Average Error: 12.5 → 12.5
Time: 10.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -9.1167379607392149 \cdot 10^{-144} \lor \neg \left(b \le 2.65254915776862487 \cdot 10^{-221}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{\left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;b \le -9.1167379607392149 \cdot 10^{-144} \lor \neg \left(b \le 2.65254915776862487 \cdot 10^{-221}\right):\\
\;\;\;\;\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 \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{\left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - 0\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 r103639 = x;
        double r103640 = y;
        double r103641 = z;
        double r103642 = r103640 * r103641;
        double r103643 = t;
        double r103644 = a;
        double r103645 = r103643 * r103644;
        double r103646 = r103642 - r103645;
        double r103647 = r103639 * r103646;
        double r103648 = b;
        double r103649 = c;
        double r103650 = r103649 * r103641;
        double r103651 = i;
        double r103652 = r103651 * r103644;
        double r103653 = r103650 - r103652;
        double r103654 = r103648 * r103653;
        double r103655 = r103647 - r103654;
        double r103656 = j;
        double r103657 = r103649 * r103643;
        double r103658 = r103651 * r103640;
        double r103659 = r103657 - r103658;
        double r103660 = r103656 * r103659;
        double r103661 = r103655 + r103660;
        return r103661;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r103662 = b;
        double r103663 = -9.116737960739215e-144;
        bool r103664 = r103662 <= r103663;
        double r103665 = 2.652549157768625e-221;
        bool r103666 = r103662 <= r103665;
        double r103667 = !r103666;
        bool r103668 = r103664 || r103667;
        double r103669 = x;
        double r103670 = y;
        double r103671 = z;
        double r103672 = r103670 * r103671;
        double r103673 = t;
        double r103674 = a;
        double r103675 = r103673 * r103674;
        double r103676 = r103672 - r103675;
        double r103677 = r103669 * r103676;
        double r103678 = c;
        double r103679 = r103678 * r103671;
        double r103680 = i;
        double r103681 = r103680 * r103674;
        double r103682 = r103679 - r103681;
        double r103683 = r103662 * r103682;
        double r103684 = r103677 - r103683;
        double r103685 = j;
        double r103686 = r103678 * r103673;
        double r103687 = r103680 * r103670;
        double r103688 = r103686 - r103687;
        double r103689 = r103685 * r103688;
        double r103690 = cbrt(r103689);
        double r103691 = r103690 * r103690;
        double r103692 = cbrt(r103688);
        double r103693 = r103692 * r103692;
        double r103694 = r103685 * r103693;
        double r103695 = r103694 * r103692;
        double r103696 = cbrt(r103695);
        double r103697 = r103691 * r103696;
        double r103698 = r103684 + r103697;
        double r103699 = 0.0;
        double r103700 = r103677 - r103699;
        double r103701 = r103700 + r103689;
        double r103702 = r103668 ? r103698 : r103701;
        return r103702;
}

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 b < -9.116737960739215e-144 or 2.652549157768625e-221 < b

    1. Initial program 10.5

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

    3. Applied add-cube-cbrt10.7

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

    5. Applied add-cube-cbrt10.7

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

    6. Applied associate-*r*10.7

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

    if -9.116737960739215e-144 < b < 2.652549157768625e-221

    1. Initial program 18.3

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

    2. Taylor expanded around 0 17.6

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{0}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.1167379607392149 \cdot 10^{-144} \lor \neg \left(b \le 2.65254915776862487 \cdot 10^{-221}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{\left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(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)))))