Average Error: 5.5 → 3.9
Time: 29.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.817835946533626758757686769633005516507 \cdot 10^{-98}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;y \le 1.919804578831060539244494100787191703918 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;y \le -4.817835946533626758757686769633005516507 \cdot 10^{-98}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\

\mathbf{elif}\;y \le 1.919804578831060539244494100787191703918 \cdot 10^{-79}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\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 r7095772 = x;
        double r7095773 = 18.0;
        double r7095774 = r7095772 * r7095773;
        double r7095775 = y;
        double r7095776 = r7095774 * r7095775;
        double r7095777 = z;
        double r7095778 = r7095776 * r7095777;
        double r7095779 = t;
        double r7095780 = r7095778 * r7095779;
        double r7095781 = a;
        double r7095782 = 4.0;
        double r7095783 = r7095781 * r7095782;
        double r7095784 = r7095783 * r7095779;
        double r7095785 = r7095780 - r7095784;
        double r7095786 = b;
        double r7095787 = c;
        double r7095788 = r7095786 * r7095787;
        double r7095789 = r7095785 + r7095788;
        double r7095790 = r7095772 * r7095782;
        double r7095791 = i;
        double r7095792 = r7095790 * r7095791;
        double r7095793 = r7095789 - r7095792;
        double r7095794 = j;
        double r7095795 = 27.0;
        double r7095796 = r7095794 * r7095795;
        double r7095797 = k;
        double r7095798 = r7095796 * r7095797;
        double r7095799 = r7095793 - r7095798;
        return r7095799;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r7095800 = y;
        double r7095801 = -4.817835946533627e-98;
        bool r7095802 = r7095800 <= r7095801;
        double r7095803 = b;
        double r7095804 = c;
        double r7095805 = r7095803 * r7095804;
        double r7095806 = t;
        double r7095807 = z;
        double r7095808 = r7095806 * r7095807;
        double r7095809 = r7095800 * r7095808;
        double r7095810 = x;
        double r7095811 = 18.0;
        double r7095812 = r7095810 * r7095811;
        double r7095813 = r7095809 * r7095812;
        double r7095814 = a;
        double r7095815 = 4.0;
        double r7095816 = r7095814 * r7095815;
        double r7095817 = r7095806 * r7095816;
        double r7095818 = r7095813 - r7095817;
        double r7095819 = r7095805 + r7095818;
        double r7095820 = r7095815 * r7095810;
        double r7095821 = i;
        double r7095822 = r7095820 * r7095821;
        double r7095823 = r7095819 - r7095822;
        double r7095824 = j;
        double r7095825 = 27.0;
        double r7095826 = k;
        double r7095827 = r7095825 * r7095826;
        double r7095828 = r7095824 * r7095827;
        double r7095829 = r7095823 - r7095828;
        double r7095830 = 1.9198045788310605e-79;
        bool r7095831 = r7095800 <= r7095830;
        double r7095832 = r7095800 * r7095807;
        double r7095833 = r7095832 * r7095806;
        double r7095834 = r7095833 * r7095812;
        double r7095835 = r7095834 - r7095817;
        double r7095836 = r7095805 + r7095835;
        double r7095837 = r7095836 - r7095822;
        double r7095838 = r7095824 * r7095826;
        double r7095839 = r7095825 * r7095838;
        double r7095840 = r7095837 - r7095839;
        double r7095841 = r7095831 ? r7095840 : r7095829;
        double r7095842 = r7095802 ? r7095829 : r7095841;
        return r7095842;
}

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 y < -4.817835946533627e-98 or 1.9198045788310605e-79 < y

    1. Initial program 8.5

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

    3. Applied associate-*l*10.5

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

    5. Applied associate-*l*10.6

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

    7. Applied associate-*l*10.6

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

    9. Applied associate-*l*6.2

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

    if -4.817835946533627e-98 < y < 1.9198045788310605e-79

    1. Initial program 0.9

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

    3. Applied associate-*l*0.7

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

    5. Applied associate-*l*0.7

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

    6. Taylor expanded around 0 0.6

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

  4. Final simplification3.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.817835946533626758757686769633005516507 \cdot 10^{-98}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;y \le 1.919804578831060539244494100787191703918 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))