Average Error: 5.4 → 1.6
Time: 37.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 3.98822022348703396 \cdot 10^{302}\right):\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) \cdot y - \sqrt[3]{{\left(4 \cdot \left(t \cdot a\right)\right)}^{3}}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;\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 = -\infty \lor \neg \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 \le 3.98822022348703396 \cdot 10^{302}\right):\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) \cdot y - \sqrt[3]{{\left(4 \cdot \left(t \cdot a\right)\right)}^{3}}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\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) - j \cdot \left(27 \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 r90812 = x;
        double r90813 = 18.0;
        double r90814 = r90812 * r90813;
        double r90815 = y;
        double r90816 = r90814 * r90815;
        double r90817 = z;
        double r90818 = r90816 * r90817;
        double r90819 = t;
        double r90820 = r90818 * r90819;
        double r90821 = a;
        double r90822 = 4.0;
        double r90823 = r90821 * r90822;
        double r90824 = r90823 * r90819;
        double r90825 = r90820 - r90824;
        double r90826 = b;
        double r90827 = c;
        double r90828 = r90826 * r90827;
        double r90829 = r90825 + r90828;
        double r90830 = r90812 * r90822;
        double r90831 = i;
        double r90832 = r90830 * r90831;
        double r90833 = r90829 - r90832;
        double r90834 = j;
        double r90835 = 27.0;
        double r90836 = r90834 * r90835;
        double r90837 = k;
        double r90838 = r90836 * r90837;
        double r90839 = r90833 - r90838;
        return r90839;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r90840 = x;
        double r90841 = 18.0;
        double r90842 = r90840 * r90841;
        double r90843 = y;
        double r90844 = r90842 * r90843;
        double r90845 = z;
        double r90846 = r90844 * r90845;
        double r90847 = t;
        double r90848 = r90846 * r90847;
        double r90849 = a;
        double r90850 = 4.0;
        double r90851 = r90849 * r90850;
        double r90852 = r90851 * r90847;
        double r90853 = r90848 - r90852;
        double r90854 = b;
        double r90855 = c;
        double r90856 = r90854 * r90855;
        double r90857 = r90853 + r90856;
        double r90858 = r90840 * r90850;
        double r90859 = i;
        double r90860 = r90858 * r90859;
        double r90861 = r90857 - r90860;
        double r90862 = -inf.0;
        bool r90863 = r90861 <= r90862;
        double r90864 = 3.988220223487034e+302;
        bool r90865 = r90861 <= r90864;
        double r90866 = !r90865;
        bool r90867 = r90863 || r90866;
        double r90868 = r90845 * r90847;
        double r90869 = r90842 * r90868;
        double r90870 = r90869 * r90843;
        double r90871 = r90847 * r90849;
        double r90872 = r90850 * r90871;
        double r90873 = 3.0;
        double r90874 = pow(r90872, r90873);
        double r90875 = cbrt(r90874);
        double r90876 = r90870 - r90875;
        double r90877 = r90876 + r90856;
        double r90878 = r90877 - r90860;
        double r90879 = j;
        double r90880 = 27.0;
        double r90881 = r90879 * r90880;
        double r90882 = k;
        double r90883 = r90881 * r90882;
        double r90884 = r90878 - r90883;
        double r90885 = r90880 * r90882;
        double r90886 = r90879 * r90885;
        double r90887 = r90861 - r90886;
        double r90888 = r90867 ? r90884 : r90887;
        return r90888;
}

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 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0 or 3.988220223487034e+302 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 58.9

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

    3. Applied associate-*l*31.9

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

    5. Applied associate-*l*7.3

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

    6. Simplified7.3

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

    8. Applied associate-*r*5.1

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

    10. Applied add-cbrt-cube8.5

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

    11. Applied add-cbrt-cube8.5

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

    12. Applied add-cbrt-cube26.8

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

    13. Applied cbrt-unprod26.8

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

    14. Applied cbrt-unprod27.5

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

    15. Simplified14.0

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

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 3.988220223487034e+302

    1. Initial program 0.4

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

    3. Applied associate-*l*0.4

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 3.98822022348703396 \cdot 10^{302}\right):\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) \cdot y - \sqrt[3]{{\left(4 \cdot \left(t \cdot a\right)\right)}^{3}}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))