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

Average Error: 11.8 → 11.4

Time: 20.6s

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}\;z \le -9.965934507395226057401973153405420066828 \cdot 10^{65}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t \cdot \left(i \cdot b\right)\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \le -4.689883489295011790407732434019287505254 \cdot 10^{-216}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \le -1.864721872398415194168523407765985541812 \cdot 10^{-272}:\\ \;\;\;\;\left(t \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;z \le -6.628575237567785096221400260672621839607 \cdot 10^{-290}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{elif}\;z \le 5.886583142604684229808502775776833451681 \cdot 10^{-202}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(a \cdot j\right) \cdot c + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \le 79.85626140011545714969543041661381721497:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\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 r571072 = x;
        double r571073 = y;
        double r571074 = z;
        double r571075 = r571073 * r571074;
        double r571076 = t;
        double r571077 = a;
        double r571078 = r571076 * r571077;
        double r571079 = r571075 - r571078;
        double r571080 = r571072 * r571079;
        double r571081 = b;
        double r571082 = c;
        double r571083 = r571082 * r571074;
        double r571084 = i;
        double r571085 = r571076 * r571084;
        double r571086 = r571083 - r571085;
        double r571087 = r571081 * r571086;
        double r571088 = r571080 - r571087;
        double r571089 = j;
        double r571090 = r571082 * r571077;
        double r571091 = r571073 * r571084;
        double r571092 = r571090 - r571091;
        double r571093 = r571089 * r571092;
        double r571094 = r571088 + r571093;
        return r571094;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r571095 = z;
        double r571096 = -9.965934507395226e+65;
        bool r571097 = r571095 <= r571096;
        double r571098 = x;
        double r571099 = y;
        double r571100 = r571099 * r571095;
        double r571101 = r571098 * r571100;
        double r571102 = a;
        double r571103 = t;
        double r571104 = r571098 * r571103;
        double r571105 = r571102 * r571104;
        double r571106 = -r571105;
        double r571107 = r571101 + r571106;
        double r571108 = b;
        double r571109 = c;
        double r571110 = r571108 * r571109;
        double r571111 = r571095 * r571110;
        double r571112 = i;
        double r571113 = r571112 * r571108;
        double r571114 = r571103 * r571113;
        double r571115 = -r571114;
        double r571116 = r571111 + r571115;
        double r571117 = r571107 - r571116;
        double r571118 = j;
        double r571119 = r571118 * r571109;
        double r571120 = r571102 * r571119;
        double r571121 = r571118 * r571099;
        double r571122 = r571112 * r571121;
        double r571123 = -r571122;
        double r571124 = r571120 + r571123;
        double r571125 = r571117 + r571124;
        double r571126 = -4.689883489295012e-216;
        bool r571127 = r571095 <= r571126;
        double r571128 = r571098 * r571099;
        double r571129 = r571128 * r571095;
        double r571130 = r571129 + r571106;
        double r571131 = r571109 * r571095;
        double r571132 = r571103 * r571112;
        double r571133 = r571131 - r571132;
        double r571134 = r571108 * r571133;
        double r571135 = r571130 - r571134;
        double r571136 = r571135 + r571124;
        double r571137 = -1.8647218723984152e-272;
        bool r571138 = r571095 <= r571137;
        double r571139 = r571111 + r571105;
        double r571140 = r571114 - r571139;
        double r571141 = r571109 * r571102;
        double r571142 = r571099 * r571112;
        double r571143 = r571141 - r571142;
        double r571144 = r571118 * r571143;
        double r571145 = r571140 + r571144;
        double r571146 = -6.628575237567785e-290;
        bool r571147 = r571095 <= r571146;
        double r571148 = r571103 * r571102;
        double r571149 = r571100 - r571148;
        double r571150 = r571098 * r571149;
        double r571151 = r571150 - r571134;
        double r571152 = cbrt(r571118);
        double r571153 = r571152 * r571152;
        double r571154 = r571152 * r571143;
        double r571155 = r571153 * r571154;
        double r571156 = r571151 + r571155;
        double r571157 = 5.886583142604684e-202;
        bool r571158 = r571095 <= r571157;
        double r571159 = r571107 - r571134;
        double r571160 = r571102 * r571118;
        double r571161 = r571160 * r571109;
        double r571162 = r571161 + r571123;
        double r571163 = r571159 + r571162;
        double r571164 = 79.85626140011546;
        bool r571165 = r571095 <= r571164;
        double r571166 = r571165 ? r571156 : r571136;
        double r571167 = r571158 ? r571163 : r571166;
        double r571168 = r571147 ? r571156 : r571167;
        double r571169 = r571138 ? r571145 : r571168;
        double r571170 = r571127 ? r571136 : r571169;
        double r571171 = r571097 ? r571125 : r571170;
        return r571171;
}

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	11.8
Target	19.6
Herbie	11.4

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

Derivation

1. Split input into 5 regimes

2. if z < -9.965934507395226e+65

   1. Initial program 19.3

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

   3. Applied sub-neg 19.3

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

   4. Applied distribute-lft-in 19.3

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

   5. Simplified 19.4

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

   7. Applied distribute-rgt-neg-out 19.4

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

   8. Simplified 19.4

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

   10. Applied sub-neg 19.4

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

   11. Applied distribute-lft-in 19.4

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

   12. Simplified 18.1

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

   14. Applied sub-neg 18.1

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

   15. Applied distribute-lft-in 18.1

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

   16. Simplified 13.0

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

   17. Simplified 12.7

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

   if -9.965934507395226e+65 < z < -4.689883489295012e-216 or 79.85626140011546 < z

   1. Initial program 12.2

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

   3. Applied sub-neg 12.2

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

   4. Applied distribute-lft-in 12.2

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

   5. Simplified 12.5

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

   7. Applied distribute-rgt-neg-out 12.5

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

   8. Simplified 12.8

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

   10. Applied sub-neg 12.8

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

   11. Applied distribute-lft-in 12.8

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

   12. Simplified 12.9

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

   14. Applied associate-*r* 12.2

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

   if -4.689883489295012e-216 < z < -1.8647218723984152e-272

   1. Initial program 8.8

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

   2. Taylor expanded around inf 16.1

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

   if -1.8647218723984152e-272 < z < -6.628575237567785e-290 or 5.886583142604684e-202 < z < 79.85626140011546

   1. Initial program 8.1

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

   3. Applied add-cube-cbrt 8.5

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

   4. Applied associate-*l* 8.4

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

   if -6.628575237567785e-290 < z < 5.886583142604684e-202

   1. Initial program 9.4

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

   3. Applied sub-neg 9.4

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

   4. Applied distribute-lft-in 9.4

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

   5. Simplified 10.5

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

   7. Applied distribute-rgt-neg-out 10.5

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

   8. Simplified 10.0

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

   10. Applied sub-neg 10.0

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

   11. Applied distribute-lft-in 10.0

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

   12. Simplified 10.0

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

   14. Applied associate-*r* 9.9

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

4. Final simplification 11.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.965934507395226057401973153405420066828 \cdot 10^{65}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t \cdot \left(i \cdot b\right)\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \le -4.689883489295011790407732434019287505254 \cdot 10^{-216}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \le -1.864721872398415194168523407765985541812 \cdot 10^{-272}:\\ \;\;\;\;\left(t \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;z \le -6.628575237567785096221400260672621839607 \cdot 10^{-290}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{elif}\;z \le 5.886583142604684229808502775776833451681 \cdot 10^{-202}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(a \cdot j\right) \cdot c + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \le 79.85626140011545714969543041661381721497:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(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 -1.46969429677770502e-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)))))