Average Error: 5.7 → 4.2
Time: 30.9s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]
\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}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\
\;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\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 r534840 = x;
        double r534841 = 18.0;
        double r534842 = r534840 * r534841;
        double r534843 = y;
        double r534844 = r534842 * r534843;
        double r534845 = z;
        double r534846 = r534844 * r534845;
        double r534847 = t;
        double r534848 = r534846 * r534847;
        double r534849 = a;
        double r534850 = 4.0;
        double r534851 = r534849 * r534850;
        double r534852 = r534851 * r534847;
        double r534853 = r534848 - r534852;
        double r534854 = b;
        double r534855 = c;
        double r534856 = r534854 * r534855;
        double r534857 = r534853 + r534856;
        double r534858 = r534840 * r534850;
        double r534859 = i;
        double r534860 = r534858 * r534859;
        double r534861 = r534857 - r534860;
        double r534862 = j;
        double r534863 = 27.0;
        double r534864 = r534862 * r534863;
        double r534865 = k;
        double r534866 = r534864 * r534865;
        double r534867 = r534861 - r534866;
        return r534867;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r534868 = z;
        double r534869 = -6.023016971486714e+129;
        bool r534870 = r534868 <= r534869;
        double r534871 = 4.983042576879065e-72;
        bool r534872 = r534868 <= r534871;
        double r534873 = !r534872;
        bool r534874 = r534870 || r534873;
        double r534875 = t;
        double r534876 = x;
        double r534877 = 18.0;
        double r534878 = r534876 * r534877;
        double r534879 = y;
        double r534880 = r534878 * r534879;
        double r534881 = r534880 * r534868;
        double r534882 = a;
        double r534883 = 4.0;
        double r534884 = r534882 * r534883;
        double r534885 = r534881 - r534884;
        double r534886 = r534875 * r534885;
        double r534887 = b;
        double r534888 = c;
        double r534889 = r534887 * r534888;
        double r534890 = r534886 + r534889;
        double r534891 = r534876 * r534883;
        double r534892 = i;
        double r534893 = r534891 * r534892;
        double r534894 = j;
        double r534895 = 27.0;
        double r534896 = k;
        double r534897 = r534895 * r534896;
        double r534898 = r534894 * r534897;
        double r534899 = r534893 + r534898;
        double r534900 = r534890 - r534899;
        double r534901 = r534879 * r534877;
        double r534902 = r534901 * r534868;
        double r534903 = r534876 * r534902;
        double r534904 = r534903 - r534884;
        double r534905 = r534875 * r534904;
        double r534906 = r534905 + r534889;
        double r534907 = r534894 * r534895;
        double r534908 = r534907 * r534896;
        double r534909 = r534893 + r534908;
        double r534910 = r534906 - r534909;
        double r534911 = r534874 ? r534900 : r534910;
        return r534911;
}

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
Target1.6
Herbie4.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.023016971486714e+129 or 4.983042576879065e-72 < z

    1. Initial program 6.7

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

    2. Simplified6.7

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

    4. Applied associate-*l*6.7

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

    if -6.023016971486714e+129 < z < 4.983042576879065e-72

    1. Initial program 5.1

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

    2. Simplified5.1

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

    4. Applied associate-*l*5.1

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

    5. Simplified5.1

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

    7. Applied associate-*l*2.5

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

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))