Average Error: 5.7 → 4.9
Time: 8.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.3782938552808126543647984854596196655 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{elif}\;t \le 1.541728241483554882113848793697671960573 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]
\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}\;t \le -8.3782938552808126543647984854596196655 \cdot 10^{-183}:\\
\;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - 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{elif}\;t \le 1.541728241483554882113848793697671960573 \cdot 10^{-174}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;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 + j \cdot \left(27 \cdot k\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 r739695 = x;
        double r739696 = 18.0;
        double r739697 = r739695 * r739696;
        double r739698 = y;
        double r739699 = r739697 * r739698;
        double r739700 = z;
        double r739701 = r739699 * r739700;
        double r739702 = t;
        double r739703 = r739701 * r739702;
        double r739704 = a;
        double r739705 = 4.0;
        double r739706 = r739704 * r739705;
        double r739707 = r739706 * r739702;
        double r739708 = r739703 - r739707;
        double r739709 = b;
        double r739710 = c;
        double r739711 = r739709 * r739710;
        double r739712 = r739708 + r739711;
        double r739713 = r739695 * r739705;
        double r739714 = i;
        double r739715 = r739713 * r739714;
        double r739716 = r739712 - r739715;
        double r739717 = j;
        double r739718 = 27.0;
        double r739719 = r739717 * r739718;
        double r739720 = k;
        double r739721 = r739719 * r739720;
        double r739722 = r739716 - r739721;
        return r739722;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r739723 = t;
        double r739724 = -8.378293855280813e-183;
        bool r739725 = r739723 <= r739724;
        double r739726 = x;
        double r739727 = 18.0;
        double r739728 = r739726 * r739727;
        double r739729 = y;
        double r739730 = z;
        double r739731 = r739729 * r739730;
        double r739732 = r739728 * r739731;
        double r739733 = a;
        double r739734 = 4.0;
        double r739735 = r739733 * r739734;
        double r739736 = r739732 - r739735;
        double r739737 = r739723 * r739736;
        double r739738 = b;
        double r739739 = c;
        double r739740 = r739738 * r739739;
        double r739741 = r739726 * r739734;
        double r739742 = i;
        double r739743 = r739741 * r739742;
        double r739744 = j;
        double r739745 = 27.0;
        double r739746 = r739744 * r739745;
        double r739747 = k;
        double r739748 = r739746 * r739747;
        double r739749 = r739743 + r739748;
        double r739750 = r739740 - r739749;
        double r739751 = r739737 + r739750;
        double r739752 = 1.5417282414835549e-174;
        bool r739753 = r739723 <= r739752;
        double r739754 = 0.0;
        double r739755 = r739754 - r739735;
        double r739756 = r739723 * r739755;
        double r739757 = cbrt(r739747);
        double r739758 = r739757 * r739757;
        double r739759 = r739746 * r739758;
        double r739760 = r739759 * r739757;
        double r739761 = r739743 + r739760;
        double r739762 = r739740 - r739761;
        double r739763 = r739756 + r739762;
        double r739764 = r739728 * r739729;
        double r739765 = r739764 * r739730;
        double r739766 = r739765 - r739735;
        double r739767 = r739723 * r739766;
        double r739768 = r739745 * r739747;
        double r739769 = r739744 * r739768;
        double r739770 = r739743 + r739769;
        double r739771 = r739740 - r739770;
        double r739772 = r739767 + r739771;
        double r739773 = r739753 ? r739763 : r739772;
        double r739774 = r739725 ? r739751 : r739773;
        return r739774;
}

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

Target

Original5.7
Target2.0
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -8.378293855280813e-183

    1. Initial program 4.3

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

    2. Simplified4.3

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

    4. Applied associate-*l*4.8

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

    if -8.378293855280813e-183 < t < 1.5417282414835549e-174

    1. Initial program 9.7

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

    2. Simplified9.7

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

    4. Applied add-cube-cbrt10.0

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

    5. Applied associate-*r*10.0

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

    6. Taylor expanded around 0 6.2

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\]

    if 1.5417282414835549e-174 < t

    1. Initial program 4.0

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

    2. Simplified4.0

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

    4. Applied associate-*l*4.0

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.3782938552808126543647984854596196655 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{elif}\;t \le 1.541728241483554882113848793697671960573 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))