Average Error: 11.3 → 8.4
Time: 24.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.286833836544238 \cdot 10^{-54}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + x \cdot \left(\left(-t\right) \cdot a\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;b \le 1.119555389693808 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(x \cdot \left(\left(-t\right) \cdot a\right) + x \cdot \left(y \cdot z\right)\right) - \left(c \cdot \left(z \cdot b\right) - \left(b \cdot i\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\left(\sqrt[3]{y \cdot z - a \cdot t} \cdot \sqrt[3]{y \cdot z - a \cdot t}\right) \cdot x\right) \cdot \sqrt[3]{y \cdot z - a \cdot t} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \end{array}\]
\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 -2.286833836544238 \cdot 10^{-54}:\\
\;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + x \cdot \left(\left(-t\right) \cdot a\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\

\mathbf{elif}\;b \le 1.119555389693808 \cdot 10^{+31}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(x \cdot \left(\left(-t\right) \cdot a\right) + x \cdot \left(y \cdot z\right)\right) - \left(c \cdot \left(z \cdot b\right) - \left(b \cdot i\right) \cdot a\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\left(\sqrt[3]{y \cdot z - a \cdot t} \cdot \sqrt[3]{y \cdot z - a \cdot t}\right) \cdot x\right) \cdot \sqrt[3]{y \cdot z - a \cdot t} - b \cdot \left(c \cdot z - a \cdot i\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 r1573618 = x;
        double r1573619 = y;
        double r1573620 = z;
        double r1573621 = r1573619 * r1573620;
        double r1573622 = t;
        double r1573623 = a;
        double r1573624 = r1573622 * r1573623;
        double r1573625 = r1573621 - r1573624;
        double r1573626 = r1573618 * r1573625;
        double r1573627 = b;
        double r1573628 = c;
        double r1573629 = r1573628 * r1573620;
        double r1573630 = i;
        double r1573631 = r1573630 * r1573623;
        double r1573632 = r1573629 - r1573631;
        double r1573633 = r1573627 * r1573632;
        double r1573634 = r1573626 - r1573633;
        double r1573635 = j;
        double r1573636 = r1573628 * r1573622;
        double r1573637 = r1573630 * r1573619;
        double r1573638 = r1573636 - r1573637;
        double r1573639 = r1573635 * r1573638;
        double r1573640 = r1573634 + r1573639;
        return r1573640;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1573641 = b;
        double r1573642 = -2.286833836544238e-54;
        bool r1573643 = r1573641 <= r1573642;
        double r1573644 = y;
        double r1573645 = z;
        double r1573646 = x;
        double r1573647 = r1573645 * r1573646;
        double r1573648 = r1573644 * r1573647;
        double r1573649 = t;
        double r1573650 = -r1573649;
        double r1573651 = a;
        double r1573652 = r1573650 * r1573651;
        double r1573653 = r1573646 * r1573652;
        double r1573654 = r1573648 + r1573653;
        double r1573655 = c;
        double r1573656 = r1573655 * r1573645;
        double r1573657 = i;
        double r1573658 = r1573651 * r1573657;
        double r1573659 = r1573656 - r1573658;
        double r1573660 = r1573641 * r1573659;
        double r1573661 = r1573654 - r1573660;
        double r1573662 = j;
        double r1573663 = r1573655 * r1573649;
        double r1573664 = r1573644 * r1573657;
        double r1573665 = r1573663 - r1573664;
        double r1573666 = r1573662 * r1573665;
        double r1573667 = r1573661 + r1573666;
        double r1573668 = 1.119555389693808e+31;
        bool r1573669 = r1573641 <= r1573668;
        double r1573670 = r1573644 * r1573645;
        double r1573671 = r1573646 * r1573670;
        double r1573672 = r1573653 + r1573671;
        double r1573673 = r1573645 * r1573641;
        double r1573674 = r1573655 * r1573673;
        double r1573675 = r1573641 * r1573657;
        double r1573676 = r1573675 * r1573651;
        double r1573677 = r1573674 - r1573676;
        double r1573678 = r1573672 - r1573677;
        double r1573679 = r1573666 + r1573678;
        double r1573680 = r1573651 * r1573649;
        double r1573681 = r1573670 - r1573680;
        double r1573682 = cbrt(r1573681);
        double r1573683 = r1573682 * r1573682;
        double r1573684 = r1573683 * r1573646;
        double r1573685 = r1573684 * r1573682;
        double r1573686 = r1573685 - r1573660;
        double r1573687 = r1573666 + r1573686;
        double r1573688 = r1573669 ? r1573679 : r1573687;
        double r1573689 = r1573643 ? r1573667 : r1573688;
        return r1573689;
}

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 < -2.286833836544238e-54

    1. Initial program 7.7

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

    3. Applied sub-neg7.7

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

    4. Applied distribute-rgt-in7.7

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

    6. Applied associate-*l*7.8

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

    if -2.286833836544238e-54 < b < 1.119555389693808e+31

    1. Initial program 14.3

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

    3. Applied sub-neg14.3

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

    4. Applied distribute-rgt-in14.3

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

    5. Taylor expanded around inf 9.1

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

    7. Applied associate-*r*9.1

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

    if 1.119555389693808e+31 < b

    1. Initial program 6.7

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

    3. Applied add-cube-cbrt6.9

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

    4. Applied associate-*r*6.9

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

  4. Final simplification8.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.286833836544238 \cdot 10^{-54}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + x \cdot \left(\left(-t\right) \cdot a\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;b \le 1.119555389693808 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(x \cdot \left(\left(-t\right) \cdot a\right) + x \cdot \left(y \cdot z\right)\right) - \left(c \cdot \left(z \cdot b\right) - \left(b \cdot i\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\left(\sqrt[3]{y \cdot z - a \cdot t} \cdot \sqrt[3]{y \cdot z - a \cdot t}\right) \cdot x\right) \cdot \sqrt[3]{y \cdot z - a \cdot t} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(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)))))