Average Error: 5.5 → 3.1
Time: 49.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i = -\infty:\\ \;\;\;\;\left(c \cdot b - \left(\left(x \cdot 4.0\right) \cdot i + \left(27.0 \cdot j\right) \cdot k\right)\right) + \left(-t\right) \cdot \left(a \cdot 4.0\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 6.210375130051423 \cdot 10^{+303}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b - \left(\left(x \cdot 4.0\right) \cdot i + \left(27.0 \cdot j\right) \cdot k\right)\right) + \left(-t\right) \cdot \left(a \cdot 4.0\right)\\ \end{array}\]
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r28523843 = x;
        double r28523844 = 18.0;
        double r28523845 = r28523843 * r28523844;
        double r28523846 = y;
        double r28523847 = r28523845 * r28523846;
        double r28523848 = z;
        double r28523849 = r28523847 * r28523848;
        double r28523850 = t;
        double r28523851 = r28523849 * r28523850;
        double r28523852 = a;
        double r28523853 = 4.0;
        double r28523854 = r28523852 * r28523853;
        double r28523855 = r28523854 * r28523850;
        double r28523856 = r28523851 - r28523855;
        double r28523857 = b;
        double r28523858 = c;
        double r28523859 = r28523857 * r28523858;
        double r28523860 = r28523856 + r28523859;
        double r28523861 = r28523843 * r28523853;
        double r28523862 = i;
        double r28523863 = r28523861 * r28523862;
        double r28523864 = r28523860 - r28523863;
        double r28523865 = j;
        double r28523866 = 27.0;
        double r28523867 = r28523865 * r28523866;
        double r28523868 = k;
        double r28523869 = r28523867 * r28523868;
        double r28523870 = r28523864 - r28523869;
        return r28523870;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r28523871 = t;
        double r28523872 = x;
        double r28523873 = 18.0;
        double r28523874 = r28523872 * r28523873;
        double r28523875 = y;
        double r28523876 = r28523874 * r28523875;
        double r28523877 = z;
        double r28523878 = r28523876 * r28523877;
        double r28523879 = r28523871 * r28523878;
        double r28523880 = a;
        double r28523881 = 4.0;
        double r28523882 = r28523880 * r28523881;
        double r28523883 = r28523882 * r28523871;
        double r28523884 = r28523879 - r28523883;
        double r28523885 = c;
        double r28523886 = b;
        double r28523887 = r28523885 * r28523886;
        double r28523888 = r28523884 + r28523887;
        double r28523889 = r28523872 * r28523881;
        double r28523890 = i;
        double r28523891 = r28523889 * r28523890;
        double r28523892 = r28523888 - r28523891;
        double r28523893 = -inf.0;
        bool r28523894 = r28523892 <= r28523893;
        double r28523895 = 27.0;
        double r28523896 = j;
        double r28523897 = r28523895 * r28523896;
        double r28523898 = k;
        double r28523899 = r28523897 * r28523898;
        double r28523900 = r28523891 + r28523899;
        double r28523901 = r28523887 - r28523900;
        double r28523902 = -r28523871;
        double r28523903 = r28523902 * r28523882;
        double r28523904 = r28523901 + r28523903;
        double r28523905 = 6.210375130051423e+303;
        bool r28523906 = r28523892 <= r28523905;
        double r28523907 = r28523892 - r28523899;
        double r28523908 = r28523906 ? r28523907 : r28523904;
        double r28523909 = r28523894 ? r28523904 : r28523908;
        return r28523909;
}


\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
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i = -\infty:\\
\;\;\;\;\left(c \cdot b - \left(\left(x \cdot 4.0\right) \cdot i + \left(27.0 \cdot j\right) \cdot k\right)\right) + \left(-t\right) \cdot \left(a \cdot 4.0\right)\\

\mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 6.210375130051423 \cdot 10^{+303}:\\
\;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(c \cdot b - \left(\left(x \cdot 4.0\right) \cdot i + \left(27.0 \cdot j\right) \cdot k\right)\right) + \left(-t\right) \cdot \left(a \cdot 4.0\right)\\

\end{array}

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

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 6.210375130051423e+303 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 57.0

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

    2. Simplified36.7

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

    3. Taylor expanded around 0 30.1

      \[\leadsto \left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + \left(x \cdot 4.0\right) \cdot i\right)\right) + \left(\color{blue}{0} - a \cdot 4.0\right) \cdot t\]

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 6.210375130051423e+303

    1. Initial program 0.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i = -\infty:\\ \;\;\;\;\left(c \cdot b - \left(\left(x \cdot 4.0\right) \cdot i + \left(27.0 \cdot j\right) \cdot k\right)\right) + \left(-t\right) \cdot \left(a \cdot 4.0\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 6.210375130051423 \cdot 10^{+303}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b - \left(\left(x \cdot 4.0\right) \cdot i + \left(27.0 \cdot j\right) \cdot k\right)\right) + \left(-t\right) \cdot \left(a \cdot 4.0\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019102 
(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)))