Average Error: 5.7 → 5.8
Time: 24.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.317510189044365137739180146305788721923 \cdot 10^{132}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \end{array}\]
\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}\;x \le -1.317510189044365137739180146305788721923 \cdot 10^{132}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(27 \cdot k\right)\right)\right)\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 r145696 = x;
        double r145697 = 18.0;
        double r145698 = r145696 * r145697;
        double r145699 = y;
        double r145700 = r145698 * r145699;
        double r145701 = z;
        double r145702 = r145700 * r145701;
        double r145703 = t;
        double r145704 = r145702 * r145703;
        double r145705 = a;
        double r145706 = 4.0;
        double r145707 = r145705 * r145706;
        double r145708 = r145707 * r145703;
        double r145709 = r145704 - r145708;
        double r145710 = b;
        double r145711 = c;
        double r145712 = r145710 * r145711;
        double r145713 = r145709 + r145712;
        double r145714 = r145696 * r145706;
        double r145715 = i;
        double r145716 = r145714 * r145715;
        double r145717 = r145713 - r145716;
        double r145718 = j;
        double r145719 = 27.0;
        double r145720 = r145718 * r145719;
        double r145721 = k;
        double r145722 = r145720 * r145721;
        double r145723 = r145717 - r145722;
        return r145723;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r145724 = x;
        double r145725 = -1.3175101890443651e+132;
        bool r145726 = r145724 <= r145725;
        double r145727 = t;
        double r145728 = 0.0;
        double r145729 = a;
        double r145730 = 4.0;
        double r145731 = r145729 * r145730;
        double r145732 = r145728 - r145731;
        double r145733 = r145727 * r145732;
        double r145734 = b;
        double r145735 = c;
        double r145736 = r145734 * r145735;
        double r145737 = r145724 * r145730;
        double r145738 = i;
        double r145739 = r145737 * r145738;
        double r145740 = j;
        double r145741 = 27.0;
        double r145742 = r145740 * r145741;
        double r145743 = k;
        double r145744 = r145742 * r145743;
        double r145745 = r145739 + r145744;
        double r145746 = r145736 - r145745;
        double r145747 = r145733 + r145746;
        double r145748 = 18.0;
        double r145749 = y;
        double r145750 = r145748 * r145749;
        double r145751 = r145724 * r145750;
        double r145752 = z;
        double r145753 = r145751 * r145752;
        double r145754 = r145753 - r145731;
        double r145755 = r145727 * r145754;
        double r145756 = cbrt(r145740);
        double r145757 = r145756 * r145756;
        double r145758 = r145741 * r145743;
        double r145759 = r145756 * r145758;
        double r145760 = r145757 * r145759;
        double r145761 = r145739 + r145760;
        double r145762 = r145736 - r145761;
        double r145763 = r145755 + r145762;
        double r145764 = r145726 ? r145747 : r145763;
        return r145764;
}

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 x < -1.3175101890443651e+132

    1. Initial program 18.8

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

    2. Simplified18.8

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

    3. Taylor expanded around 0 15.5

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\]

    if -1.3175101890443651e+132 < x

    1. Initial program 4.6

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

    2. Simplified4.6

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

    4. Applied associate-*l*4.6

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

    6. Applied associate-*l*4.7

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

    8. Applied add-cube-cbrt4.9

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

    9. Applied associate-*l*4.9

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

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.317510189044365137739180146305788721923 \cdot 10^{132}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019298 
(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)))