Average Error: 5.1 → 3.3
Time: 52.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.464171748847571 \cdot 10^{-29}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \le 1.806067450876909 \cdot 10^{-128}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(y \cdot \left(x \cdot 18.0\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\sqrt{t} \cdot \left(\left(z \cdot \left(y \cdot \left(x \cdot 18.0\right)\right)\right) \cdot \sqrt{t}\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\ \end{array}\]
\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 -1.464171748847571 \cdot 10^{-29}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\

\mathbf{elif}\;t \le 1.806067450876909 \cdot 10^{-128}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(y \cdot \left(x \cdot 18.0\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\sqrt{t} \cdot \left(\left(z \cdot \left(y \cdot \left(x \cdot 18.0\right)\right)\right) \cdot \sqrt{t}\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\

\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 r12318667 = x;
        double r12318668 = 18.0;
        double r12318669 = r12318667 * r12318668;
        double r12318670 = y;
        double r12318671 = r12318669 * r12318670;
        double r12318672 = z;
        double r12318673 = r12318671 * r12318672;
        double r12318674 = t;
        double r12318675 = r12318673 * r12318674;
        double r12318676 = a;
        double r12318677 = 4.0;
        double r12318678 = r12318676 * r12318677;
        double r12318679 = r12318678 * r12318674;
        double r12318680 = r12318675 - r12318679;
        double r12318681 = b;
        double r12318682 = c;
        double r12318683 = r12318681 * r12318682;
        double r12318684 = r12318680 + r12318683;
        double r12318685 = r12318667 * r12318677;
        double r12318686 = i;
        double r12318687 = r12318685 * r12318686;
        double r12318688 = r12318684 - r12318687;
        double r12318689 = j;
        double r12318690 = 27.0;
        double r12318691 = r12318689 * r12318690;
        double r12318692 = k;
        double r12318693 = r12318691 * r12318692;
        double r12318694 = r12318688 - r12318693;
        return r12318694;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r12318695 = t;
        double r12318696 = -1.464171748847571e-29;
        bool r12318697 = r12318695 <= r12318696;
        double r12318698 = b;
        double r12318699 = c;
        double r12318700 = r12318698 * r12318699;
        double r12318701 = x;
        double r12318702 = 18.0;
        double r12318703 = y;
        double r12318704 = r12318702 * r12318703;
        double r12318705 = r12318701 * r12318704;
        double r12318706 = z;
        double r12318707 = r12318705 * r12318706;
        double r12318708 = r12318707 * r12318695;
        double r12318709 = a;
        double r12318710 = 4.0;
        double r12318711 = r12318709 * r12318710;
        double r12318712 = r12318711 * r12318695;
        double r12318713 = r12318708 - r12318712;
        double r12318714 = r12318700 + r12318713;
        double r12318715 = r12318710 * r12318701;
        double r12318716 = i;
        double r12318717 = r12318715 * r12318716;
        double r12318718 = r12318714 - r12318717;
        double r12318719 = 27.0;
        double r12318720 = j;
        double r12318721 = k;
        double r12318722 = r12318720 * r12318721;
        double r12318723 = r12318719 * r12318722;
        double r12318724 = r12318718 - r12318723;
        double r12318725 = 1.806067450876909e-128;
        bool r12318726 = r12318695 <= r12318725;
        double r12318727 = r12318695 * r12318706;
        double r12318728 = r12318701 * r12318702;
        double r12318729 = r12318703 * r12318728;
        double r12318730 = r12318727 * r12318729;
        double r12318731 = r12318730 - r12318712;
        double r12318732 = r12318700 + r12318731;
        double r12318733 = r12318732 - r12318717;
        double r12318734 = r12318719 * r12318720;
        double r12318735 = r12318734 * r12318721;
        double r12318736 = r12318733 - r12318735;
        double r12318737 = sqrt(r12318695);
        double r12318738 = r12318706 * r12318729;
        double r12318739 = r12318738 * r12318737;
        double r12318740 = r12318737 * r12318739;
        double r12318741 = r12318740 - r12318712;
        double r12318742 = r12318700 + r12318741;
        double r12318743 = r12318742 - r12318717;
        double r12318744 = r12318743 - r12318735;
        double r12318745 = r12318726 ? r12318736 : r12318744;
        double r12318746 = r12318697 ? r12318724 : r12318745;
        return r12318746;
}

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 t < -1.464171748847571e-29

    1. Initial program 1.6

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

    3. Applied associate-*l*1.7

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

    4. Taylor expanded around inf 1.7

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

    if -1.464171748847571e-29 < t < 1.806067450876909e-128

    1. Initial program 8.0

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

    3. Applied associate-*l*4.3

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

    if 1.806067450876909e-128 < t

    1. Initial program 3.1

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

    3. Applied add-sqr-sqrt3.1

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

    4. Applied associate-*r*3.1

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.464171748847571 \cdot 10^{-29}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \le 1.806067450876909 \cdot 10^{-128}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(y \cdot \left(x \cdot 18.0\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\sqrt{t} \cdot \left(\left(z \cdot \left(y \cdot \left(x \cdot 18.0\right)\right)\right) \cdot \sqrt{t}\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot j\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2019119 
(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)))