Average Error: 11.3 → 11.2
Time: 30.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.645805544531443 \cdot 10^{-232}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\ \mathbf{elif}\;x \le 2.7793681624166355 \cdot 10^{-219}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(z \cdot c - i \cdot a\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\ \end{array}\]
\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 -3.645805544531443 \cdot 10^{-232}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\

\mathbf{elif}\;x \le 2.7793681624166355 \cdot 10^{-219}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(z \cdot c - i \cdot a\right) \cdot \left(-b\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]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\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 r5934719 = x;
        double r5934720 = y;
        double r5934721 = z;
        double r5934722 = r5934720 * r5934721;
        double r5934723 = t;
        double r5934724 = a;
        double r5934725 = r5934723 * r5934724;
        double r5934726 = r5934722 - r5934725;
        double r5934727 = r5934719 * r5934726;
        double r5934728 = b;
        double r5934729 = c;
        double r5934730 = r5934729 * r5934721;
        double r5934731 = i;
        double r5934732 = r5934731 * r5934724;
        double r5934733 = r5934730 - r5934732;
        double r5934734 = r5934728 * r5934733;
        double r5934735 = r5934727 - r5934734;
        double r5934736 = j;
        double r5934737 = r5934729 * r5934723;
        double r5934738 = r5934731 * r5934720;
        double r5934739 = r5934737 - r5934738;
        double r5934740 = r5934736 * r5934739;
        double r5934741 = r5934735 + r5934740;
        return r5934741;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r5934742 = x;
        double r5934743 = -3.645805544531443e-232;
        bool r5934744 = r5934742 <= r5934743;
        double r5934745 = c;
        double r5934746 = t;
        double r5934747 = r5934745 * r5934746;
        double r5934748 = i;
        double r5934749 = y;
        double r5934750 = r5934748 * r5934749;
        double r5934751 = r5934747 - r5934750;
        double r5934752 = j;
        double r5934753 = r5934751 * r5934752;
        double r5934754 = z;
        double r5934755 = r5934749 * r5934754;
        double r5934756 = a;
        double r5934757 = r5934756 * r5934746;
        double r5934758 = r5934755 - r5934757;
        double r5934759 = r5934758 * r5934742;
        double r5934760 = b;
        double r5934761 = r5934754 * r5934745;
        double r5934762 = r5934748 * r5934756;
        double r5934763 = r5934761 - r5934762;
        double r5934764 = r5934760 * r5934763;
        double r5934765 = cbrt(r5934764);
        double r5934766 = cbrt(r5934763);
        double r5934767 = cbrt(r5934760);
        double r5934768 = r5934766 * r5934767;
        double r5934769 = r5934765 * r5934768;
        double r5934770 = r5934765 * r5934769;
        double r5934771 = r5934759 - r5934770;
        double r5934772 = r5934753 + r5934771;
        double r5934773 = 2.7793681624166355e-219;
        bool r5934774 = r5934742 <= r5934773;
        double r5934775 = -r5934760;
        double r5934776 = r5934763 * r5934775;
        double r5934777 = r5934753 + r5934776;
        double r5934778 = r5934774 ? r5934777 : r5934772;
        double r5934779 = r5934744 ? r5934772 : r5934778;
        return r5934779;
}

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 < -3.645805544531443e-232 or 2.7793681624166355e-219 < x

    1. Initial program 10.1

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

    3. Applied add-cube-cbrt10.4

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

    5. Applied cbrt-prod10.4

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

    if -3.645805544531443e-232 < x < 2.7793681624166355e-219

    1. Initial program 16.5

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

    2. Taylor expanded around 0 15.4

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

  4. Final simplification11.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.645805544531443 \cdot 10^{-232}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\ \mathbf{elif}\;x \le 2.7793681624166355 \cdot 10^{-219}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(z \cdot c - i \cdot a\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))))