Average Error: 5.9 → 2.2
Time: 28.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.776984382821296984516260974198729562529 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18 - 4 \cdot a\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \le 7.289027731463515002673382915959472142239 \cdot 10^{-83}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(18 \cdot x\right) \cdot \left(y \cdot \left(t \cdot z\right)\right) - \left(4 \cdot a\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - \left(4 \cdot a\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;t \le -3.776984382821296984516260974198729562529 \cdot 10^{-79}:\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18 - 4 \cdot a\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\

\mathbf{elif}\;t \le 7.289027731463515002673382915959472142239 \cdot 10^{-83}:\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(18 \cdot x\right) \cdot \left(y \cdot \left(t \cdot z\right)\right) - \left(4 \cdot a\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - \left(4 \cdot a\right) \cdot t\right) + c \cdot b\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 r5614889 = x;
        double r5614890 = 18.0;
        double r5614891 = r5614889 * r5614890;
        double r5614892 = y;
        double r5614893 = r5614891 * r5614892;
        double r5614894 = z;
        double r5614895 = r5614893 * r5614894;
        double r5614896 = t;
        double r5614897 = r5614895 * r5614896;
        double r5614898 = a;
        double r5614899 = 4.0;
        double r5614900 = r5614898 * r5614899;
        double r5614901 = r5614900 * r5614896;
        double r5614902 = r5614897 - r5614901;
        double r5614903 = b;
        double r5614904 = c;
        double r5614905 = r5614903 * r5614904;
        double r5614906 = r5614902 + r5614905;
        double r5614907 = r5614889 * r5614899;
        double r5614908 = i;
        double r5614909 = r5614907 * r5614908;
        double r5614910 = r5614906 - r5614909;
        double r5614911 = j;
        double r5614912 = 27.0;
        double r5614913 = r5614911 * r5614912;
        double r5614914 = k;
        double r5614915 = r5614913 * r5614914;
        double r5614916 = r5614910 - r5614915;
        return r5614916;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r5614917 = t;
        double r5614918 = -3.776984382821297e-79;
        bool r5614919 = r5614917 <= r5614918;
        double r5614920 = c;
        double r5614921 = b;
        double r5614922 = r5614920 * r5614921;
        double r5614923 = x;
        double r5614924 = y;
        double r5614925 = z;
        double r5614926 = r5614924 * r5614925;
        double r5614927 = r5614923 * r5614926;
        double r5614928 = 18.0;
        double r5614929 = r5614927 * r5614928;
        double r5614930 = 4.0;
        double r5614931 = a;
        double r5614932 = r5614930 * r5614931;
        double r5614933 = r5614929 - r5614932;
        double r5614934 = r5614933 * r5614917;
        double r5614935 = r5614922 + r5614934;
        double r5614936 = r5614923 * r5614930;
        double r5614937 = i;
        double r5614938 = r5614936 * r5614937;
        double r5614939 = r5614935 - r5614938;
        double r5614940 = j;
        double r5614941 = 27.0;
        double r5614942 = k;
        double r5614943 = r5614941 * r5614942;
        double r5614944 = r5614940 * r5614943;
        double r5614945 = r5614939 - r5614944;
        double r5614946 = 7.289027731463515e-83;
        bool r5614947 = r5614917 <= r5614946;
        double r5614948 = r5614928 * r5614923;
        double r5614949 = r5614917 * r5614925;
        double r5614950 = r5614924 * r5614949;
        double r5614951 = r5614948 * r5614950;
        double r5614952 = r5614932 * r5614917;
        double r5614953 = r5614951 - r5614952;
        double r5614954 = r5614922 + r5614953;
        double r5614955 = r5614954 - r5614938;
        double r5614956 = r5614942 * r5614940;
        double r5614957 = r5614956 * r5614941;
        double r5614958 = r5614955 - r5614957;
        double r5614959 = r5614917 * r5614927;
        double r5614960 = r5614928 * r5614959;
        double r5614961 = r5614960 - r5614952;
        double r5614962 = r5614961 + r5614922;
        double r5614963 = r5614962 - r5614938;
        double r5614964 = r5614963 - r5614944;
        double r5614965 = r5614947 ? r5614958 : r5614964;
        double r5614966 = r5614919 ? r5614945 : r5614965;
        return r5614966;
}

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 3 regimes

  2. if t < -3.776984382821297e-79

    1. Initial program 3.0

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

    3. Applied associate-*l*8.2

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

    5. Applied associate-*l*9.4

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

    7. Applied associate-*l*9.3

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

    8. Taylor expanded around inf 3.0

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

    9. Simplified3.0

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

    if -3.776984382821297e-79 < t < 7.289027731463515e-83

    1. Initial program 9.0

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

    3. Applied associate-*l*4.6

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

    5. Applied associate-*l*1.3

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

    7. Applied associate-*l*1.3

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

    8. Taylor expanded around 0 1.2

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

    if 7.289027731463515e-83 < t

    1. Initial program 3.0

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

    3. Applied associate-*l*7.1

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

    5. Applied associate-*l*8.8

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

    7. Applied associate-*l*8.9

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

    8. Taylor expanded around inf 3.0

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.776984382821296984516260974198729562529 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18 - 4 \cdot a\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \le 7.289027731463515002673382915959472142239 \cdot 10^{-83}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(18 \cdot x\right) \cdot \left(y \cdot \left(t \cdot z\right)\right) - \left(4 \cdot a\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - \left(4 \cdot a\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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)))