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

Average Error: 12.3 → 11.2

Time: 23.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;j \le -22910070.9165217392146587371826171875:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) + \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\left(\sqrt[3]{a} \cdot j\right) \cdot c\right) + \left(i \cdot y\right) \cdot \left(-j\right)\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;j \le -7.867962692305981669371960735265674041139 \cdot 10^{-174}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) + \left(\left(t \cdot i\right) \cdot b - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;j \le -1.564337481163701803716112508040619347212 \cdot 10^{-232}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(c \cdot j\right) \cdot a + \left(i \cdot y\right) \cdot \left(-j\right)\right)\right) + \left(i \cdot \left(b \cdot t\right) - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;j \le 1.42932352777029364191431798014284398257 \cdot 10^{-82}:\\ \;\;\;\;\left(\left(\left(-i\right) \cdot \left(j \cdot y\right) + c \cdot \left(a \cdot j\right)\right) + \left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;j \le 1.708691545176934437811367991434167485084 \cdot 10^{-27} \lor \neg \left(j \le 1.797841690387996792815929876315347308672 \cdot 10^{129}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) + \left(\left(i \cdot b\right) \cdot t - \left(c \cdot z\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) + \left(\left(t \cdot i\right) \cdot b - \left(b \cdot z\right) \cdot c\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r443071 = x;
        double r443072 = y;
        double r443073 = z;
        double r443074 = r443072 * r443073;
        double r443075 = t;
        double r443076 = a;
        double r443077 = r443075 * r443076;
        double r443078 = r443074 - r443077;
        double r443079 = r443071 * r443078;
        double r443080 = b;
        double r443081 = c;
        double r443082 = r443081 * r443073;
        double r443083 = i;
        double r443084 = r443075 * r443083;
        double r443085 = r443082 - r443084;
        double r443086 = r443080 * r443085;
        double r443087 = r443079 - r443086;
        double r443088 = j;
        double r443089 = r443081 * r443076;
        double r443090 = r443072 * r443083;
        double r443091 = r443089 - r443090;
        double r443092 = r443088 * r443091;
        double r443093 = r443087 + r443092;
        return r443093;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r443094 = j;
        double r443095 = -22910070.91652174;
        bool r443096 = r443094 <= r443095;
        double r443097 = x;
        double r443098 = z;
        double r443099 = r443097 * r443098;
        double r443100 = y;
        double r443101 = r443099 * r443100;
        double r443102 = t;
        double r443103 = r443102 * r443097;
        double r443104 = a;
        double r443105 = r443103 * r443104;
        double r443106 = r443101 - r443105;
        double r443107 = cbrt(r443104);
        double r443108 = r443107 * r443107;
        double r443109 = r443107 * r443094;
        double r443110 = c;
        double r443111 = r443109 * r443110;
        double r443112 = r443108 * r443111;
        double r443113 = i;
        double r443114 = r443113 * r443100;
        double r443115 = -r443094;
        double r443116 = r443114 * r443115;
        double r443117 = r443112 + r443116;
        double r443118 = r443106 + r443117;
        double r443119 = r443102 * r443113;
        double r443120 = r443110 * r443098;
        double r443121 = r443119 - r443120;
        double r443122 = b;
        double r443123 = r443121 * r443122;
        double r443124 = r443118 + r443123;
        double r443125 = -7.867962692305982e-174;
        bool r443126 = r443094 <= r443125;
        double r443127 = r443097 * r443100;
        double r443128 = r443127 * r443098;
        double r443129 = r443104 * r443097;
        double r443130 = r443129 * r443102;
        double r443131 = r443128 - r443130;
        double r443132 = r443104 * r443110;
        double r443133 = r443132 - r443114;
        double r443134 = r443094 * r443133;
        double r443135 = r443131 + r443134;
        double r443136 = r443119 * r443122;
        double r443137 = r443122 * r443098;
        double r443138 = r443137 * r443110;
        double r443139 = r443136 - r443138;
        double r443140 = r443135 + r443139;
        double r443141 = -1.5643374811637018e-232;
        bool r443142 = r443094 <= r443141;
        double r443143 = r443100 * r443098;
        double r443144 = r443104 * r443102;
        double r443145 = r443143 - r443144;
        double r443146 = r443097 * r443145;
        double r443147 = r443110 * r443094;
        double r443148 = r443147 * r443104;
        double r443149 = r443148 + r443116;
        double r443150 = r443146 + r443149;
        double r443151 = r443122 * r443102;
        double r443152 = r443113 * r443151;
        double r443153 = r443110 * r443122;
        double r443154 = r443153 * r443098;
        double r443155 = r443152 - r443154;
        double r443156 = r443150 + r443155;
        double r443157 = 1.4293235277702936e-82;
        bool r443158 = r443094 <= r443157;
        double r443159 = -r443113;
        double r443160 = r443094 * r443100;
        double r443161 = r443159 * r443160;
        double r443162 = r443104 * r443094;
        double r443163 = r443110 * r443162;
        double r443164 = r443161 + r443163;
        double r443165 = r443164 + r443131;
        double r443166 = r443165 + r443123;
        double r443167 = 1.7086915451769344e-27;
        bool r443168 = r443094 <= r443167;
        double r443169 = 1.7978416903879968e+129;
        bool r443170 = r443094 <= r443169;
        double r443171 = !r443170;
        bool r443172 = r443168 || r443171;
        double r443173 = r443146 + r443134;
        double r443174 = r443113 * r443122;
        double r443175 = r443174 * r443102;
        double r443176 = r443120 * r443122;
        double r443177 = r443175 - r443176;
        double r443178 = r443173 + r443177;
        double r443179 = r443172 ? r443178 : r443140;
        double r443180 = r443158 ? r443166 : r443179;
        double r443181 = r443142 ? r443156 : r443180;
        double r443182 = r443126 ? r443140 : r443181;
        double r443183 = r443096 ? r443124 : r443182;
        return r443183;
}

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	20.2
Herbie	11.2

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

Derivation

1. Split input into 5 regimes

2. if j < -22910070.91652174

   1. Initial program 8.0

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

   2. Simplified 8.0

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

   4. Applied sub-neg 8.0

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

   5. Applied distribute-lft-in 8.0

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

   6. Simplified 12.5

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

   7. Simplified 12.5

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

   8. Taylor expanded around inf 12.9

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

   9. Simplified 13.5

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

   11. Applied add-cube-cbrt 13.7

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

   12. Applied associate-*l* 13.7

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

   13. Simplified 12.2

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

   if -22910070.91652174 < j < -7.867962692305982e-174 or 1.7086915451769344e-27 < j < 1.7978416903879968e+129

   1. Initial program 11.1

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

   2. Simplified 11.1

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

   3. Taylor expanded around inf 11.1

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

   4. Simplified 10.9

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

   5. Taylor expanded around inf 10.7

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

   6. Simplified 11.1

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

   if -7.867962692305982e-174 < j < -1.5643374811637018e-232

   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. Using strategy rm

   4. Applied sub-neg 15.8

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

   5. Applied distribute-lft-in 15.8

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

   6. Simplified 13.2

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

   7. Simplified 13.2

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

   8. Taylor expanded around inf 15.2

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

   9. Simplified 15.8

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

   if -1.5643374811637018e-232 < j < 1.4293235277702936e-82

   1. Initial program 17.6

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

   2. Simplified 17.6

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

   3. Taylor expanded around inf 17.7

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

   4. Simplified 18.0

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

   6. Applied sub-neg 18.0

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

   7. Applied distribute-lft-in 18.0

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

   8. Simplified 14.8

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

   9. Simplified 11.4

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

   if 1.4293235277702936e-82 < j < 1.7086915451769344e-27 or 1.7978416903879968e+129 < j

   1. Initial program 7.9

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

   2. Simplified 7.9

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

   3. Taylor expanded around inf 8.3

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

   4. Simplified 7.9

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

4. Final simplification 11.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -22910070.9165217392146587371826171875:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) + \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\left(\sqrt[3]{a} \cdot j\right) \cdot c\right) + \left(i \cdot y\right) \cdot \left(-j\right)\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;j \le -7.867962692305981669371960735265674041139 \cdot 10^{-174}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) + \left(\left(t \cdot i\right) \cdot b - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;j \le -1.564337481163701803716112508040619347212 \cdot 10^{-232}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(c \cdot j\right) \cdot a + \left(i \cdot y\right) \cdot \left(-j\right)\right)\right) + \left(i \cdot \left(b \cdot t\right) - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;j \le 1.42932352777029364191431798014284398257 \cdot 10^{-82}:\\ \;\;\;\;\left(\left(\left(-i\right) \cdot \left(j \cdot y\right) + c \cdot \left(a \cdot j\right)\right) + \left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;j \le 1.708691545176934437811367991434167485084 \cdot 10^{-27} \lor \neg \left(j \le 1.797841690387996792815929876315347308672 \cdot 10^{129}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) + \left(\left(i \cdot b\right) \cdot t - \left(c \cdot z\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) + \left(\left(t \cdot i\right) \cdot b - \left(b \cdot z\right) \cdot c\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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)))))