Average Error: 11.8 → 12.2
Time: 49.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.76962084709095 \cdot 10^{+171}:\\ \;\;\;\;b \cdot \left(i \cdot a - z \cdot c\right) - \left(x \cdot t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;(j \cdot \left(t \cdot c - i \cdot y\right) + \left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right)\right))_*\\ \end{array}\]
\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}\;a \le -2.76962084709095 \cdot 10^{+171}:\\
\;\;\;\;b \cdot \left(i \cdot a - z \cdot c\right) - \left(x \cdot t\right) \cdot a\\

\mathbf{else}:\\
\;\;\;\;(j \cdot \left(t \cdot c - i \cdot y\right) + \left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(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 r12657645 = x;
        double r12657646 = y;
        double r12657647 = z;
        double r12657648 = r12657646 * r12657647;
        double r12657649 = t;
        double r12657650 = a;
        double r12657651 = r12657649 * r12657650;
        double r12657652 = r12657648 - r12657651;
        double r12657653 = r12657645 * r12657652;
        double r12657654 = b;
        double r12657655 = c;
        double r12657656 = r12657655 * r12657647;
        double r12657657 = i;
        double r12657658 = r12657657 * r12657650;
        double r12657659 = r12657656 - r12657658;
        double r12657660 = r12657654 * r12657659;
        double r12657661 = r12657653 - r12657660;
        double r12657662 = j;
        double r12657663 = r12657655 * r12657649;
        double r12657664 = r12657657 * r12657646;
        double r12657665 = r12657663 - r12657664;
        double r12657666 = r12657662 * r12657665;
        double r12657667 = r12657661 + r12657666;
        return r12657667;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r12657668 = a;
        double r12657669 = -2.76962084709095e+171;
        bool r12657670 = r12657668 <= r12657669;
        double r12657671 = b;
        double r12657672 = i;
        double r12657673 = r12657672 * r12657668;
        double r12657674 = z;
        double r12657675 = c;
        double r12657676 = r12657674 * r12657675;
        double r12657677 = r12657673 - r12657676;
        double r12657678 = r12657671 * r12657677;
        double r12657679 = x;
        double r12657680 = t;
        double r12657681 = r12657679 * r12657680;
        double r12657682 = r12657681 * r12657668;
        double r12657683 = r12657678 - r12657682;
        double r12657684 = j;
        double r12657685 = r12657680 * r12657675;
        double r12657686 = y;
        double r12657687 = r12657672 * r12657686;
        double r12657688 = r12657685 - r12657687;
        double r12657689 = r12657674 * r12657686;
        double r12657690 = r12657680 * r12657668;
        double r12657691 = r12657689 - r12657690;
        double r12657692 = r12657691 * r12657679;
        double r12657693 = r12657676 - r12657673;
        double r12657694 = r12657671 * r12657693;
        double r12657695 = cbrt(r12657694);
        double r12657696 = cbrt(r12657671);
        double r12657697 = cbrt(r12657693);
        double r12657698 = r12657696 * r12657697;
        double r12657699 = r12657698 * r12657695;
        double r12657700 = r12657695 * r12657699;
        double r12657701 = r12657692 - r12657700;
        double r12657702 = fma(r12657684, r12657688, r12657701);
        double r12657703 = r12657670 ? r12657683 : r12657702;
        return r12657703;
}

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

Derivation

  1. Split input into 2 regimes

  2. if a < -2.76962084709095e+171

    1. Initial program 23.8

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Simplified23.8

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

    3. Taylor expanded around -inf 19.4

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

    4. Simplified26.7

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

    if -2.76962084709095e+171 < a

    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. Simplified10.9

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

    4. Applied add-cube-cbrt11.2

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

    6. Applied cbrt-prod11.2

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.76962084709095 \cdot 10^{+171}:\\ \;\;\;\;b \cdot \left(i \cdot a - z \cdot c\right) - \left(x \cdot t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;(j \cdot \left(t \cdot c - i \cdot y\right) + \left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right)\right))_*\\ \end{array}\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(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)))))