Average Error: 11.3 → 8.4
Time: 27.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.286833836544238 \cdot 10^{-54}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + x \cdot \left(\left(-t\right) \cdot a\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;b \le 1.119555389693808 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(x \cdot \left(\left(-t\right) \cdot a\right) + x \cdot \left(y \cdot z\right)\right) - \left(c \cdot \left(z \cdot b\right) - \left(b \cdot i\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\left(\sqrt[3]{y \cdot z - a \cdot t} \cdot \sqrt[3]{y \cdot z - a \cdot t}\right) \cdot x\right) \cdot \sqrt[3]{y \cdot z - a \cdot t} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \end{array}\]
\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}\;b \le -2.286833836544238 \cdot 10^{-54}:\\
\;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + x \cdot \left(\left(-t\right) \cdot a\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\

\mathbf{elif}\;b \le 1.119555389693808 \cdot 10^{+31}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(x \cdot \left(\left(-t\right) \cdot a\right) + x \cdot \left(y \cdot z\right)\right) - \left(c \cdot \left(z \cdot b\right) - \left(b \cdot i\right) \cdot a\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\left(\sqrt[3]{y \cdot z - a \cdot t} \cdot \sqrt[3]{y \cdot z - a \cdot t}\right) \cdot x\right) \cdot \sqrt[3]{y \cdot z - a \cdot t} - b \cdot \left(c \cdot z - a \cdot i\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 r1902957 = x;
        double r1902958 = y;
        double r1902959 = z;
        double r1902960 = r1902958 * r1902959;
        double r1902961 = t;
        double r1902962 = a;
        double r1902963 = r1902961 * r1902962;
        double r1902964 = r1902960 - r1902963;
        double r1902965 = r1902957 * r1902964;
        double r1902966 = b;
        double r1902967 = c;
        double r1902968 = r1902967 * r1902959;
        double r1902969 = i;
        double r1902970 = r1902969 * r1902962;
        double r1902971 = r1902968 - r1902970;
        double r1902972 = r1902966 * r1902971;
        double r1902973 = r1902965 - r1902972;
        double r1902974 = j;
        double r1902975 = r1902967 * r1902961;
        double r1902976 = r1902969 * r1902958;
        double r1902977 = r1902975 - r1902976;
        double r1902978 = r1902974 * r1902977;
        double r1902979 = r1902973 + r1902978;
        return r1902979;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1902980 = b;
        double r1902981 = -2.286833836544238e-54;
        bool r1902982 = r1902980 <= r1902981;
        double r1902983 = y;
        double r1902984 = z;
        double r1902985 = x;
        double r1902986 = r1902984 * r1902985;
        double r1902987 = r1902983 * r1902986;
        double r1902988 = t;
        double r1902989 = -r1902988;
        double r1902990 = a;
        double r1902991 = r1902989 * r1902990;
        double r1902992 = r1902985 * r1902991;
        double r1902993 = r1902987 + r1902992;
        double r1902994 = c;
        double r1902995 = r1902994 * r1902984;
        double r1902996 = i;
        double r1902997 = r1902990 * r1902996;
        double r1902998 = r1902995 - r1902997;
        double r1902999 = r1902980 * r1902998;
        double r1903000 = r1902993 - r1902999;
        double r1903001 = j;
        double r1903002 = r1902994 * r1902988;
        double r1903003 = r1902983 * r1902996;
        double r1903004 = r1903002 - r1903003;
        double r1903005 = r1903001 * r1903004;
        double r1903006 = r1903000 + r1903005;
        double r1903007 = 1.119555389693808e+31;
        bool r1903008 = r1902980 <= r1903007;
        double r1903009 = r1902983 * r1902984;
        double r1903010 = r1902985 * r1903009;
        double r1903011 = r1902992 + r1903010;
        double r1903012 = r1902984 * r1902980;
        double r1903013 = r1902994 * r1903012;
        double r1903014 = r1902980 * r1902996;
        double r1903015 = r1903014 * r1902990;
        double r1903016 = r1903013 - r1903015;
        double r1903017 = r1903011 - r1903016;
        double r1903018 = r1903005 + r1903017;
        double r1903019 = r1902990 * r1902988;
        double r1903020 = r1903009 - r1903019;
        double r1903021 = cbrt(r1903020);
        double r1903022 = r1903021 * r1903021;
        double r1903023 = r1903022 * r1902985;
        double r1903024 = r1903023 * r1903021;
        double r1903025 = r1903024 - r1902999;
        double r1903026 = r1903005 + r1903025;
        double r1903027 = r1903008 ? r1903018 : r1903026;
        double r1903028 = r1902982 ? r1903006 : r1903027;
        return r1903028;
}

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 b < -2.286833836544238e-54

    1. Initial program 7.7

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

    3. Applied sub-neg7.7

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

    4. Applied distribute-rgt-in7.7

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

    6. Applied associate-*l*7.8

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

    if -2.286833836544238e-54 < b < 1.119555389693808e+31

    1. Initial program 14.3

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

    3. Applied sub-neg14.3

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

    4. Applied distribute-rgt-in14.3

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

    5. Taylor expanded around -inf 9.1

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

    7. Applied associate-*r*9.1

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

    if 1.119555389693808e+31 < b

    1. Initial program 6.7

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

    3. Applied add-cube-cbrt6.9

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

    4. Applied associate-*r*6.9

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

  4. Final simplification8.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.286833836544238 \cdot 10^{-54}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + x \cdot \left(\left(-t\right) \cdot a\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;b \le 1.119555389693808 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(x \cdot \left(\left(-t\right) \cdot a\right) + x \cdot \left(y \cdot z\right)\right) - \left(c \cdot \left(z \cdot b\right) - \left(b \cdot i\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\left(\sqrt[3]{y \cdot z - a \cdot t} \cdot \sqrt[3]{y \cdot z - a \cdot t}\right) \cdot x\right) \cdot \sqrt[3]{y \cdot z - a \cdot t} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(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)))))