Average Error: 12.0 → 11.7
Time: 8.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -4.77502645119979784 \cdot 10^{121}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 2.50669701620376095 \cdot 10^{189}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;j \le -4.77502645119979784 \cdot 10^{121}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{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)\\

\mathbf{elif}\;j \le 2.50669701620376095 \cdot 10^{189}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(0 - \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)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r106652 = x;
        double r106653 = y;
        double r106654 = z;
        double r106655 = r106653 * r106654;
        double r106656 = t;
        double r106657 = a;
        double r106658 = r106656 * r106657;
        double r106659 = r106655 - r106658;
        double r106660 = r106652 * r106659;
        double r106661 = b;
        double r106662 = c;
        double r106663 = r106662 * r106654;
        double r106664 = i;
        double r106665 = r106664 * r106657;
        double r106666 = r106663 - r106665;
        double r106667 = r106661 * r106666;
        double r106668 = r106660 - r106667;
        double r106669 = j;
        double r106670 = r106662 * r106656;
        double r106671 = r106664 * r106653;
        double r106672 = r106670 - r106671;
        double r106673 = r106669 * r106672;
        double r106674 = r106668 + r106673;
        return r106674;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r106675 = j;
        double r106676 = -4.775026451199798e+121;
        bool r106677 = r106675 <= r106676;
        double r106678 = x;
        double r106679 = y;
        double r106680 = z;
        double r106681 = r106679 * r106680;
        double r106682 = t;
        double r106683 = a;
        double r106684 = r106682 * r106683;
        double r106685 = r106681 - r106684;
        double r106686 = r106678 * r106685;
        double r106687 = b;
        double r106688 = cbrt(r106687);
        double r106689 = c;
        double r106690 = r106689 * r106680;
        double r106691 = i;
        double r106692 = r106691 * r106683;
        double r106693 = r106690 - r106692;
        double r106694 = cbrt(r106693);
        double r106695 = r106688 * r106694;
        double r106696 = r106687 * r106693;
        double r106697 = cbrt(r106696);
        double r106698 = r106695 * r106697;
        double r106699 = r106698 * r106697;
        double r106700 = r106686 - r106699;
        double r106701 = r106689 * r106682;
        double r106702 = r106691 * r106679;
        double r106703 = r106701 - r106702;
        double r106704 = r106675 * r106703;
        double r106705 = r106700 + r106704;
        double r106706 = 2.506697016203761e+189;
        bool r106707 = r106675 <= r106706;
        double r106708 = r106686 - r106696;
        double r106709 = r106675 * r106689;
        double r106710 = r106682 * r106709;
        double r106711 = -r106675;
        double r106712 = r106711 * r106702;
        double r106713 = r106710 + r106712;
        double r106714 = r106708 + r106713;
        double r106715 = 0.0;
        double r106716 = r106697 * r106697;
        double r106717 = r106716 * r106697;
        double r106718 = r106715 - r106717;
        double r106719 = r106718 + r106704;
        double r106720 = r106707 ? r106714 : r106719;
        double r106721 = r106677 ? r106705 : r106720;
        return r106721;
}

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 j < -4.775026451199798e+121

    1. Initial program 7.3

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

    3. Applied add-cube-cbrt7.5

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

    5. Applied cbrt-prod7.5

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

    if -4.775026451199798e+121 < j < 2.506697016203761e+189

    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 add-cube-cbrt13.1

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

    4. Applied associate-*l*13.1

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

    6. Applied sub-neg13.1

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

    7. Applied distribute-lft-in13.1

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

    8. Applied distribute-lft-in13.1

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

    9. Simplified12.1

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

    10. Simplified12.0

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

    if 2.506697016203761e+189 < j

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt7.0

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

    4. Taylor expanded around 0 14.0

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

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -4.77502645119979784 \cdot 10^{121}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 2.50669701620376095 \cdot 10^{189}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))