Average Error: 5.6 → 5.3
Time: 20.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.814761326386550777279758521488119181836 \cdot 10^{156}:\\ \;\;\;\;b \cdot c - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;x \le 2.490620401820025423975805319912306702311 \cdot 10^{-84}:\\ \;\;\;\;\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) + t \cdot \left(-a \cdot 4\right)\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]
\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}\;x \le -2.814761326386550777279758521488119181836 \cdot 10^{156}:\\
\;\;\;\;b \cdot c - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\

\mathbf{elif}\;x \le 2.490620401820025423975805319912306702311 \cdot 10^{-84}:\\
\;\;\;\;\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) + t \cdot \left(-a \cdot 4\right)\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \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 r160792 = x;
        double r160793 = 18.0;
        double r160794 = r160792 * r160793;
        double r160795 = y;
        double r160796 = r160794 * r160795;
        double r160797 = z;
        double r160798 = r160796 * r160797;
        double r160799 = t;
        double r160800 = r160798 * r160799;
        double r160801 = a;
        double r160802 = 4.0;
        double r160803 = r160801 * r160802;
        double r160804 = r160803 * r160799;
        double r160805 = r160800 - r160804;
        double r160806 = b;
        double r160807 = c;
        double r160808 = r160806 * r160807;
        double r160809 = r160805 + r160808;
        double r160810 = r160792 * r160802;
        double r160811 = i;
        double r160812 = r160810 * r160811;
        double r160813 = r160809 - r160812;
        double r160814 = j;
        double r160815 = 27.0;
        double r160816 = r160814 * r160815;
        double r160817 = k;
        double r160818 = r160816 * r160817;
        double r160819 = r160813 - r160818;
        return r160819;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r160820 = x;
        double r160821 = -2.8147613263865508e+156;
        bool r160822 = r160820 <= r160821;
        double r160823 = b;
        double r160824 = c;
        double r160825 = r160823 * r160824;
        double r160826 = 4.0;
        double r160827 = i;
        double r160828 = r160826 * r160827;
        double r160829 = r160820 * r160828;
        double r160830 = j;
        double r160831 = 27.0;
        double r160832 = k;
        double r160833 = r160831 * r160832;
        double r160834 = r160830 * r160833;
        double r160835 = r160829 + r160834;
        double r160836 = r160825 - r160835;
        double r160837 = 2.4906204018200254e-84;
        bool r160838 = r160820 <= r160837;
        double r160839 = t;
        double r160840 = cbrt(r160839);
        double r160841 = r160840 * r160840;
        double r160842 = 18.0;
        double r160843 = r160820 * r160842;
        double r160844 = y;
        double r160845 = r160843 * r160844;
        double r160846 = z;
        double r160847 = r160845 * r160846;
        double r160848 = a;
        double r160849 = r160848 * r160826;
        double r160850 = r160847 - r160849;
        double r160851 = r160840 * r160850;
        double r160852 = r160841 * r160851;
        double r160853 = r160852 + r160825;
        double r160854 = r160820 * r160826;
        double r160855 = r160854 * r160827;
        double r160856 = r160830 * r160831;
        double r160857 = r160856 * r160832;
        double r160858 = r160855 + r160857;
        double r160859 = r160853 - r160858;
        double r160860 = r160846 * r160844;
        double r160861 = r160820 * r160860;
        double r160862 = r160839 * r160861;
        double r160863 = r160842 * r160862;
        double r160864 = -r160849;
        double r160865 = r160839 * r160864;
        double r160866 = r160863 + r160865;
        double r160867 = r160866 + r160825;
        double r160868 = r160867 - r160858;
        double r160869 = r160838 ? r160859 : r160868;
        double r160870 = r160822 ? r160836 : r160869;
        return r160870;
}

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 x < -2.8147613263865508e+156

    1. Initial program 19.9

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

    2. Simplified19.9

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

    4. Applied associate-*l*19.9

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

    6. Applied associate-*l*19.8

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

    8. Applied associate-*l*19.7

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

    9. Taylor expanded around 0 22.6

      \[\leadsto \left(\color{blue}{0} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\]

    if -2.8147613263865508e+156 < x < 2.4906204018200254e-84

    1. Initial program 3.0

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

    2. Simplified3.0

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

    4. Applied add-cube-cbrt3.4

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

    5. Applied associate-*l*3.4

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

    if 2.4906204018200254e-84 < x

    1. Initial program 8.8

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

    2. Simplified8.8

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

    4. Applied sub-neg8.8

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

    5. Applied distribute-lft-in8.8

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

    6. Simplified6.0

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

  4. Final simplification5.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.814761326386550777279758521488119181836 \cdot 10^{156}:\\ \;\;\;\;b \cdot c - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;x \le 2.490620401820025423975805319912306702311 \cdot 10^{-84}:\\ \;\;\;\;\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) + t \cdot \left(-a \cdot 4\right)\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(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)))