Average Error: 27.0 → 28.8
Time: 40.9s
Precision: 64
\[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.3859811544496863 \cdot 10^{-150}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \le -1.8301320911536272 \cdot 10^{-302}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(i \cdot \left(j \cdot \left(y1 \cdot x\right)\right) + y0 \cdot \left(z \cdot \left(k \cdot b\right)\right)\right)\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \le 5.6732046777558966 \cdot 10^{-241}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) - \left(y0 \cdot \left(z \cdot \left(y3 \cdot c\right)\right) + a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \le 5.1710861254145052 \cdot 10^{-82}:\\ \;\;\;\;\left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \end{array}\]
\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.3859811544496863 \cdot 10^{-150}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\

\mathbf{elif}\;z \le -1.8301320911536272 \cdot 10^{-302}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(i \cdot \left(j \cdot \left(y1 \cdot x\right)\right) + y0 \cdot \left(z \cdot \left(k \cdot b\right)\right)\right)\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\

\mathbf{elif}\;z \le 5.6732046777558966 \cdot 10^{-241}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) - \left(y0 \cdot \left(z \cdot \left(y3 \cdot c\right)\right) + a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\

\mathbf{elif}\;z \le 5.1710861254145052 \cdot 10^{-82}:\\
\;\;\;\;\left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
        double r106145 = x;
        double r106146 = y;
        double r106147 = r106145 * r106146;
        double r106148 = z;
        double r106149 = t;
        double r106150 = r106148 * r106149;
        double r106151 = r106147 - r106150;
        double r106152 = a;
        double r106153 = b;
        double r106154 = r106152 * r106153;
        double r106155 = c;
        double r106156 = i;
        double r106157 = r106155 * r106156;
        double r106158 = r106154 - r106157;
        double r106159 = r106151 * r106158;
        double r106160 = j;
        double r106161 = r106145 * r106160;
        double r106162 = k;
        double r106163 = r106148 * r106162;
        double r106164 = r106161 - r106163;
        double r106165 = y0;
        double r106166 = r106165 * r106153;
        double r106167 = y1;
        double r106168 = r106167 * r106156;
        double r106169 = r106166 - r106168;
        double r106170 = r106164 * r106169;
        double r106171 = r106159 - r106170;
        double r106172 = y2;
        double r106173 = r106145 * r106172;
        double r106174 = y3;
        double r106175 = r106148 * r106174;
        double r106176 = r106173 - r106175;
        double r106177 = r106165 * r106155;
        double r106178 = r106167 * r106152;
        double r106179 = r106177 - r106178;
        double r106180 = r106176 * r106179;
        double r106181 = r106171 + r106180;
        double r106182 = r106149 * r106160;
        double r106183 = r106146 * r106162;
        double r106184 = r106182 - r106183;
        double r106185 = y4;
        double r106186 = r106185 * r106153;
        double r106187 = y5;
        double r106188 = r106187 * r106156;
        double r106189 = r106186 - r106188;
        double r106190 = r106184 * r106189;
        double r106191 = r106181 + r106190;
        double r106192 = r106149 * r106172;
        double r106193 = r106146 * r106174;
        double r106194 = r106192 - r106193;
        double r106195 = r106185 * r106155;
        double r106196 = r106187 * r106152;
        double r106197 = r106195 - r106196;
        double r106198 = r106194 * r106197;
        double r106199 = r106191 - r106198;
        double r106200 = r106162 * r106172;
        double r106201 = r106160 * r106174;
        double r106202 = r106200 - r106201;
        double r106203 = r106185 * r106167;
        double r106204 = r106187 * r106165;
        double r106205 = r106203 - r106204;
        double r106206 = r106202 * r106205;
        double r106207 = r106199 + r106206;
        return r106207;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
        double r106208 = z;
        double r106209 = -1.3859811544496863e-150;
        bool r106210 = r106208 <= r106209;
        double r106211 = x;
        double r106212 = y;
        double r106213 = r106211 * r106212;
        double r106214 = t;
        double r106215 = r106208 * r106214;
        double r106216 = r106213 - r106215;
        double r106217 = a;
        double r106218 = b;
        double r106219 = r106217 * r106218;
        double r106220 = c;
        double r106221 = i;
        double r106222 = r106220 * r106221;
        double r106223 = r106219 - r106222;
        double r106224 = r106216 * r106223;
        double r106225 = j;
        double r106226 = r106211 * r106225;
        double r106227 = k;
        double r106228 = r106208 * r106227;
        double r106229 = r106226 - r106228;
        double r106230 = y0;
        double r106231 = r106230 * r106218;
        double r106232 = y1;
        double r106233 = r106232 * r106221;
        double r106234 = r106231 - r106233;
        double r106235 = r106229 * r106234;
        double r106236 = r106224 - r106235;
        double r106237 = y2;
        double r106238 = r106211 * r106237;
        double r106239 = y3;
        double r106240 = r106208 * r106239;
        double r106241 = r106238 - r106240;
        double r106242 = r106230 * r106220;
        double r106243 = r106232 * r106217;
        double r106244 = r106242 - r106243;
        double r106245 = r106241 * r106244;
        double r106246 = r106236 + r106245;
        double r106247 = r106214 * r106225;
        double r106248 = r106212 * r106227;
        double r106249 = r106247 - r106248;
        double r106250 = y4;
        double r106251 = r106250 * r106218;
        double r106252 = y5;
        double r106253 = r106252 * r106221;
        double r106254 = r106251 - r106253;
        double r106255 = r106249 * r106254;
        double r106256 = r106246 + r106255;
        double r106257 = r106212 * r106252;
        double r106258 = r106239 * r106257;
        double r106259 = r106217 * r106258;
        double r106260 = r106250 * r106220;
        double r106261 = r106239 * r106260;
        double r106262 = r106212 * r106261;
        double r106263 = r106237 * r106214;
        double r106264 = r106217 * r106263;
        double r106265 = r106252 * r106264;
        double r106266 = r106262 + r106265;
        double r106267 = r106259 - r106266;
        double r106268 = r106256 - r106267;
        double r106269 = r106227 * r106237;
        double r106270 = r106225 * r106239;
        double r106271 = r106269 - r106270;
        double r106272 = r106250 * r106232;
        double r106273 = r106252 * r106230;
        double r106274 = r106272 - r106273;
        double r106275 = r106271 * r106274;
        double r106276 = r106268 + r106275;
        double r106277 = -1.8301320911536272e-302;
        bool r106278 = r106208 <= r106277;
        double r106279 = r106208 * r106232;
        double r106280 = r106221 * r106279;
        double r106281 = r106227 * r106280;
        double r106282 = r106232 * r106211;
        double r106283 = r106225 * r106282;
        double r106284 = r106221 * r106283;
        double r106285 = r106227 * r106218;
        double r106286 = r106208 * r106285;
        double r106287 = r106230 * r106286;
        double r106288 = r106284 + r106287;
        double r106289 = r106281 - r106288;
        double r106290 = r106224 - r106289;
        double r106291 = r106290 + r106245;
        double r106292 = r106291 + r106255;
        double r106293 = r106214 * r106237;
        double r106294 = r106212 * r106239;
        double r106295 = r106293 - r106294;
        double r106296 = r106252 * r106217;
        double r106297 = r106260 - r106296;
        double r106298 = r106295 * r106297;
        double r106299 = r106292 - r106298;
        double r106300 = r106299 + r106275;
        double r106301 = 5.6732046777558966e-241;
        bool r106302 = r106208 <= r106301;
        double r106303 = r106232 * r106208;
        double r106304 = r106239 * r106303;
        double r106305 = r106217 * r106304;
        double r106306 = r106239 * r106220;
        double r106307 = r106208 * r106306;
        double r106308 = r106230 * r106307;
        double r106309 = r106237 * r106232;
        double r106310 = r106211 * r106309;
        double r106311 = r106217 * r106310;
        double r106312 = r106308 + r106311;
        double r106313 = r106305 - r106312;
        double r106314 = r106236 + r106313;
        double r106315 = r106314 + r106255;
        double r106316 = r106315 - r106298;
        double r106317 = r106316 + r106275;
        double r106318 = 5.171086125414505e-82;
        bool r106319 = r106208 <= r106318;
        double r106320 = r106208 * r106220;
        double r106321 = r106221 * r106320;
        double r106322 = r106214 * r106321;
        double r106323 = r106212 * r106211;
        double r106324 = r106220 * r106323;
        double r106325 = r106221 * r106324;
        double r106326 = r106208 * r106218;
        double r106327 = r106214 * r106326;
        double r106328 = r106217 * r106327;
        double r106329 = r106325 + r106328;
        double r106330 = r106322 - r106329;
        double r106331 = r106330 - r106235;
        double r106332 = r106331 + r106245;
        double r106333 = r106332 + r106255;
        double r106334 = r106333 - r106298;
        double r106335 = r106334 + r106275;
        double r106336 = r106319 ? r106335 : r106276;
        double r106337 = r106302 ? r106317 : r106336;
        double r106338 = r106278 ? r106300 : r106337;
        double r106339 = r106210 ? r106276 : r106338;
        return r106339;
}

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

Bits error versus k

Bits error versus y0

Bits error versus y1

Bits error versus y2

Bits error versus y3

Bits error versus y4

Bits error versus y5

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if z < -1.3859811544496863e-150 or 5.171086125414505e-82 < z

    1. Initial program 27.2

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    2. Taylor expanded around inf 29.2

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \color{blue}{\left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if -1.3859811544496863e-150 < z < -1.8301320911536272e-302

    1. Initial program 25.1

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    2. Taylor expanded around inf 27.5

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \color{blue}{\left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(i \cdot \left(j \cdot \left(y1 \cdot x\right)\right) + y0 \cdot \left(z \cdot \left(k \cdot b\right)\right)\right)\right)}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if -1.8301320911536272e-302 < z < 5.6732046777558966e-241

    1. Initial program 27.1

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    2. Taylor expanded around inf 29.5

      \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \color{blue}{\left(a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) - \left(y0 \cdot \left(z \cdot \left(y3 \cdot c\right)\right) + a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)\right)\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    if 5.6732046777558966e-241 < z < 5.171086125414505e-82

    1. Initial program 28.0

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

    2. Taylor expanded around inf 28.7

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right)} - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification28.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.3859811544496863 \cdot 10^{-150}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \le -1.8301320911536272 \cdot 10^{-302}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(i \cdot \left(j \cdot \left(y1 \cdot x\right)\right) + y0 \cdot \left(z \cdot \left(k \cdot b\right)\right)\right)\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \le 5.6732046777558966 \cdot 10^{-241}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) - \left(y0 \cdot \left(z \cdot \left(y3 \cdot c\right)\right) + a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \le 5.1710861254145052 \cdot 10^{-82}:\\ \;\;\;\;\left(\left(\left(\left(\left(t \cdot \left(i \cdot \left(z \cdot c\right)\right) - \left(i \cdot \left(c \cdot \left(y \cdot x\right)\right) + a \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right) - \left(y \cdot \left(y3 \cdot \left(y4 \cdot c\right)\right) + y5 \cdot \left(a \cdot \left(y2 \cdot t\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64
  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))