Average Error: 11.9 → 9.3
Time: 10.7s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -384187009615644786688 \lor \neg \left(b \le 6.000359978067976008555703308677062250401 \cdot 10^{82}\right):\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + 1 \cdot \left(-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;b \le -384187009615644786688 \lor \neg \left(b \le 6.000359978067976008555703308677062250401 \cdot 10^{82}\right):\\
\;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + 1 \cdot \left(-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\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 r144681 = x;
        double r144682 = y;
        double r144683 = z;
        double r144684 = r144682 * r144683;
        double r144685 = t;
        double r144686 = a;
        double r144687 = r144685 * r144686;
        double r144688 = r144684 - r144687;
        double r144689 = r144681 * r144688;
        double r144690 = b;
        double r144691 = c;
        double r144692 = r144691 * r144683;
        double r144693 = i;
        double r144694 = r144693 * r144686;
        double r144695 = r144692 - r144694;
        double r144696 = r144690 * r144695;
        double r144697 = r144689 - r144696;
        double r144698 = j;
        double r144699 = r144691 * r144685;
        double r144700 = r144693 * r144682;
        double r144701 = r144699 - r144700;
        double r144702 = r144698 * r144701;
        double r144703 = r144697 + r144702;
        return r144703;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r144704 = b;
        double r144705 = -3.841870096156448e+20;
        bool r144706 = r144704 <= r144705;
        double r144707 = 6.000359978067976e+82;
        bool r144708 = r144704 <= r144707;
        double r144709 = !r144708;
        bool r144710 = r144706 || r144709;
        double r144711 = x;
        double r144712 = y;
        double r144713 = z;
        double r144714 = r144712 * r144713;
        double r144715 = t;
        double r144716 = a;
        double r144717 = r144715 * r144716;
        double r144718 = r144714 - r144717;
        double r144719 = cbrt(r144718);
        double r144720 = r144719 * r144719;
        double r144721 = r144711 * r144720;
        double r144722 = r144721 * r144719;
        double r144723 = c;
        double r144724 = r144723 * r144713;
        double r144725 = i;
        double r144726 = r144725 * r144716;
        double r144727 = r144724 - r144726;
        double r144728 = r144704 * r144727;
        double r144729 = r144722 - r144728;
        double r144730 = j;
        double r144731 = r144723 * r144715;
        double r144732 = r144725 * r144712;
        double r144733 = r144731 - r144732;
        double r144734 = r144730 * r144733;
        double r144735 = r144729 + r144734;
        double r144736 = r144711 * r144718;
        double r144737 = r144704 * r144723;
        double r144738 = r144713 * r144737;
        double r144739 = 1.0;
        double r144740 = -1.0;
        double r144741 = r144725 * r144704;
        double r144742 = r144716 * r144741;
        double r144743 = r144740 * r144742;
        double r144744 = r144739 * r144743;
        double r144745 = r144738 + r144744;
        double r144746 = r144736 - r144745;
        double r144747 = r144746 + r144734;
        double r144748 = r144710 ? r144735 : r144747;
        return r144748;
}

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 < -3.841870096156448e+20 or 6.000359978067976e+82 < b

    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-cbrt7.6

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

    4. Applied associate-*r*7.6

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

    if -3.841870096156448e+20 < b < 6.000359978067976e+82

    1. Initial program 13.8

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

    3. Applied add-cube-cbrt14.0

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

    4. Applied associate-*l*14.0

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

    6. Applied sub-neg14.0

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

    7. Applied distribute-lft-in14.0

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

    8. Applied distribute-lft-in14.0

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

    9. Simplified12.1

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

    10. Simplified12.0

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

    12. Applied *-un-lft-identity12.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \color{blue}{\left(1 \cdot \left(-b\right)\right)} \cdot \left(i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    13. Applied associate-*l*12.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \color{blue}{1 \cdot \left(\left(-b\right) \cdot \left(i \cdot a\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    14. Simplified10.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + 1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -384187009615644786688 \lor \neg \left(b \le 6.000359978067976008555703308677062250401 \cdot 10^{82}\right):\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + 1 \cdot \left(-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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)))))