylor expanded around inf 10.8

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

   4. Simplified 10.8

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

   6. Applied sub-neg 10.8

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

   7. Applied distribute-lft-in 10.8

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

   8. Simplified 11.3

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

   9. Simplified 11.8

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

4. Final simplification 9.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.725138153910988730936648146499484432334 \cdot 10^{76}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - \left(x \cdot a\right) \cdot t\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -6.544881131462384959170183205645892072607 \cdot 10^{-94}:\\ \;\;\;\;\left(\left(\left(-\left(y \cdot j\right) \cdot i\right) + c \cdot \left(j \cdot a\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(t \cdot b\right) \cdot i - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le -6.651701605731016043167399068212918503952 \cdot 10^{-134}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(i \cdot b\right)\right) - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le -2.965523078545726390551901853798335915023 \cdot 10^{-204}:\\ \;\;\;\;\left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right) + \left(\left(\left(y \cdot x\right) \cdot z - a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{elif}\;b \le 4.944497479843419684921438322625378474248 \cdot 10^{-214}:\\ \;\;\;\;\left(\left(\left(-\left(y \cdot j\right) \cdot i\right) + c \cdot \left(j \cdot a\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(t \cdot b\right) \cdot i - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le 2.700938591604041463230149378622378934965 \cdot 10^{-81}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(j \cdot c\right) \cdot a + y \cdot \left(i \cdot \left(-j\right)\right)\right)\right) + \left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le 1.75607632423487995539322255985778127624 \cdot 10^{80}:\\ \;\;\;\;\left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right) + \left(\left(\left(y \cdot x\right) \cdot z - a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{elif}\;b \le 2.149640478734169986509788916183067553901 \cdot 10^{89}:\\ \;\;\;\;\left(\left(\left(-\left(y \cdot j\right) \cdot i\right) + c \cdot \left(j \cdot a\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(t \cdot b\right) \cdot i - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;b \le 5.591290094756511996649968865827829365135 \cdot 10^{130}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(j \cdot c\right) \cdot a + y \cdot \left(i \cdot \left(-j\right)\right)\right)\right) + \left(t \cdot \left(i \cdot b\right) - z \cdot \left(c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - \left(x \cdot a\right) \cdot t\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* 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) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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