Average Error: 11.4 → 8.8
Time: 1.5m
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.04441798709494 \cdot 10^{+141}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right)\right)\\ \mathbf{elif}\;x \le 1.0040934126982047 \cdot 10^{+45}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + \left(\left(\left(c \cdot t - i \cdot y\right) \cdot j - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right)\right)\\ \end{array}\]
\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 -2.04441798709494 \cdot 10^{+141}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right)\right)\\

\mathbf{elif}\;x \le 1.0040934126982047 \cdot 10^{+45}:\\
\;\;\;\;\left(z \cdot x\right) \cdot y + \left(\left(\left(c \cdot t - i \cdot y\right) \cdot j - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\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 r13817983 = x;
        double r13817984 = y;
        double r13817985 = z;
        double r13817986 = r13817984 * r13817985;
        double r13817987 = t;
        double r13817988 = a;
        double r13817989 = r13817987 * r13817988;
        double r13817990 = r13817986 - r13817989;
        double r13817991 = r13817983 * r13817990;
        double r13817992 = b;
        double r13817993 = c;
        double r13817994 = r13817993 * r13817985;
        double r13817995 = i;
        double r13817996 = r13817995 * r13817988;
        double r13817997 = r13817994 - r13817996;
        double r13817998 = r13817992 * r13817997;
        double r13817999 = r13817991 - r13817998;
        double r13818000 = j;
        double r13818001 = r13817993 * r13817987;
        double r13818002 = r13817995 * r13817984;
        double r13818003 = r13818001 - r13818002;
        double r13818004 = r13818000 * r13818003;
        double r13818005 = r13817999 + r13818004;
        return r13818005;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r13818006 = x;
        double r13818007 = -2.04441798709494e+141;
        bool r13818008 = r13818006 <= r13818007;
        double r13818009 = c;
        double r13818010 = t;
        double r13818011 = r13818009 * r13818010;
        double r13818012 = i;
        double r13818013 = y;
        double r13818014 = r13818012 * r13818013;
        double r13818015 = r13818011 - r13818014;
        double r13818016 = j;
        double r13818017 = r13818015 * r13818016;
        double r13818018 = z;
        double r13818019 = r13818013 * r13818018;
        double r13818020 = a;
        double r13818021 = r13818020 * r13818010;
        double r13818022 = r13818019 - r13818021;
        double r13818023 = r13818022 * r13818006;
        double r13818024 = r13818018 * r13818009;
        double r13818025 = r13818012 * r13818020;
        double r13818026 = r13818024 - r13818025;
        double r13818027 = cbrt(r13818026);
        double r13818028 = b;
        double r13818029 = r13818027 * r13818027;
        double r13818030 = r13818028 * r13818029;
        double r13818031 = r13818027 * r13818030;
        double r13818032 = r13818023 - r13818031;
        double r13818033 = r13818017 + r13818032;
        double r13818034 = 1.0040934126982047e+45;
        bool r13818035 = r13818006 <= r13818034;
        double r13818036 = r13818018 * r13818006;
        double r13818037 = r13818036 * r13818013;
        double r13818038 = r13818006 * r13818010;
        double r13818039 = r13818038 * r13818020;
        double r13818040 = r13818017 - r13818039;
        double r13818041 = r13818028 * r13818026;
        double r13818042 = r13818040 - r13818041;
        double r13818043 = r13818037 + r13818042;
        double r13818044 = r13818035 ? r13818043 : r13818033;
        double r13818045 = r13818008 ? r13818033 : r13818044;
        return r13818045;
}

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 2 regimes

  2. if x < -2.04441798709494e+141 or 1.0040934126982047e+45 < x

    1. Initial program 7.1

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

    3. Applied add-cube-cbrt7.3

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

    4. Applied associate-*r*7.3

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

    if -2.04441798709494e+141 < x < 1.0040934126982047e+45

    1. Initial program 12.9

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

    3. Applied sub-neg12.9

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

    4. Applied distribute-rgt-in12.9

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

    5. Applied associate--l+12.9

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

    6. Applied associate-+l+12.9

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

    7. Simplified11.4

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

    9. Applied associate-*l*9.4

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

    11. Applied add-cube-cbrt9.5

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

    12. Applied associate-*l*9.5

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

    13. Taylor expanded around inf 9.3

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

  4. Final simplification8.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.04441798709494 \cdot 10^{+141}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right)\right)\\ \mathbf{elif}\;x \le 1.0040934126982047 \cdot 10^{+45}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + \left(\left(\left(c \cdot t - i \cdot y\right) \cdot j - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019128 
(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)))))