Average Error: 27.1 → 27.2
Time: 37.6s
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 r147001 = x;
        double r147002 = y;
        double r147003 = r147001 * r147002;
        double r147004 = z;
        double r147005 = t;
        double r147006 = r147004 * r147005;
        double r147007 = r147003 - r147006;
        double r147008 = a;
        double r147009 = b;
        double r147010 = r147008 * r147009;
        double r147011 = c;
        double r147012 = i;
        double r147013 = r147011 * r147012;
        double r147014 = r147010 - r147013;
        double r147015 = r147007 * r147014;
        double r147016 = j;
        double r147017 = r147001 * r147016;
        double r147018 = k;
        double r147019 = r147004 * r147018;
        double r147020 = r147017 - r147019;
        double r147021 = y0;
        double r147022 = r147021 * r147009;
        double r147023 = y1;
        double r147024 = r147023 * r147012;
        double r147025 = r147022 - r147024;
        double r147026 = r147020 * r147025;
        double r147027 = r147015 - r147026;
        double r147028 = y2;
        double r147029 = r147001 * r147028;
        double r147030 = y3;
        double r147031 = r147004 * r147030;
        double r147032 = r147029 - r147031;
        double r147033 = r147021 * r147011;
        double r147034 = r147023 * r147008;
        double r147035 = r147033 - r147034;
        double r147036 = r147032 * r147035;
        double r147037 = r147027 + r147036;
        double r147038 = r147005 * r147016;
        double r147039 = r147002 * r147018;
        double r147040 = r147038 - r147039;
        double r147041 = y4;
        double r147042 = r147041 * r147009;
        double r147043 = y5;
        double r147044 = r147043 * r147012;
        double r147045 = r147042 - r147044;
        double r147046 = r147040 * r147045;
        double r147047 = r147037 + r147046;
        double r147048 = r147005 * r147028;
        double r147049 = r147002 * r147030;
        double r147050 = r147048 - r147049;
        double r147051 = r147041 * r147011;
        double r147052 = r147043 * r147008;
        double r147053 = r147051 - r147052;
        double r147054 = r147050 * r147053;
        double r147055 = r147047 - r147054;
        double r147056 = r147018 * r147028;
        double r147057 = r147016 * r147030;
        double r147058 = r147056 - r147057;
        double r147059 = r147041 * r147023;
        double r147060 = r147043 * r147021;
        double r147061 = r147059 - r147060;
        double r147062 = r147058 * r147061;
        double r147063 = r147055 + r147062;
        return r147063;
}
↓
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 r147064 = x;
        double r147065 = y;
        double r147066 = r147064 * r147065;
        double r147067 = z;
        double r147068 = t;
        double r147069 = r147067 * r147068;
        double r147070 = r147066 - r147069;
        double r147071 = a;
        double r147072 = b;
        double r147073 = r147071 * r147072;
        double r147074 = c;
        double r147075 = i;
        double r147076 = r147074 * r147075;
        double r147077 = r147073 - r147076;
        double r147078 = r147070 * r147077;
        double r147079 = j;
        double r147080 = r147064 * r147079;
        double r147081 = k;
        double r147082 = r147067 * r147081;
        double r147083 = r147080 - r147082;
        double r147084 = y0;
        double r147085 = r147084 * r147072;
        double r147086 = y1;
        double r147087 = r147086 * r147075;
        double r147088 = r147085 - r147087;
        double r147089 = r147083 * r147088;
        double r147090 = cbrt(r147089);
        double r147091 = r147090 * r147090;
        double r147092 = cbrt(r147083);
        double r147093 = r147092 * r147092;
        double r147094 = r147092 * r147088;
        double r147095 = r147093 * r147094;
        double r147096 = cbrt(r147095);
        double r147097 = r147091 * r147096;
        double r147098 = r147078 - r147097;
        double r147099 = y2;
        double r147100 = r147064 * r147099;
        double r147101 = y3;
        double r147102 = r147067 * r147101;
        double r147103 = r147100 - r147102;
        double r147104 = r147084 * r147074;
        double r147105 = r147086 * r147071;
        double r147106 = r147104 - r147105;
        double r147107 = r147103 * r147106;
        double r147108 = r147098 + r147107;
        double r147109 = r147068 * r147079;
        double r147110 = r147065 * r147081;
        double r147111 = r147109 - r147110;
        double r147112 = y4;
        double r147113 = r147112 * r147072;
        double r147114 = y5;
        double r147115 = r147114 * r147075;
        double r147116 = r147113 - r147115;
        double r147117 = r147111 * r147116;
        double r147118 = r147108 + r147117;
        double r147119 = r147068 * r147099;
        double r147120 = r147065 * r147101;
        double r147121 = r147119 - r147120;
        double r147122 = r147112 * r147074;
        double r147123 = r147114 * r147071;
        double r147124 = r147122 - r147123;
        double r147125 = r147121 * r147124;
        double r147126 = r147118 - r147125;
        double r147127 = r147081 * r147099;
        double r147128 = r147079 * r147101;
        double r147129 = r147127 - r147128;
        double r147130 = r147112 * r147086;
        double r147131 = r147114 * r147084;
        double r147132 = r147130 - r147131;
        double r147133 = r147129 * r147132;
        double r147134 = r147126 + r147133;
        return r147134;
}

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)))))