Average Error: 5.1 → 3.5
Time: 6.0s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.05110049757782854 \cdot 10^{65}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right) \cdot t - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \le 3.21315296623720254 \cdot 10^{-90}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z\right) \cdot t - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;t \le -2.05110049757782854 \cdot 10^{65}:\\
\;\;\;\;\left(\left(\left(\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right) \cdot t - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{elif}\;t \le 3.21315296623720254 \cdot 10^{-90}:\\
\;\;\;\;\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\

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

\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 r154827 = x;
        double r154828 = 18.0;
        double r154829 = r154827 * r154828;
        double r154830 = y;
        double r154831 = r154829 * r154830;
        double r154832 = z;
        double r154833 = r154831 * r154832;
        double r154834 = t;
        double r154835 = r154833 * r154834;
        double r154836 = a;
        double r154837 = 4.0;
        double r154838 = r154836 * r154837;
        double r154839 = r154838 * r154834;
        double r154840 = r154835 - r154839;
        double r154841 = b;
        double r154842 = c;
        double r154843 = r154841 * r154842;
        double r154844 = r154840 + r154843;
        double r154845 = r154827 * r154837;
        double r154846 = i;
        double r154847 = r154845 * r154846;
        double r154848 = r154844 - r154847;
        double r154849 = j;
        double r154850 = 27.0;
        double r154851 = r154849 * r154850;
        double r154852 = k;
        double r154853 = r154851 * r154852;
        double r154854 = r154848 - r154853;
        return r154854;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r154855 = t;
        double r154856 = -2.0511004975778285e+65;
        bool r154857 = r154855 <= r154856;
        double r154858 = x;
        double r154859 = 18.0;
        double r154860 = y;
        double r154861 = r154859 * r154860;
        double r154862 = z;
        double r154863 = r154861 * r154862;
        double r154864 = r154858 * r154863;
        double r154865 = r154864 * r154855;
        double r154866 = a;
        double r154867 = 4.0;
        double r154868 = r154867 * r154855;
        double r154869 = r154866 * r154868;
        double r154870 = r154865 - r154869;
        double r154871 = b;
        double r154872 = c;
        double r154873 = r154871 * r154872;
        double r154874 = r154870 + r154873;
        double r154875 = r154858 * r154867;
        double r154876 = i;
        double r154877 = r154875 * r154876;
        double r154878 = r154874 - r154877;
        double r154879 = j;
        double r154880 = 27.0;
        double r154881 = r154879 * r154880;
        double r154882 = k;
        double r154883 = r154881 * r154882;
        double r154884 = r154878 - r154883;
        double r154885 = 3.2131529662372025e-90;
        bool r154886 = r154855 <= r154885;
        double r154887 = r154858 * r154861;
        double r154888 = r154862 * r154855;
        double r154889 = r154887 * r154888;
        double r154890 = r154889 - r154869;
        double r154891 = r154890 + r154873;
        double r154892 = r154891 - r154877;
        double r154893 = r154892 - r154883;
        double r154894 = r154887 * r154862;
        double r154895 = r154894 * r154855;
        double r154896 = r154895 - r154869;
        double r154897 = r154896 + r154873;
        double r154898 = r154897 - r154877;
        double r154899 = r154880 * r154882;
        double r154900 = r154879 * r154899;
        double r154901 = r154898 - r154900;
        double r154902 = r154886 ? r154893 : r154901;
        double r154903 = r154857 ? r154884 : r154902;
        return r154903;
}

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 3 regimes

  2. if t < -2.0511004975778285e+65

    1. Initial program 1.2

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

    3. Applied associate-*l*1.2

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

    5. Applied associate-*l*1.4

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

    7. Applied associate-*l*1.9

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

    if -2.0511004975778285e+65 < t < 3.2131529662372025e-90

    1. Initial program 7.0

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

    3. Applied associate-*l*7.0

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

    5. Applied associate-*l*7.0

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

    7. Applied associate-*l*4.2

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

    if 3.2131529662372025e-90 < t

    1. Initial program 2.7

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

    3. Applied associate-*l*2.7

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

    5. Applied associate-*l*2.8

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

    7. Applied associate-*l*2.7

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.05110049757782854 \cdot 10^{65}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right)\right) \cdot t - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \le 3.21315296623720254 \cdot 10^{-90}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z\right) \cdot t - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))