Average Error: 5.6 → 2.0
Time: 47.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.626211434592408442050935797592645449118 \cdot 10^{-36}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \le 21885021756705142739042304:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;x \le -7.626211434592408442050935797592645449118 \cdot 10^{-36}:\\
\;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\

\mathbf{elif}\;x \le 21885021756705142739042304:\\
\;\;\;\;\left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{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)\\

\mathbf{else}:\\
\;\;\;\;\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) - 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 r76981 = x;
        double r76982 = 18.0;
        double r76983 = r76981 * r76982;
        double r76984 = y;
        double r76985 = r76983 * r76984;
        double r76986 = z;
        double r76987 = r76985 * r76986;
        double r76988 = t;
        double r76989 = r76987 * r76988;
        double r76990 = a;
        double r76991 = 4.0;
        double r76992 = r76990 * r76991;
        double r76993 = r76992 * r76988;
        double r76994 = r76989 - r76993;
        double r76995 = b;
        double r76996 = c;
        double r76997 = r76995 * r76996;
        double r76998 = r76994 + r76997;
        double r76999 = r76981 * r76991;
        double r77000 = i;
        double r77001 = r76999 * r77000;
        double r77002 = r76998 - r77001;
        double r77003 = j;
        double r77004 = 27.0;
        double r77005 = r77003 * r77004;
        double r77006 = k;
        double r77007 = r77005 * r77006;
        double r77008 = r77002 - r77007;
        return r77008;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r77009 = x;
        double r77010 = -7.626211434592408e-36;
        bool r77011 = r77009 <= r77010;
        double r77012 = 18.0;
        double r77013 = r77009 * r77012;
        double r77014 = y;
        double r77015 = z;
        double r77016 = r77014 * r77015;
        double r77017 = t;
        double r77018 = r77016 * r77017;
        double r77019 = r77013 * r77018;
        double r77020 = a;
        double r77021 = 4.0;
        double r77022 = r77020 * r77021;
        double r77023 = r77022 * r77017;
        double r77024 = r77019 - r77023;
        double r77025 = b;
        double r77026 = c;
        double r77027 = r77025 * r77026;
        double r77028 = r77024 + r77027;
        double r77029 = r77009 * r77021;
        double r77030 = i;
        double r77031 = r77029 * r77030;
        double r77032 = r77028 - r77031;
        double r77033 = 27.0;
        double r77034 = k;
        double r77035 = j;
        double r77036 = r77034 * r77035;
        double r77037 = r77033 * r77036;
        double r77038 = r77032 - r77037;
        double r77039 = 2.1885021756705143e+25;
        bool r77040 = r77009 <= r77039;
        double r77041 = r77013 * r77014;
        double r77042 = cbrt(r77015);
        double r77043 = r77042 * r77042;
        double r77044 = r77041 * r77043;
        double r77045 = r77044 * r77042;
        double r77046 = r77045 * r77017;
        double r77047 = r77046 - r77023;
        double r77048 = r77047 + r77027;
        double r77049 = r77048 - r77031;
        double r77050 = r77033 * r77034;
        double r77051 = r77035 * r77050;
        double r77052 = r77049 - r77051;
        double r77053 = r77015 * r77017;
        double r77054 = r77014 * r77053;
        double r77055 = r77013 * r77054;
        double r77056 = r77055 - r77023;
        double r77057 = r77056 + r77027;
        double r77058 = r77057 - r77031;
        double r77059 = r77058 - r77051;
        double r77060 = r77040 ? r77052 : r77059;
        double r77061 = r77011 ? r77038 : r77060;
        return r77061;
}

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 x < -7.626211434592408e-36

    1. Initial program 11.3

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

    3. Applied associate-*l*11.3

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

    5. Applied associate-*l*7.3

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

    7. Applied associate-*l*2.6

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

    8. Taylor expanded around 0 2.5

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

    if -7.626211434592408e-36 < x < 2.1885021756705143e+25

    1. Initial program 1.6

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

    3. Applied associate-*l*1.7

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

    5. Applied add-cube-cbrt1.8

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

    6. Applied associate-*r*1.8

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

    if 2.1885021756705143e+25 < x

    1. Initial program 13.6

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

    3. Applied associate-*l*13.8

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

    5. Applied associate-*l*7.7

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

    7. Applied associate-*l*1.9

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

    9. Applied associate-*l*1.9

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.626211434592408442050935797592645449118 \cdot 10^{-36}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \le 21885021756705142739042304:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))