Average Error: 5.7 → 4.2
Time: 31.6s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]
\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}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\
\;\;\;\;\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 + j \cdot \left(27 \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\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 r82760 = x;
        double r82761 = 18.0;
        double r82762 = r82760 * r82761;
        double r82763 = y;
        double r82764 = r82762 * r82763;
        double r82765 = z;
        double r82766 = r82764 * r82765;
        double r82767 = t;
        double r82768 = r82766 * r82767;
        double r82769 = a;
        double r82770 = 4.0;
        double r82771 = r82769 * r82770;
        double r82772 = r82771 * r82767;
        double r82773 = r82768 - r82772;
        double r82774 = b;
        double r82775 = c;
        double r82776 = r82774 * r82775;
        double r82777 = r82773 + r82776;
        double r82778 = r82760 * r82770;
        double r82779 = i;
        double r82780 = r82778 * r82779;
        double r82781 = r82777 - r82780;
        double r82782 = j;
        double r82783 = 27.0;
        double r82784 = r82782 * r82783;
        double r82785 = k;
        double r82786 = r82784 * r82785;
        double r82787 = r82781 - r82786;
        return r82787;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r82788 = z;
        double r82789 = -6.023016971486714e+129;
        bool r82790 = r82788 <= r82789;
        double r82791 = 4.983042576879065e-72;
        bool r82792 = r82788 <= r82791;
        double r82793 = !r82792;
        bool r82794 = r82790 || r82793;
        double r82795 = t;
        double r82796 = x;
        double r82797 = 18.0;
        double r82798 = r82796 * r82797;
        double r82799 = y;
        double r82800 = r82798 * r82799;
        double r82801 = r82800 * r82788;
        double r82802 = a;
        double r82803 = 4.0;
        double r82804 = r82802 * r82803;
        double r82805 = r82801 - r82804;
        double r82806 = r82795 * r82805;
        double r82807 = b;
        double r82808 = c;
        double r82809 = r82807 * r82808;
        double r82810 = r82806 + r82809;
        double r82811 = r82796 * r82803;
        double r82812 = i;
        double r82813 = r82811 * r82812;
        double r82814 = j;
        double r82815 = 27.0;
        double r82816 = k;
        double r82817 = r82815 * r82816;
        double r82818 = r82814 * r82817;
        double r82819 = r82813 + r82818;
        double r82820 = r82810 - r82819;
        double r82821 = r82799 * r82797;
        double r82822 = r82821 * r82788;
        double r82823 = r82796 * r82822;
        double r82824 = r82823 - r82804;
        double r82825 = r82795 * r82824;
        double r82826 = r82825 + r82809;
        double r82827 = r82814 * r82815;
        double r82828 = r82827 * r82816;
        double r82829 = r82813 + r82828;
        double r82830 = r82826 - r82829;
        double r82831 = r82794 ? r82820 : r82830;
        return r82831;
}

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 z < -6.023016971486714e+129 or 4.983042576879065e-72 < z

    1. Initial program 6.7

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

    2. Simplified6.7

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

    4. Applied associate-*l*6.7

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

    if -6.023016971486714e+129 < z < 4.983042576879065e-72

    1. Initial program 5.1

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

    2. Simplified5.1

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

    4. Applied associate-*l*5.1

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

    5. Simplified5.1

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

    7. Applied associate-*l*2.5

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

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))