Average Error: 27.1 → 27.2
Time: 38.8s
Precision: 64
\[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
↓
\[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)} \cdot \sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \sqrt[3]{x \cdot j - z \cdot k}\right) \cdot \left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
\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)
↓
\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)} \cdot \sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \sqrt[3]{x \cdot j - z \cdot k}\right) \cdot \left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \left(y0 \cdot b - y1 \cdot i\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)
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 r148131 = x;
        double r148132 = y;
        double r148133 = r148131 * r148132;
        double r148134 = z;
        double r148135 = t;
        double r148136 = r148134 * r148135;
        double r148137 = r148133 - r148136;
        double r148138 = a;
        double r148139 = b;
        double r148140 = r148138 * r148139;
        double r148141 = c;
        double r148142 = i;
        double r148143 = r148141 * r148142;
        double r148144 = r148140 - r148143;
        double r148145 = r148137 * r148144;
        double r148146 = j;
        double r148147 = r148131 * r148146;
        double r148148 = k;
        double r148149 = r148134 * r148148;
        double r148150 = r148147 - r148149;
        double r148151 = y0;
        double r148152 = r148151 * r148139;
        double r148153 = y1;
        double r148154 = r148153 * r148142;
        double r148155 = r148152 - r148154;
        double r148156 = r148150 * r148155;
        double r148157 = r148145 - r148156;
        double r148158 = y2;
        double r148159 = r148131 * r148158;
        double r148160 = y3;
        double r148161 = r148134 * r148160;
        double r148162 = r148159 - r148161;
        double r148163 = r148151 * r148141;
        double r148164 = r148153 * r148138;
        double r148165 = r148163 - r148164;
        double r148166 = r148162 * r148165;
        double r148167 = r148157 + r148166;
        double r148168 = r148135 * r148146;
        double r148169 = r148132 * r148148;
        double r148170 = r148168 - r148169;
        double r148171 = y4;
        double r148172 = r148171 * r148139;
        double r148173 = y5;
        double r148174 = r148173 * r148142;
        double r148175 = r148172 - r148174;
        double r148176 = r148170 * r148175;
        double r148177 = r148167 + r148176;
        double r148178 = r148135 * r148158;
        double r148179 = r148132 * r148160;
        double r148180 = r148178 - r148179;
        double r148181 = r148171 * r148141;
        double r148182 = r148173 * r148138;
        double r148183 = r148181 - r148182;
        double r148184 = r148180 * r148183;
        double r148185 = r148177 - r148184;
        double r148186 = r148148 * r148158;
        double r148187 = r148146 * r148160;
        double r148188 = r148186 - r148187;
        double r148189 = r148171 * r148153;
        double r148190 = r148173 * r148151;
        double r148191 = r148189 - r148190;
        double r148192 = r148188 * r148191;
        double r148193 = r148185 + r148192;
        return r148193;
}
↓
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 r148194 = x;
        double r148195 = y;
        double r148196 = r148194 * r148195;
        double r148197 = z;
        double r148198 = t;
        double r148199 = r148197 * r148198;
        double r148200 = r148196 - r148199;
        double r148201 = a;
        double r148202 = b;
        double r148203 = r148201 * r148202;
        double r148204 = c;
        double r148205 = i;
        double r148206 = r148204 * r148205;
        double r148207 = r148203 - r148206;
        double r148208 = r148200 * r148207;
        double r148209 = j;
        double r148210 = r148194 * r148209;
        double r148211 = k;
        double r148212 = r148197 * r148211;
        double r148213 = r148210 - r148212;
        double r148214 = y0;
        double r148215 = r148214 * r148202;
        double r148216 = y1;
        double r148217 = r148216 * r148205;
        double r148218 = r148215 - r148217;
        double r148219 = r148213 * r148218;
        double r148220 = cbrt(r148219);
        double r148221 = r148220 * r148220;
        double r148222 = cbrt(r148213);
        double r148223 = r148222 * r148222;
        double r148224 = r148222 * r148218;
        double r148225 = r148223 * r148224;
        double r148226 = cbrt(r148225);
        double r148227 = r148221 * r148226;
        double r148228 = r148208 - r148227;
        double r148229 = y2;
        double r148230 = r148194 * r148229;
        double r148231 = y3;
        double r148232 = r148197 * r148231;
        double r148233 = r148230 - r148232;
        double r148234 = r148214 * r148204;
        double r148235 = r148216 * r148201;
        double r148236 = r148234 - r148235;
        double r148237 = r148233 * r148236;
        double r148238 = r148228 + r148237;
        double r148239 = r148198 * r148209;
        double r148240 = r148195 * r148211;
        double r148241 = r148239 - r148240;
        double r148242 = y4;
        double r148243 = r148242 * r148202;
        double r148244 = y5;
        double r148245 = r148244 * r148205;
        double r148246 = r148243 - r148245;
        double r148247 = r148241 * r148246;
        double r148248 = r148238 + r148247;
        double r148249 = r148198 * r148229;
        double r148250 = r148195 * r148231;
        double r148251 = r148249 - r148250;
        double r148252 = r148242 * r148204;
        double r148253 = r148244 * r148201;
        double r148254 = r148252 - r148253;
        double r148255 = r148251 * r148254;
        double r148256 = r148248 - r148255;
        double r148257 = r148211 * r148229;
        double r148258 = r148209 * r148231;
        double r148259 = r148257 - r148258;
        double r148260 = r148242 * r148216;
        double r148261 = r148244 * r148214;
        double r148262 = r148260 - r148261;
        double r148263 = r148259 * r148262;
        double r148264 = r148256 + r148263;
        return r148264;
}

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. 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. Using strategy rm

  3. Applied add-cube-cbrt27.2

    \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \color{blue}{\left(\sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)} \cdot \sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right) \cdot \sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)}}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]
  4. Using strategy rm

  5. Applied add-cube-cbrt27.2

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

  6. Applied associate-*l*27.2

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

  7. Final simplification27.2

    \[\leadsto \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)} \cdot \sqrt[3]{\left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \sqrt[3]{x \cdot j - z \cdot k}\right) \cdot \left(\sqrt[3]{x \cdot j - z \cdot k} \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\]

Reproduce

herbie shell --seed 2019353 
(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)))))