Average Error: 5.7 → 2.2
Time: 18.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.1240441509892456 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right) + t \cdot \left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - a \cdot 4.0\right)\\ \mathbf{elif}\;t \le 1.0458702014704218 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - \left(j \cdot \left(27.0 \cdot k\right) + 4.0 \cdot \left(x \cdot i\right)\right)\right) + \left(18.0 \cdot \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot y\right) - \left(t \cdot a\right) \cdot 4.0\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right)\right) + \left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right)\\ \end{array}\]
\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 -3.1240441509892456 \cdot 10^{-20}:\\
\;\;\;\;\left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right) + t \cdot \left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - a \cdot 4.0\right)\\

\mathbf{elif}\;t \le 1.0458702014704218 \cdot 10^{+56}:\\
\;\;\;\;\left(b \cdot c - \left(j \cdot \left(27.0 \cdot k\right) + 4.0 \cdot \left(x \cdot i\right)\right)\right) + \left(18.0 \cdot \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot y\right) - \left(t \cdot a\right) \cdot 4.0\right)\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right)\right) + \left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\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 r14401651 = x;
        double r14401652 = 18.0;
        double r14401653 = r14401651 * r14401652;
        double r14401654 = y;
        double r14401655 = r14401653 * r14401654;
        double r14401656 = z;
        double r14401657 = r14401655 * r14401656;
        double r14401658 = t;
        double r14401659 = r14401657 * r14401658;
        double r14401660 = a;
        double r14401661 = 4.0;
        double r14401662 = r14401660 * r14401661;
        double r14401663 = r14401662 * r14401658;
        double r14401664 = r14401659 - r14401663;
        double r14401665 = b;
        double r14401666 = c;
        double r14401667 = r14401665 * r14401666;
        double r14401668 = r14401664 + r14401667;
        double r14401669 = r14401651 * r14401661;
        double r14401670 = i;
        double r14401671 = r14401669 * r14401670;
        double r14401672 = r14401668 - r14401671;
        double r14401673 = j;
        double r14401674 = 27.0;
        double r14401675 = r14401673 * r14401674;
        double r14401676 = k;
        double r14401677 = r14401675 * r14401676;
        double r14401678 = r14401672 - r14401677;
        return r14401678;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r14401679 = t;
        double r14401680 = -3.1240441509892456e-20;
        bool r14401681 = r14401679 <= r14401680;
        double r14401682 = b;
        double r14401683 = c;
        double r14401684 = r14401682 * r14401683;
        double r14401685 = 4.0;
        double r14401686 = x;
        double r14401687 = i;
        double r14401688 = r14401686 * r14401687;
        double r14401689 = r14401685 * r14401688;
        double r14401690 = 27.0;
        double r14401691 = j;
        double r14401692 = r14401690 * r14401691;
        double r14401693 = k;
        double r14401694 = r14401692 * r14401693;
        double r14401695 = r14401689 + r14401694;
        double r14401696 = r14401684 - r14401695;
        double r14401697 = z;
        double r14401698 = 18.0;
        double r14401699 = y;
        double r14401700 = r14401698 * r14401699;
        double r14401701 = r14401697 * r14401700;
        double r14401702 = r14401686 * r14401701;
        double r14401703 = a;
        double r14401704 = r14401703 * r14401685;
        double r14401705 = r14401702 - r14401704;
        double r14401706 = r14401679 * r14401705;
        double r14401707 = r14401696 + r14401706;
        double r14401708 = 1.0458702014704218e+56;
        bool r14401709 = r14401679 <= r14401708;
        double r14401710 = r14401690 * r14401693;
        double r14401711 = r14401691 * r14401710;
        double r14401712 = r14401711 + r14401689;
        double r14401713 = r14401684 - r14401712;
        double r14401714 = r14401686 * r14401679;
        double r14401715 = r14401697 * r14401714;
        double r14401716 = r14401715 * r14401699;
        double r14401717 = r14401698 * r14401716;
        double r14401718 = r14401679 * r14401703;
        double r14401719 = r14401718 * r14401685;
        double r14401720 = r14401717 - r14401719;
        double r14401721 = r14401713 + r14401720;
        double r14401722 = cbrt(r14401679);
        double r14401723 = r14401722 * r14401722;
        double r14401724 = r14401686 * r14401699;
        double r14401725 = r14401697 * r14401698;
        double r14401726 = r14401724 * r14401725;
        double r14401727 = r14401726 - r14401704;
        double r14401728 = r14401723 * r14401727;
        double r14401729 = r14401722 * r14401728;
        double r14401730 = r14401729 + r14401696;
        double r14401731 = r14401709 ? r14401721 : r14401730;
        double r14401732 = r14401681 ? r14401707 : r14401731;
        return r14401732;
}

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
Target1.8
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18.0 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4.0\right) - \left(\left(k \cdot j\right) \cdot 27.0 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.68027943805222:\\ \;\;\;\;\left(\left(18.0 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4.0\right) + \left(c \cdot b - 27.0 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18.0 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4.0\right) - \left(\left(k \cdot j\right) \cdot 27.0 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -3.1240441509892456e-20

    1. Initial program 2.4

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

    2. Simplified2.4

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

    4. Applied *-un-lft-identity2.4

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

    5. Applied associate-*r*2.4

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

    6. Simplified2.3

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

    if -3.1240441509892456e-20 < t < 1.0458702014704218e+56

    1. Initial program 7.5

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

    2. Simplified7.4

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

    3. Taylor expanded around inf 7.7

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

    5. Applied associate-*r*5.4

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

    7. Applied associate-*r*2.0

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

    9. Applied associate-*r*2.1

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

    if 1.0458702014704218e+56 < t

    1. Initial program 1.9

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

    2. Simplified1.9

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

    4. Applied add-cube-cbrt2.5

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

    5. Applied associate-*r*2.5

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.1240441509892456 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right) + t \cdot \left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - a \cdot 4.0\right)\\ \mathbf{elif}\;t \le 1.0458702014704218 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - \left(j \cdot \left(27.0 \cdot k\right) + 4.0 \cdot \left(x \cdot i\right)\right)\right) + \left(18.0 \cdot \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot y\right) - \left(t \cdot a\right) \cdot 4.0\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right)\right) + \left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))