Average Error: 11.8 → 11.9
Time: 48.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.581084728359023 \cdot 10^{-272}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}}\\ \mathbf{elif}\;x \le 8.416028997892155 \cdot 10^{-179}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}}\right) \cdot \sqrt[3]{b}\right)\right)\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.581084728359023 \cdot 10^{-272}:\\
\;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}}\\

\mathbf{elif}\;x \le 8.416028997892155 \cdot 10^{-179}:\\
\;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}}\right) \cdot \sqrt[3]{b}\right)\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 r15050975 = x;
        double r15050976 = y;
        double r15050977 = z;
        double r15050978 = r15050976 * r15050977;
        double r15050979 = t;
        double r15050980 = a;
        double r15050981 = r15050979 * r15050980;
        double r15050982 = r15050978 - r15050981;
        double r15050983 = r15050975 * r15050982;
        double r15050984 = b;
        double r15050985 = c;
        double r15050986 = r15050985 * r15050977;
        double r15050987 = i;
        double r15050988 = r15050987 * r15050980;
        double r15050989 = r15050986 - r15050988;
        double r15050990 = r15050984 * r15050989;
        double r15050991 = r15050983 - r15050990;
        double r15050992 = j;
        double r15050993 = r15050985 * r15050979;
        double r15050994 = r15050987 * r15050976;
        double r15050995 = r15050993 - r15050994;
        double r15050996 = r15050992 * r15050995;
        double r15050997 = r15050991 + r15050996;
        return r15050997;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r15050998 = x;
        double r15050999 = -1.581084728359023e-272;
        bool r15051000 = r15050998 <= r15050999;
        double r15051001 = y;
        double r15051002 = z;
        double r15051003 = r15051001 * r15051002;
        double r15051004 = a;
        double r15051005 = t;
        double r15051006 = r15051004 * r15051005;
        double r15051007 = r15051003 - r15051006;
        double r15051008 = r15051007 * r15050998;
        double r15051009 = b;
        double r15051010 = c;
        double r15051011 = r15051002 * r15051010;
        double r15051012 = i;
        double r15051013 = r15051012 * r15051004;
        double r15051014 = r15051011 - r15051013;
        double r15051015 = r15051009 * r15051014;
        double r15051016 = r15051008 - r15051015;
        double r15051017 = j;
        double r15051018 = r15051010 * r15051005;
        double r15051019 = r15051012 * r15051001;
        double r15051020 = r15051018 - r15051019;
        double r15051021 = r15051017 * r15051020;
        double r15051022 = cbrt(r15051021);
        double r15051023 = r15051022 * r15051022;
        double r15051024 = cbrt(r15051020);
        double r15051025 = r15051024 * r15051024;
        double r15051026 = r15051025 * r15051017;
        double r15051027 = r15051026 * r15051024;
        double r15051028 = cbrt(r15051027);
        double r15051029 = r15051023 * r15051028;
        double r15051030 = r15051016 + r15051029;
        double r15051031 = 8.416028997892155e-179;
        bool r15051032 = r15050998 <= r15051031;
        double r15051033 = -r15051009;
        double r15051034 = r15051033 * r15051014;
        double r15051035 = r15051022 * r15051023;
        double r15051036 = r15051034 + r15051035;
        double r15051037 = cbrt(r15051015);
        double r15051038 = cbrt(r15051014);
        double r15051039 = r15051038 * r15051038;
        double r15051040 = cbrt(r15051039);
        double r15051041 = cbrt(r15051038);
        double r15051042 = r15051040 * r15051041;
        double r15051043 = cbrt(r15051009);
        double r15051044 = r15051042 * r15051043;
        double r15051045 = r15051037 * r15051044;
        double r15051046 = r15051037 * r15051045;
        double r15051047 = r15051008 - r15051046;
        double r15051048 = r15051021 + r15051047;
        double r15051049 = r15051032 ? r15051036 : r15051048;
        double r15051050 = r15051000 ? r15051030 : r15051049;
        return r15051050;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if x < -1.581084728359023e-272

    1. Initial program 10.9

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

    3. Applied add-cube-cbrt11.2

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

    5. Applied add-cube-cbrt11.1

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

    6. Applied associate-*r*11.1

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

    if -1.581084728359023e-272 < x < 8.416028997892155e-179

    1. Initial program 17.8

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

    3. Applied add-cube-cbrt18.1

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

    4. Taylor expanded around 0 17.0

      \[\leadsto \left(\color{blue}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\]

    if 8.416028997892155e-179 < x

    1. Initial program 10.1

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

    3. Applied add-cube-cbrt10.4

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

    5. Applied cbrt-prod10.3

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

    7. Applied add-cube-cbrt10.3

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

    8. Applied cbrt-prod10.4

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

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.581084728359023 \cdot 10^{-272}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}}\\ \mathbf{elif}\;x \le 8.416028997892155 \cdot 10^{-179}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}}\right) \cdot \sqrt[3]{b}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))