Average Error: 12.1 → 12.0
Time: 29.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.596778456688688 \cdot 10^{+165}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{elif}\;z \le 1.0422704831254364 \cdot 10^{-259}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{c \cdot z - i \cdot a} \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot b\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{elif}\;z \le 2.2139058582803834 \cdot 10^{+221}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{elif}\;z \le 3.900370725857475 \cdot 10^{+273}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x - \left(t \cdot x\right) \cdot a\right) - \left(\left(b \cdot a\right) \cdot \left(-i\right) + z \cdot \left(c \cdot b\right)\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]
\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}\;z \le -3.596778456688688 \cdot 10^{+165}:\\
\;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\mathbf{elif}\;z \le 1.0422704831254364 \cdot 10^{-259}:\\
\;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{c \cdot z - i \cdot a} \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot b\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\mathbf{elif}\;z \le 2.2139058582803834 \cdot 10^{+221}:\\
\;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\mathbf{elif}\;z \le 3.900370725857475 \cdot 10^{+273}:\\
\;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x - \left(t \cdot x\right) \cdot a\right) - \left(\left(b \cdot a\right) \cdot \left(-i\right) + z \cdot \left(c \cdot b\right)\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4959746 = x;
        double r4959747 = y;
        double r4959748 = z;
        double r4959749 = r4959747 * r4959748;
        double r4959750 = t;
        double r4959751 = a;
        double r4959752 = r4959750 * r4959751;
        double r4959753 = r4959749 - r4959752;
        double r4959754 = r4959746 * r4959753;
        double r4959755 = b;
        double r4959756 = c;
        double r4959757 = r4959756 * r4959748;
        double r4959758 = i;
        double r4959759 = r4959758 * r4959751;
        double r4959760 = r4959757 - r4959759;
        double r4959761 = r4959755 * r4959760;
        double r4959762 = r4959754 - r4959761;
        double r4959763 = j;
        double r4959764 = r4959756 * r4959750;
        double r4959765 = r4959758 * r4959747;
        double r4959766 = r4959764 - r4959765;
        double r4959767 = r4959763 * r4959766;
        double r4959768 = r4959762 + r4959767;
        return r4959768;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4959769 = z;
        double r4959770 = -3.596778456688688e+165;
        bool r4959771 = r4959769 <= r4959770;
        double r4959772 = x;
        double r4959773 = r4959772 * r4959769;
        double r4959774 = y;
        double r4959775 = r4959773 * r4959774;
        double r4959776 = t;
        double r4959777 = r4959776 * r4959772;
        double r4959778 = a;
        double r4959779 = r4959777 * r4959778;
        double r4959780 = r4959775 - r4959779;
        double r4959781 = c;
        double r4959782 = r4959781 * r4959769;
        double r4959783 = i;
        double r4959784 = r4959783 * r4959778;
        double r4959785 = r4959782 - r4959784;
        double r4959786 = b;
        double r4959787 = r4959785 * r4959786;
        double r4959788 = r4959780 - r4959787;
        double r4959789 = r4959781 * r4959776;
        double r4959790 = r4959783 * r4959774;
        double r4959791 = r4959789 - r4959790;
        double r4959792 = j;
        double r4959793 = r4959791 * r4959792;
        double r4959794 = r4959788 + r4959793;
        double r4959795 = 1.0422704831254364e-259;
        bool r4959796 = r4959769 <= r4959795;
        double r4959797 = r4959774 * r4959769;
        double r4959798 = r4959778 * r4959776;
        double r4959799 = r4959797 - r4959798;
        double r4959800 = r4959799 * r4959772;
        double r4959801 = cbrt(r4959785);
        double r4959802 = r4959801 * r4959801;
        double r4959803 = r4959802 * r4959786;
        double r4959804 = r4959801 * r4959803;
        double r4959805 = r4959800 - r4959804;
        double r4959806 = r4959805 + r4959793;
        double r4959807 = 2.2139058582803834e+221;
        bool r4959808 = r4959769 <= r4959807;
        double r4959809 = 3.900370725857475e+273;
        bool r4959810 = r4959769 <= r4959809;
        double r4959811 = r4959797 * r4959772;
        double r4959812 = r4959811 - r4959779;
        double r4959813 = r4959786 * r4959778;
        double r4959814 = -r4959783;
        double r4959815 = r4959813 * r4959814;
        double r4959816 = r4959781 * r4959786;
        double r4959817 = r4959769 * r4959816;
        double r4959818 = r4959815 + r4959817;
        double r4959819 = r4959812 - r4959818;
        double r4959820 = r4959819 + r4959793;
        double r4959821 = r4959810 ? r4959820 : r4959794;
        double r4959822 = r4959808 ? r4959794 : r4959821;
        double r4959823 = r4959796 ? r4959806 : r4959822;
        double r4959824 = r4959771 ? r4959794 : r4959823;
        return r4959824;
}

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 z < -3.596778456688688e+165 or 1.0422704831254364e-259 < z < 2.2139058582803834e+221 or 3.900370725857475e+273 < z

    1. Initial program 13.4

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

    3. Applied add-cube-cbrt13.7

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

    4. Applied associate-*l*13.7

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

    5. Taylor expanded around inf 13.7

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

    7. Applied associate-*r*13.7

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

    8. Taylor expanded around inf 12.6

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

    9. Simplified13.4

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

    if -3.596778456688688e+165 < z < 1.0422704831254364e-259

    1. Initial program 10.3

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

    3. Applied add-cube-cbrt10.6

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

    4. Applied associate-*r*10.6

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

    if 2.2139058582803834e+221 < z < 3.900370725857475e+273

    1. Initial program 19.5

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

    3. Applied add-cube-cbrt19.8

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

    4. Applied associate-*l*19.8

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

    5. Taylor expanded around inf 19.8

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

    7. Applied sub-neg19.8

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

    8. Applied distribute-lft-in19.8

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

    9. Applied distribute-lft-in19.8

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

    10. Simplified14.4

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

    11. Simplified12.4

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

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.596778456688688 \cdot 10^{+165}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{elif}\;z \le 1.0422704831254364 \cdot 10^{-259}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{c \cdot z - i \cdot a} \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot b\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{elif}\;z \le 2.2139058582803834 \cdot 10^{+221}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{elif}\;z \le 3.900370725857475 \cdot 10^{+273}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x - \left(t \cdot x\right) \cdot a\right) - \left(\left(b \cdot a\right) \cdot \left(-i\right) + z \cdot \left(c \cdot b\right)\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - \left(t \cdot x\right) \cdot a\right) - \left(c \cdot z - i \cdot a\right) \cdot b\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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)))))