Average Error: 11.1 → 11.7
Time: 27.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.486872471409811 \cdot 10^{-131}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(-x\right) \cdot \left(a \cdot t\right) + \sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)}\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{elif}\;b \le 7.820861133577622 \cdot 10^{-253}:\\ \;\;\;\;\left(\left(-x\right) \cdot \left(a \cdot t\right) + \left(z \cdot y\right) \cdot x\right) + \left(c \cdot t - y \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(z \cdot y\right) \cdot x + \left(t \cdot \left(-x\right)\right) \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \end{array}\]
\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}\;b \le -6.486872471409811 \cdot 10^{-131}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(-x\right) \cdot \left(a \cdot t\right) + \sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)}\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\

\mathbf{elif}\;b \le 7.820861133577622 \cdot 10^{-253}:\\
\;\;\;\;\left(\left(-x\right) \cdot \left(a \cdot t\right) + \left(z \cdot y\right) \cdot x\right) + \left(c \cdot t - y \cdot i\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(z \cdot y\right) \cdot x + \left(t \cdot \left(-x\right)\right) \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\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 r1676680 = x;
        double r1676681 = y;
        double r1676682 = z;
        double r1676683 = r1676681 * r1676682;
        double r1676684 = t;
        double r1676685 = a;
        double r1676686 = r1676684 * r1676685;
        double r1676687 = r1676683 - r1676686;
        double r1676688 = r1676680 * r1676687;
        double r1676689 = b;
        double r1676690 = c;
        double r1676691 = r1676690 * r1676682;
        double r1676692 = i;
        double r1676693 = r1676692 * r1676685;
        double r1676694 = r1676691 - r1676693;
        double r1676695 = r1676689 * r1676694;
        double r1676696 = r1676688 - r1676695;
        double r1676697 = j;
        double r1676698 = r1676690 * r1676684;
        double r1676699 = r1676692 * r1676681;
        double r1676700 = r1676698 - r1676699;
        double r1676701 = r1676697 * r1676700;
        double r1676702 = r1676696 + r1676701;
        return r1676702;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1676703 = b;
        double r1676704 = -6.486872471409811e-131;
        bool r1676705 = r1676703 <= r1676704;
        double r1676706 = c;
        double r1676707 = t;
        double r1676708 = r1676706 * r1676707;
        double r1676709 = y;
        double r1676710 = i;
        double r1676711 = r1676709 * r1676710;
        double r1676712 = r1676708 - r1676711;
        double r1676713 = j;
        double r1676714 = r1676712 * r1676713;
        double r1676715 = x;
        double r1676716 = -r1676715;
        double r1676717 = a;
        double r1676718 = r1676717 * r1676707;
        double r1676719 = r1676716 * r1676718;
        double r1676720 = cbrt(r1676715);
        double r1676721 = z;
        double r1676722 = r1676721 * r1676709;
        double r1676723 = r1676720 * r1676722;
        double r1676724 = r1676720 * r1676720;
        double r1676725 = r1676723 * r1676724;
        double r1676726 = cbrt(r1676725);
        double r1676727 = r1676726 * r1676726;
        double r1676728 = r1676726 * r1676727;
        double r1676729 = r1676719 + r1676728;
        double r1676730 = r1676706 * r1676721;
        double r1676731 = r1676710 * r1676717;
        double r1676732 = r1676730 - r1676731;
        double r1676733 = r1676703 * r1676732;
        double r1676734 = r1676729 - r1676733;
        double r1676735 = r1676714 + r1676734;
        double r1676736 = 7.820861133577622e-253;
        bool r1676737 = r1676703 <= r1676736;
        double r1676738 = r1676722 * r1676715;
        double r1676739 = r1676719 + r1676738;
        double r1676740 = r1676739 + r1676714;
        double r1676741 = r1676707 * r1676716;
        double r1676742 = r1676741 * r1676717;
        double r1676743 = r1676738 + r1676742;
        double r1676744 = r1676743 - r1676733;
        double r1676745 = r1676714 + r1676744;
        double r1676746 = r1676737 ? r1676740 : r1676745;
        double r1676747 = r1676705 ? r1676735 : r1676746;
        return r1676747;
}

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 b < -6.486872471409811e-131

    1. Initial program 8.2

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

    3. Applied sub-neg8.2

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

    4. Applied distribute-lft-in8.2

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

    6. Applied add-cube-cbrt8.3

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

    7. Applied associate-*l*8.3

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

    9. Applied add-cube-cbrt8.4

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

    if -6.486872471409811e-131 < b < 7.820861133577622e-253

    1. Initial program 16.0

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

    3. Applied sub-neg16.0

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

    4. Applied distribute-lft-in16.0

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

    5. Taylor expanded around 0 17.7

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - \color{blue}{0}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if 7.820861133577622e-253 < 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 sub-neg10.5

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

    4. Applied distribute-lft-in10.5

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

    6. Applied distribute-lft-neg-in10.5

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

    7. Applied associate-*r*10.8

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

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.486872471409811 \cdot 10^{-131}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(-x\right) \cdot \left(a \cdot t\right) + \sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \left(z \cdot y\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)}\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{elif}\;b \le 7.820861133577622 \cdot 10^{-253}:\\ \;\;\;\;\left(\left(-x\right) \cdot \left(a \cdot t\right) + \left(z \cdot y\right) \cdot x\right) + \left(c \cdot t - y \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(z \cdot y\right) \cdot x + \left(t \cdot \left(-x\right)\right) \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 
(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)))))