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

Average Error: 12.7 → 11.3

Time: 16.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -14000959500.1202220916748046875:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;a \le 3.137840021978250235813255271558351573377 \cdot 10^{-179}:\\ \;\;\;\;\left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t \cdot \left(i \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;a \le 2.443250679644193482510416222749876525206 \cdot 10^{-151}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;a \le 1.022883629570418632375689571046330564205 \cdot 10^{-30}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(j \cdot \left(\sqrt[3]{c \cdot a - y \cdot i} \cdot \sqrt[3]{c \cdot a - y \cdot i}\right)\right) \cdot \sqrt[3]{c \cdot a - y \cdot i}\\ \mathbf{elif}\;a \le 4.257938883112592501203590710749532366243 \cdot 10^{101}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r927193 = x;
        double r927194 = y;
        double r927195 = z;
        double r927196 = r927194 * r927195;
        double r927197 = t;
        double r927198 = a;
        double r927199 = r927197 * r927198;
        double r927200 = r927196 - r927199;
        double r927201 = r927193 * r927200;
        double r927202 = b;
        double r927203 = c;
        double r927204 = r927203 * r927195;
        double r927205 = i;
        double r927206 = r927197 * r927205;
        double r927207 = r927204 - r927206;
        double r927208 = r927202 * r927207;
        double r927209 = r927201 - r927208;
        double r927210 = j;
        double r927211 = r927203 * r927198;
        double r927212 = r927194 * r927205;
        double r927213 = r927211 - r927212;
        double r927214 = r927210 * r927213;
        double r927215 = r927209 + r927214;
        return r927215;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r927216 = a;
        double r927217 = -14000959500.120222;
        bool r927218 = r927216 <= r927217;
        double r927219 = x;
        double r927220 = z;
        double r927221 = y;
        double r927222 = r927220 * r927221;
        double r927223 = r927219 * r927222;
        double r927224 = t;
        double r927225 = r927219 * r927224;
        double r927226 = r927216 * r927225;
        double r927227 = -r927226;
        double r927228 = r927223 + r927227;
        double r927229 = b;
        double r927230 = c;
        double r927231 = r927229 * r927230;
        double r927232 = r927220 * r927231;
        double r927233 = i;
        double r927234 = r927224 * r927233;
        double r927235 = -r927234;
        double r927236 = r927229 * r927235;
        double r927237 = r927232 + r927236;
        double r927238 = r927228 - r927237;
        double r927239 = j;
        double r927240 = r927239 * r927230;
        double r927241 = r927216 * r927240;
        double r927242 = r927221 * r927233;
        double r927243 = -r927242;
        double r927244 = r927243 * r927239;
        double r927245 = r927241 + r927244;
        double r927246 = r927238 + r927245;
        double r927247 = 3.13784002197825e-179;
        bool r927248 = r927216 <= r927247;
        double r927249 = r927221 * r927220;
        double r927250 = r927224 * r927216;
        double r927251 = r927249 - r927250;
        double r927252 = r927219 * r927251;
        double r927253 = r927233 * r927229;
        double r927254 = r927224 * r927253;
        double r927255 = -r927254;
        double r927256 = r927232 + r927255;
        double r927257 = r927252 - r927256;
        double r927258 = r927245 + r927257;
        double r927259 = 2.4432506796441935e-151;
        bool r927260 = r927216 <= r927259;
        double r927261 = r927220 * r927229;
        double r927262 = r927261 * r927230;
        double r927263 = r927262 + r927236;
        double r927264 = r927252 - r927263;
        double r927265 = r927264 + r927245;
        double r927266 = 1.0228836295704186e-30;
        bool r927267 = r927216 <= r927266;
        double r927268 = r927252 - r927237;
        double r927269 = r927230 * r927216;
        double r927270 = r927269 - r927242;
        double r927271 = cbrt(r927270);
        double r927272 = r927271 * r927271;
        double r927273 = r927239 * r927272;
        double r927274 = r927273 * r927271;
        double r927275 = r927268 + r927274;
        double r927276 = 4.2579388831125925e+101;
        bool r927277 = r927216 <= r927276;
        double r927278 = r927239 * r927221;
        double r927279 = r927233 * r927278;
        double r927280 = -r927279;
        double r927281 = r927241 + r927280;
        double r927282 = r927268 + r927281;
        double r927283 = r927277 ? r927282 : r927246;
        double r927284 = r927267 ? r927275 : r927283;
        double r927285 = r927260 ? r927265 : r927284;
        double r927286 = r927248 ? r927258 : r927285;
        double r927287 = r927218 ? r927246 : r927286;
        return r927287;
}

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	12.7
Target	20.4
Herbie	11.3

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

Derivation

1. Split input into 5 regimes

2. if a < -14000959500.120222 or 4.2579388831125925e+101 < a

   1. Initial program 19.5

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

   3. Applied sub-neg 19.5

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

   4. Applied distribute-lft-in 19.5

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

   5. Simplified 19.9

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

   7. Applied sub-neg 19.9

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

   8. Applied distribute-lft-in 19.9

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

   9. Simplified 15.1

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

   10. Simplified 15.1

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

   12. Applied sub-neg 15.1

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

   13. Applied distribute-lft-in 15.1

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

   14. Simplified 15.1

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

   15. Simplified 9.3

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

   if -14000959500.120222 < a < 3.13784002197825e-179

   1. Initial program 9.6

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

   3. Applied sub-neg 9.6

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

   4. Applied distribute-lft-in 9.6

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

   5. Simplified 10.5

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

   7. Applied sub-neg 10.5

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

   8. Applied distribute-lft-in 10.5

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

   9. Simplified 13.2

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

   10. Simplified 13.2

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

   12. Applied *-un-lft-identity 13.2

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \color{blue}{\left(1 \cdot b\right)} \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\]

   13. Applied associate-*l* 13.2

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \color{blue}{1 \cdot \left(b \cdot \left(-t \cdot i\right)\right)}\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\]

   14. Simplified 12.5

       \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + 1 \cdot \color{blue}{\left(-t \cdot \left(i \cdot b\right)\right)}\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\]

   if 3.13784002197825e-179 < a < 2.4432506796441935e-151

   1. Initial program 11.8

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

   3. Applied sub-neg 11.8

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

   4. Applied distribute-lft-in 11.8

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

   5. Simplified 12.9

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

   7. Applied sub-neg 12.9

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

   8. Applied distribute-lft-in 12.9

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

   9. Simplified 16.8

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

   10. Simplified 16.8

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

   12. Applied associate-*r* 15.4

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

   if 2.4432506796441935e-151 < a < 1.0228836295704186e-30

   1. Initial program 8.6

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

   3. Applied sub-neg 8.6

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

   4. Applied distribute-lft-in 8.6

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

   5. Simplified 10.5

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

   7. Applied add-cube-cbrt 10.9

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

   8. Applied associate-*r* 10.8

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

   if 1.0228836295704186e-30 < a < 4.2579388831125925e+101

   1. Initial program 11.9

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

   3. Applied sub-neg 11.9

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

   4. Applied distribute-lft-in 11.9

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

   5. Simplified 12.5

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

   7. Applied sub-neg 12.5

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

   8. Applied distribute-lft-in 12.5

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

   9. Simplified 11.5

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

   10. Simplified 11.5

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

   12. Applied distribute-lft-neg-out 11.5

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

   13. Simplified 10.9

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

4. Final simplification 11.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -14000959500.1202220916748046875:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;a \le 3.137840021978250235813255271558351573377 \cdot 10^{-179}:\\ \;\;\;\;\left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-t \cdot \left(i \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;a \le 2.443250679644193482510416222749876525206 \cdot 10^{-151}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;a \le 1.022883629570418632375689571046330564205 \cdot 10^{-30}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(j \cdot \left(\sqrt[3]{c \cdot a - y \cdot i} \cdot \sqrt[3]{c \cdot a - y \cdot i}\right)\right) \cdot \sqrt[3]{c \cdot a - y \cdot i}\\ \mathbf{elif}\;a \le 4.257938883112592501203590710749532366243 \cdot 10^{101}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-t \cdot i\right)\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 
(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 -1.469694296777705e-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)))))