Average Error: 4.9 → 4.7
Time: 44.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\left(c \cdot b - \left(i \cdot \left(x \cdot 4.0\right) + \sqrt{27.0} \cdot \left(k \cdot \left(\sqrt{27.0} \cdot j\right)\right)\right)\right) + t \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\left(c \cdot b - \left(i \cdot \left(x \cdot 4.0\right) + \sqrt{27.0} \cdot \left(k \cdot \left(\sqrt{27.0} \cdot j\right)\right)\right)\right) + t \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r14449867 = x;
        double r14449868 = 18.0;
        double r14449869 = r14449867 * r14449868;
        double r14449870 = y;
        double r14449871 = r14449869 * r14449870;
        double r14449872 = z;
        double r14449873 = r14449871 * r14449872;
        double r14449874 = t;
        double r14449875 = r14449873 * r14449874;
        double r14449876 = a;
        double r14449877 = 4.0;
        double r14449878 = r14449876 * r14449877;
        double r14449879 = r14449878 * r14449874;
        double r14449880 = r14449875 - r14449879;
        double r14449881 = b;
        double r14449882 = c;
        double r14449883 = r14449881 * r14449882;
        double r14449884 = r14449880 + r14449883;
        double r14449885 = r14449867 * r14449877;
        double r14449886 = i;
        double r14449887 = r14449885 * r14449886;
        double r14449888 = r14449884 - r14449887;
        double r14449889 = j;
        double r14449890 = 27.0;
        double r14449891 = r14449889 * r14449890;
        double r14449892 = k;
        double r14449893 = r14449891 * r14449892;
        double r14449894 = r14449888 - r14449893;
        return r14449894;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r14449895 = c;
        double r14449896 = b;
        double r14449897 = r14449895 * r14449896;
        double r14449898 = i;
        double r14449899 = x;
        double r14449900 = 4.0;
        double r14449901 = r14449899 * r14449900;
        double r14449902 = r14449898 * r14449901;
        double r14449903 = 27.0;
        double r14449904 = sqrt(r14449903);
        double r14449905 = k;
        double r14449906 = j;
        double r14449907 = r14449904 * r14449906;
        double r14449908 = r14449905 * r14449907;
        double r14449909 = r14449904 * r14449908;
        double r14449910 = r14449902 + r14449909;
        double r14449911 = r14449897 - r14449910;
        double r14449912 = t;
        double r14449913 = z;
        double r14449914 = r14449913 * r14449899;
        double r14449915 = y;
        double r14449916 = 18.0;
        double r14449917 = r14449915 * r14449916;
        double r14449918 = r14449914 * r14449917;
        double r14449919 = a;
        double r14449920 = r14449900 * r14449919;
        double r14449921 = r14449918 - r14449920;
        double r14449922 = r14449912 * r14449921;
        double r14449923 = r14449911 + r14449922;
        return r14449923;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.9

    \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

  2. Simplified4.7

    \[\leadsto \color{blue}{\left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + \left(x \cdot 4.0\right) \cdot i\right)\right) + \left(y \cdot \left(\left(x \cdot 18.0\right) \cdot z\right) - a \cdot 4.0\right) \cdot t}\]

  3. Taylor expanded around inf 5.8

    \[\leadsto \left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + \left(x \cdot 4.0\right) \cdot i\right)\right) + \color{blue}{\left(18.0 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) - 4.0 \cdot \left(t \cdot a\right)\right)}\]

  4. Simplified4.7

    \[\leadsto \left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + \left(x \cdot 4.0\right) \cdot i\right)\right) + \color{blue}{t \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)}\]
  5. Using strategy rm

  6. Applied associate-*l*4.6

    \[\leadsto \left(c \cdot b - \left(\color{blue}{27.0 \cdot \left(j \cdot k\right)} + \left(x \cdot 4.0\right) \cdot i\right)\right) + t \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt4.6

    \[\leadsto \left(c \cdot b - \left(\color{blue}{\left(\sqrt{27.0} \cdot \sqrt{27.0}\right)} \cdot \left(j \cdot k\right) + \left(x \cdot 4.0\right) \cdot i\right)\right) + t \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)\]

  9. Applied associate-*l*4.7

    \[\leadsto \left(c \cdot b - \left(\color{blue}{\sqrt{27.0} \cdot \left(\sqrt{27.0} \cdot \left(j \cdot k\right)\right)} + \left(x \cdot 4.0\right) \cdot i\right)\right) + t \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)\]
  10. Using strategy rm

  11. Applied associate-*r*4.7

    \[\leadsto \left(c \cdot b - \left(\sqrt{27.0} \cdot \color{blue}{\left(\left(\sqrt{27.0} \cdot j\right) \cdot k\right)} + \left(x \cdot 4.0\right) \cdot i\right)\right) + t \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)\]

  12. Final simplification4.7

    \[\leadsto \left(c \cdot b - \left(i \cdot \left(x \cdot 4.0\right) + \sqrt{27.0} \cdot \left(k \cdot \left(\sqrt{27.0} \cdot j\right)\right)\right)\right) + t \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot a\right)\]

Reproduce

herbie shell --seed 2019112 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))