Average Error: 5.7 → 5.5
Time: 6.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.0971657083756821 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(\sqrt[3]{j \cdot \left(27 \cdot k\right)} \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right) \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right)\right)\\ \mathbf{elif}\;t \le 3.49457155414947748 \cdot 10^{-145}:\\ \;\;\;\;0 + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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 -2.0971657083756821 \cdot 10^{-234}:\\
\;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(\sqrt[3]{j \cdot \left(27 \cdot k\right)} \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right) \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right)\right)\\

\mathbf{elif}\;t \le 3.49457155414947748 \cdot 10^{-145}:\\
\;\;\;\;0 + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(j \cdot 27\right) \cdot 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 + \left(j \cdot 27\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 r693823 = x;
        double r693824 = 18.0;
        double r693825 = r693823 * r693824;
        double r693826 = y;
        double r693827 = r693825 * r693826;
        double r693828 = z;
        double r693829 = r693827 * r693828;
        double r693830 = t;
        double r693831 = r693829 * r693830;
        double r693832 = a;
        double r693833 = 4.0;
        double r693834 = r693832 * r693833;
        double r693835 = r693834 * r693830;
        double r693836 = r693831 - r693835;
        double r693837 = b;
        double r693838 = c;
        double r693839 = r693837 * r693838;
        double r693840 = r693836 + r693839;
        double r693841 = r693823 * r693833;
        double r693842 = i;
        double r693843 = r693841 * r693842;
        double r693844 = r693840 - r693843;
        double r693845 = j;
        double r693846 = 27.0;
        double r693847 = r693845 * r693846;
        double r693848 = k;
        double r693849 = r693847 * r693848;
        double r693850 = r693844 - r693849;
        return r693850;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r693851 = t;
        double r693852 = -2.097165708375682e-234;
        bool r693853 = r693851 <= r693852;
        double r693854 = x;
        double r693855 = 18.0;
        double r693856 = y;
        double r693857 = r693855 * r693856;
        double r693858 = r693854 * r693857;
        double r693859 = z;
        double r693860 = r693858 * r693859;
        double r693861 = a;
        double r693862 = 4.0;
        double r693863 = r693861 * r693862;
        double r693864 = r693860 - r693863;
        double r693865 = r693851 * r693864;
        double r693866 = b;
        double r693867 = c;
        double r693868 = r693866 * r693867;
        double r693869 = i;
        double r693870 = r693862 * r693869;
        double r693871 = r693854 * r693870;
        double r693872 = j;
        double r693873 = 27.0;
        double r693874 = k;
        double r693875 = r693873 * r693874;
        double r693876 = r693872 * r693875;
        double r693877 = cbrt(r693876);
        double r693878 = r693877 * r693877;
        double r693879 = r693878 * r693877;
        double r693880 = r693871 + r693879;
        double r693881 = r693868 - r693880;
        double r693882 = r693865 + r693881;
        double r693883 = 3.4945715541494775e-145;
        bool r693884 = r693851 <= r693883;
        double r693885 = 0.0;
        double r693886 = r693872 * r693873;
        double r693887 = r693886 * r693874;
        double r693888 = r693871 + r693887;
        double r693889 = r693868 - r693888;
        double r693890 = r693885 + r693889;
        double r693891 = r693854 * r693855;
        double r693892 = r693891 * r693856;
        double r693893 = r693892 * r693859;
        double r693894 = r693893 - r693863;
        double r693895 = r693851 * r693894;
        double r693896 = r693854 * r693862;
        double r693897 = r693896 * r693869;
        double r693898 = r693897 + r693887;
        double r693899 = r693868 - r693898;
        double r693900 = r693895 + r693899;
        double r693901 = r693884 ? r693890 : r693900;
        double r693902 = r693853 ? r693882 : r693901;
        return r693902;
}

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
Herbie5.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.680279438052224:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -2.097165708375682e-234

    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*4.7

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

    6. Applied associate-*l*4.7

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

    8. Applied associate-*l*4.7

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

    10. Applied add-cube-cbrt5.0

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

    if -2.097165708375682e-234 < t < 3.4945715541494775e-145

    1. Initial program 10.3

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

    2. Simplified10.3

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

    4. Applied associate-*l*10.2

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

    6. Applied associate-*l*10.3

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

    7. Taylor expanded around 0 8.8

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

    if 3.4945715541494775e-145 < t

    1. Initial program 3.5

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

    2. Simplified3.5

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

  4. Final simplification5.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.0971657083756821 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(\sqrt[3]{j \cdot \left(27 \cdot k\right)} \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right) \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right)\right)\\ \mathbf{elif}\;t \le 3.49457155414947748 \cdot 10^{-145}:\\ \;\;\;\;0 + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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)))