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

Average Error: 12.3 → 9.2

Time: 25.7s

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 -1.885820288721452747199851344770466863725 \cdot 10^{95}:\\ \;\;\;\;\left(\left(\sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} + j \cdot \left(a \cdot c - y \cdot i\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -1.758338690148164602644415584605192188924 \cdot 10^{-166}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 5.504662105172458263088453427769459127963 \cdot 10^{-251}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right) + \left(\left(\left(j \cdot c\right) \cdot a + \left(-\left(y \cdot j\right) \cdot i\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 6.454516511442097649947162038850472776326 \cdot 10^{-203}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 6.877712242978713089253008401315914491855 \cdot 10^{-78}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \sqrt[3]{z} \cdot \left(\left(c \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot b\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 60816444.42864446341991424560546875:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot i - c \cdot z\right) \cdot \sqrt{b}\right) \cdot \sqrt{b} + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\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 r681538 = x;
        double r681539 = y;
        double r681540 = z;
        double r681541 = r681539 * r681540;
        double r681542 = t;
        double r681543 = a;
        double r681544 = r681542 * r681543;
        double r681545 = r681541 - r681544;
        double r681546 = r681538 * r681545;
        double r681547 = b;
        double r681548 = c;
        double r681549 = r681548 * r681540;
        double r681550 = i;
        double r681551 = r681542 * r681550;
        double r681552 = r681549 - r681551;
        double r681553 = r681547 * r681552;
        double r681554 = r681546 - r681553;
        double r681555 = j;
        double r681556 = r681548 * r681543;
        double r681557 = r681539 * r681550;
        double r681558 = r681556 - r681557;
        double r681559 = r681555 * r681558;
        double r681560 = r681554 + r681559;
        return r681560;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r681561 = b;
        double r681562 = -1.8858202887214527e+95;
        bool r681563 = r681561 <= r681562;
        double r681564 = y;
        double r681565 = z;
        double r681566 = r681564 * r681565;
        double r681567 = a;
        double r681568 = t;
        double r681569 = r681567 * r681568;
        double r681570 = r681566 - r681569;
        double r681571 = x;
        double r681572 = r681570 * r681571;
        double r681573 = cbrt(r681572);
        double r681574 = r681573 * r681573;
        double r681575 = r681574 * r681573;
        double r681576 = j;
        double r681577 = c;
        double r681578 = r681567 * r681577;
        double r681579 = i;
        double r681580 = r681564 * r681579;
        double r681581 = r681578 - r681580;
        double r681582 = r681576 * r681581;
        double r681583 = r681575 + r681582;
        double r681584 = r681568 * r681579;
        double r681585 = r681577 * r681565;
        double r681586 = r681584 - r681585;
        double r681587 = r681586 * r681561;
        double r681588 = r681583 + r681587;
        double r681589 = -1.7583386901481646e-166;
        bool r681590 = r681561 <= r681589;
        double r681591 = r681565 * r681571;
        double r681592 = r681591 * r681564;
        double r681593 = r681571 * r681568;
        double r681594 = r681593 * r681567;
        double r681595 = r681592 - r681594;
        double r681596 = r681576 * r681579;
        double r681597 = r681564 * r681596;
        double r681598 = -r681597;
        double r681599 = r681576 * r681567;
        double r681600 = r681577 * r681599;
        double r681601 = r681598 + r681600;
        double r681602 = r681595 + r681601;
        double r681603 = r681568 * r681561;
        double r681604 = r681603 * r681579;
        double r681605 = r681577 * r681561;
        double r681606 = r681605 * r681565;
        double r681607 = r681604 - r681606;
        double r681608 = r681602 + r681607;
        double r681609 = 5.504662105172458e-251;
        bool r681610 = r681561 <= r681609;
        double r681611 = r681576 * r681577;
        double r681612 = r681611 * r681567;
        double r681613 = r681564 * r681576;
        double r681614 = r681613 * r681579;
        double r681615 = -r681614;
        double r681616 = r681612 + r681615;
        double r681617 = r681616 + r681572;
        double r681618 = r681607 + r681617;
        double r681619 = 6.454516511442098e-203;
        bool r681620 = r681561 <= r681619;
        double r681621 = 6.877712242978713e-78;
        bool r681622 = r681561 <= r681621;
        double r681623 = cbrt(r681565);
        double r681624 = r681623 * r681623;
        double r681625 = r681577 * r681624;
        double r681626 = r681625 * r681561;
        double r681627 = r681623 * r681626;
        double r681628 = r681604 - r681627;
        double r681629 = r681582 + r681572;
        double r681630 = r681628 + r681629;
        double r681631 = 60816444.42864446;
        bool r681632 = r681561 <= r681631;
        double r681633 = sqrt(r681561);
        double r681634 = r681586 * r681633;
        double r681635 = r681634 * r681633;
        double r681636 = r681635 + r681629;
        double r681637 = r681632 ? r681608 : r681636;
        double r681638 = r681622 ? r681630 : r681637;
        double r681639 = r681620 ? r681608 : r681638;
        double r681640 = r681610 ? r681618 : r681639;
        double r681641 = r681590 ? r681608 : r681640;
        double r681642 = r681563 ? r681588 : r681641;
        return r681642;
}

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	12.3
Target	19.7
Herbie	9.2

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

Derivation

1. Split input into 5 regimes

2. if b < -1.8858202887214527e+95

   1. Initial program 6.4

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

   2. Simplified 6.4

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

   4. Applied add-cube-cbrt 6.6

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

   if -1.8858202887214527e+95 < b < -1.7583386901481646e-166 or 5.504662105172458e-251 < b < 6.454516511442098e-203 or 6.877712242978713e-78 < b < 60816444.42864446

   1. Initial program 13.0

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

   2. Simplified 13.0

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

   3. Taylor expanded around inf 10.0

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

   4. Simplified 10.1

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

   5. Taylor expanded around inf 10.9

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

   6. Simplified 9.8

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

   8. Applied associate-*r* 10.1

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

   10. Applied sub-neg 10.1

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

   11. Applied distribute-lft-in 10.1

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

   12. Simplified 10.3

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

   13. Simplified 9.3

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

   if -1.7583386901481646e-166 < b < 5.504662105172458e-251

   1. Initial program 17.3

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

   2. Simplified 17.3

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

   3. Taylor expanded around inf 10.9

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

   4. Simplified 10.9

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

   6. Applied sub-neg 10.9

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

   7. Applied distribute-lft-in 10.9

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

   8. Simplified 11.9

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

   9. Simplified 10.8

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

   if 6.454516511442098e-203 < b < 6.877712242978713e-78

   1. Initial program 15.8

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

   2. Simplified 15.8

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

   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

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

   6. Applied add-cube-cbrt 10.5

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

   7. Applied associate-*r* 10.5

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

   8. Simplified 11.5

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

   if 60816444.42864446 < b

   1. Initial program 7.2

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

   2. Simplified 7.2

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

   4. Applied add-sqr-sqrt 7.4

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

   5. Applied associate-*r* 7.4

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

   6. Simplified 7.4

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

4. Final simplification 9.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.885820288721452747199851344770466863725 \cdot 10^{95}:\\ \;\;\;\;\left(\left(\sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} + j \cdot \left(a \cdot c - y \cdot i\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -1.758338690148164602644415584605192188924 \cdot 10^{-166}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 5.504662105172458263088453427769459127963 \cdot 10^{-251}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right) + \left(\left(\left(j \cdot c\right) \cdot a + \left(-\left(y \cdot j\right) \cdot i\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 6.454516511442097649947162038850472776326 \cdot 10^{-203}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 6.877712242978713089253008401315914491855 \cdot 10^{-78}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \sqrt[3]{z} \cdot \left(\left(c \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot b\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 60816444.42864446341991424560546875:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot i - c \cdot z\right) \cdot \sqrt{b}\right) \cdot \sqrt{b} + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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)))))