Average Error: 5.7 → 0.8
Time: 43.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 1.332226899097801573653352800247938704487 \cdot 10^{292}\right):\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(y \cdot \left(x \cdot \left(t \cdot z\right)\right)\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 1.332226899097801573653352800247938704487 \cdot 10^{292}\right):\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(y \cdot \left(x \cdot \left(t \cdot z\right)\right)\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\

\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 r111843 = x;
        double r111844 = 18.0;
        double r111845 = r111843 * r111844;
        double r111846 = y;
        double r111847 = r111845 * r111846;
        double r111848 = z;
        double r111849 = r111847 * r111848;
        double r111850 = t;
        double r111851 = r111849 * r111850;
        double r111852 = a;
        double r111853 = 4.0;
        double r111854 = r111852 * r111853;
        double r111855 = r111854 * r111850;
        double r111856 = r111851 - r111855;
        double r111857 = b;
        double r111858 = c;
        double r111859 = r111857 * r111858;
        double r111860 = r111856 + r111859;
        double r111861 = r111843 * r111853;
        double r111862 = i;
        double r111863 = r111861 * r111862;
        double r111864 = r111860 - r111863;
        double r111865 = j;
        double r111866 = 27.0;
        double r111867 = r111865 * r111866;
        double r111868 = k;
        double r111869 = r111867 * r111868;
        double r111870 = r111864 - r111869;
        return r111870;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r111871 = t;
        double r111872 = x;
        double r111873 = 18.0;
        double r111874 = r111872 * r111873;
        double r111875 = y;
        double r111876 = r111874 * r111875;
        double r111877 = z;
        double r111878 = r111876 * r111877;
        double r111879 = r111871 * r111878;
        double r111880 = a;
        double r111881 = 4.0;
        double r111882 = r111880 * r111881;
        double r111883 = r111882 * r111871;
        double r111884 = r111879 - r111883;
        double r111885 = c;
        double r111886 = b;
        double r111887 = r111885 * r111886;
        double r111888 = r111884 + r111887;
        double r111889 = r111872 * r111881;
        double r111890 = i;
        double r111891 = r111889 * r111890;
        double r111892 = r111888 - r111891;
        double r111893 = -inf.0;
        bool r111894 = r111892 <= r111893;
        double r111895 = 1.3322268990978016e+292;
        bool r111896 = r111892 <= r111895;
        double r111897 = !r111896;
        bool r111898 = r111894 || r111897;
        double r111899 = r111871 * r111877;
        double r111900 = r111872 * r111899;
        double r111901 = r111875 * r111900;
        double r111902 = r111901 * r111873;
        double r111903 = r111902 - r111883;
        double r111904 = r111887 + r111903;
        double r111905 = r111904 - r111891;
        double r111906 = k;
        double r111907 = j;
        double r111908 = 27.0;
        double r111909 = r111907 * r111908;
        double r111910 = r111906 * r111909;
        double r111911 = r111905 - r111910;
        double r111912 = r111906 * r111908;
        double r111913 = r111912 * r111907;
        double r111914 = r111892 - r111913;
        double r111915 = r111898 ? r111911 : r111914;
        return r111915;
}

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. Split input into 2 regimes

  2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0 or 1.3322268990978016e+292 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 50.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Taylor expanded around inf 32.1

      \[\leadsto \left(\left(\left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    3. Simplified7.7

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right) \cdot 18} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied *-un-lft-identity7.7

      \[\leadsto \left(\left(\left(\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot y\right)}\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    6. Applied associate-*r*7.7

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot 1\right) \cdot y\right)} \cdot 18 - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    7. Simplified5.1

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(z \cdot t\right)\right)} \cdot y\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.3322268990978016e+292

    1. Initial program 0.3

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*0.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{j \cdot \left(27 \cdot k\right)}\]

    4. Simplified0.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \color{blue}{\left(k \cdot 27\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 1.332226899097801573653352800247938704487 \cdot 10^{292}\right):\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(y \cdot \left(x \cdot \left(t \cdot z\right)\right)\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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)))