Average Error: 5.3 → 2.1
Time: 1.2m
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3265662515.3631783:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot 18.0\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{elif}\;t \le 4.353619239620954 \cdot 10^{+120}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot 27.0\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot 18.0\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]
\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}\;t \le -3265662515.3631783:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot 18.0\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\

\mathbf{elif}\;t \le 4.353619239620954 \cdot 10^{+120}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot 27.0\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot 18.0\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\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 r8015777 = x;
        double r8015778 = 18.0;
        double r8015779 = r8015777 * r8015778;
        double r8015780 = y;
        double r8015781 = r8015779 * r8015780;
        double r8015782 = z;
        double r8015783 = r8015781 * r8015782;
        double r8015784 = t;
        double r8015785 = r8015783 * r8015784;
        double r8015786 = a;
        double r8015787 = 4.0;
        double r8015788 = r8015786 * r8015787;
        double r8015789 = r8015788 * r8015784;
        double r8015790 = r8015785 - r8015789;
        double r8015791 = b;
        double r8015792 = c;
        double r8015793 = r8015791 * r8015792;
        double r8015794 = r8015790 + r8015793;
        double r8015795 = r8015777 * r8015787;
        double r8015796 = i;
        double r8015797 = r8015795 * r8015796;
        double r8015798 = r8015794 - r8015797;
        double r8015799 = j;
        double r8015800 = 27.0;
        double r8015801 = r8015799 * r8015800;
        double r8015802 = k;
        double r8015803 = r8015801 * r8015802;
        double r8015804 = r8015798 - r8015803;
        return r8015804;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r8015805 = t;
        double r8015806 = -3265662515.3631783;
        bool r8015807 = r8015805 <= r8015806;
        double r8015808 = b;
        double r8015809 = c;
        double r8015810 = r8015808 * r8015809;
        double r8015811 = y;
        double r8015812 = x;
        double r8015813 = r8015811 * r8015812;
        double r8015814 = z;
        double r8015815 = r8015813 * r8015814;
        double r8015816 = 18.0;
        double r8015817 = r8015815 * r8015816;
        double r8015818 = r8015817 * r8015805;
        double r8015819 = a;
        double r8015820 = 4.0;
        double r8015821 = r8015819 * r8015820;
        double r8015822 = r8015821 * r8015805;
        double r8015823 = r8015818 - r8015822;
        double r8015824 = r8015810 + r8015823;
        double r8015825 = r8015812 * r8015820;
        double r8015826 = i;
        double r8015827 = r8015825 * r8015826;
        double r8015828 = r8015824 - r8015827;
        double r8015829 = k;
        double r8015830 = j;
        double r8015831 = 27.0;
        double r8015832 = r8015830 * r8015831;
        double r8015833 = r8015829 * r8015832;
        double r8015834 = r8015828 - r8015833;
        double r8015835 = 4.353619239620954e+120;
        bool r8015836 = r8015805 <= r8015835;
        double r8015837 = r8015805 * r8015814;
        double r8015838 = r8015811 * r8015837;
        double r8015839 = r8015812 * r8015816;
        double r8015840 = r8015838 * r8015839;
        double r8015841 = r8015840 - r8015822;
        double r8015842 = r8015810 + r8015841;
        double r8015843 = r8015842 - r8015827;
        double r8015844 = r8015829 * r8015831;
        double r8015845 = r8015844 * r8015830;
        double r8015846 = r8015843 - r8015845;
        double r8015847 = r8015836 ? r8015846 : r8015834;
        double r8015848 = r8015807 ? r8015834 : r8015847;
        return r8015848;
}

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 t < -3265662515.3631783 or 4.353619239620954e+120 < t

    1. Initial program 1.4

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

    3. Applied *-un-lft-identity1.4

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    4. Applied associate-*r*1.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot 1\right) \cdot t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    5. Simplified1.4

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

    if -3265662515.3631783 < t < 4.353619239620954e+120

    1. Initial program 6.7

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

    3. Applied associate-*l*4.2

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

    5. Applied associate-*l*2.3

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

    7. Applied associate-*l*2.3

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3265662515.3631783:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot 18.0\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{elif}\;t \le 4.353619239620954 \cdot 10^{+120}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot 27.0\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot 18.0\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(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)))