Average Error: 5.6 → 4.8
Time: 24.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.556070220324067637922052949506160381905 \cdot 10^{-307}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \mathbf{elif}\;t \le 4.461860870917308238894980463712832079364 \cdot 10^{-94}:\\ \;\;\;\;\left(\left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \end{array}\]
\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}\;t \le -2.556070220324067637922052949506160381905 \cdot 10^{-307}:\\
\;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\

\mathbf{elif}\;t \le 4.461860870917308238894980463712832079364 \cdot 10^{-94}:\\
\;\;\;\;\left(\left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\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 r4774780 = x;
        double r4774781 = 18.0;
        double r4774782 = r4774780 * r4774781;
        double r4774783 = y;
        double r4774784 = r4774782 * r4774783;
        double r4774785 = z;
        double r4774786 = r4774784 * r4774785;
        double r4774787 = t;
        double r4774788 = r4774786 * r4774787;
        double r4774789 = a;
        double r4774790 = 4.0;
        double r4774791 = r4774789 * r4774790;
        double r4774792 = r4774791 * r4774787;
        double r4774793 = r4774788 - r4774792;
        double r4774794 = b;
        double r4774795 = c;
        double r4774796 = r4774794 * r4774795;
        double r4774797 = r4774793 + r4774796;
        double r4774798 = r4774780 * r4774790;
        double r4774799 = i;
        double r4774800 = r4774798 * r4774799;
        double r4774801 = r4774797 - r4774800;
        double r4774802 = j;
        double r4774803 = 27.0;
        double r4774804 = r4774802 * r4774803;
        double r4774805 = k;
        double r4774806 = r4774804 * r4774805;
        double r4774807 = r4774801 - r4774806;
        return r4774807;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r4774808 = t;
        double r4774809 = -2.5560702203240676e-307;
        bool r4774810 = r4774808 <= r4774809;
        double r4774811 = b;
        double r4774812 = c;
        double r4774813 = r4774811 * r4774812;
        double r4774814 = 4.0;
        double r4774815 = i;
        double r4774816 = x;
        double r4774817 = r4774815 * r4774816;
        double r4774818 = r4774814 * r4774817;
        double r4774819 = j;
        double r4774820 = 27.0;
        double r4774821 = r4774819 * r4774820;
        double r4774822 = k;
        double r4774823 = r4774821 * r4774822;
        double r4774824 = r4774818 + r4774823;
        double r4774825 = r4774813 - r4774824;
        double r4774826 = z;
        double r4774827 = 18.0;
        double r4774828 = r4774826 * r4774827;
        double r4774829 = r4774816 * r4774828;
        double r4774830 = y;
        double r4774831 = r4774829 * r4774830;
        double r4774832 = a;
        double r4774833 = r4774832 * r4774814;
        double r4774834 = r4774831 - r4774833;
        double r4774835 = r4774808 * r4774834;
        double r4774836 = r4774825 + r4774835;
        double r4774837 = 4.461860870917308e-94;
        bool r4774838 = r4774808 <= r4774837;
        double r4774839 = r4774827 * r4774816;
        double r4774840 = r4774839 * r4774830;
        double r4774841 = r4774808 * r4774826;
        double r4774842 = r4774840 * r4774841;
        double r4774843 = r4774808 * r4774833;
        double r4774844 = r4774842 - r4774843;
        double r4774845 = r4774844 + r4774813;
        double r4774846 = r4774816 * r4774814;
        double r4774847 = r4774846 * r4774815;
        double r4774848 = r4774845 - r4774847;
        double r4774849 = r4774822 * r4774820;
        double r4774850 = r4774849 * r4774819;
        double r4774851 = r4774848 - r4774850;
        double r4774852 = r4774838 ? r4774851 : r4774836;
        double r4774853 = r4774810 ? r4774836 : r4774852;
        return r4774853;
}

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 < -2.5560702203240676e-307 or 4.461860870917308e-94 < t

    1. Initial program 4.7

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

    2. Simplified4.7

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

    4. Applied associate-*l*5.0

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

    if -2.5560702203240676e-307 < t < 4.461860870917308e-94

    1. Initial program 8.4

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

    3. Applied associate-*l*8.4

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

    5. Applied associate-*l*4.0

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

  4. Final simplification4.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.556070220324067637922052949506160381905 \cdot 10^{-307}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \mathbf{elif}\;t \le 4.461860870917308238894980463712832079364 \cdot 10^{-94}:\\ \;\;\;\;\left(\left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(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)))