Average Error: 12.4 → 10.9
Time: 38.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.262228259703944418388054681956517640133 \cdot 10^{72}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{x} \cdot \left(\left(y \cdot z - t \cdot a\right) \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{elif}\;x \le 7.708714260711597468016611731654685252532 \cdot 10^{86}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(z \cdot \left(y \cdot x\right) + \left(x \cdot a\right) \cdot \left(-t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array}\]
\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 -6.262228259703944418388054681956517640133 \cdot 10^{72}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{x} \cdot \left(\left(y \cdot z - t \cdot a\right) \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\

\mathbf{elif}\;x \le 7.708714260711597468016611731654685252532 \cdot 10^{86}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(z \cdot \left(y \cdot x\right) + \left(x \cdot a\right) \cdot \left(-t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - t \cdot a\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r5252590 = x;
        double r5252591 = y;
        double r5252592 = z;
        double r5252593 = r5252591 * r5252592;
        double r5252594 = t;
        double r5252595 = a;
        double r5252596 = r5252594 * r5252595;
        double r5252597 = r5252593 - r5252596;
        double r5252598 = r5252590 * r5252597;
        double r5252599 = b;
        double r5252600 = c;
        double r5252601 = r5252600 * r5252592;
        double r5252602 = i;
        double r5252603 = r5252602 * r5252595;
        double r5252604 = r5252601 - r5252603;
        double r5252605 = r5252599 * r5252604;
        double r5252606 = r5252598 - r5252605;
        double r5252607 = j;
        double r5252608 = r5252600 * r5252594;
        double r5252609 = r5252602 * r5252591;
        double r5252610 = r5252608 - r5252609;
        double r5252611 = r5252607 * r5252610;
        double r5252612 = r5252606 + r5252611;
        return r5252612;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r5252613 = x;
        double r5252614 = -6.2622282597039444e+72;
        bool r5252615 = r5252613 <= r5252614;
        double r5252616 = c;
        double r5252617 = t;
        double r5252618 = r5252616 * r5252617;
        double r5252619 = y;
        double r5252620 = i;
        double r5252621 = r5252619 * r5252620;
        double r5252622 = r5252618 - r5252621;
        double r5252623 = j;
        double r5252624 = r5252622 * r5252623;
        double r5252625 = cbrt(r5252613);
        double r5252626 = z;
        double r5252627 = r5252619 * r5252626;
        double r5252628 = a;
        double r5252629 = r5252617 * r5252628;
        double r5252630 = r5252627 - r5252629;
        double r5252631 = r5252630 * r5252625;
        double r5252632 = r5252625 * r5252631;
        double r5252633 = r5252632 * r5252625;
        double r5252634 = b;
        double r5252635 = r5252616 * r5252626;
        double r5252636 = r5252628 * r5252620;
        double r5252637 = r5252635 - r5252636;
        double r5252638 = r5252634 * r5252637;
        double r5252639 = r5252633 - r5252638;
        double r5252640 = r5252624 + r5252639;
        double r5252641 = 7.708714260711597e+86;
        bool r5252642 = r5252613 <= r5252641;
        double r5252643 = r5252619 * r5252613;
        double r5252644 = r5252626 * r5252643;
        double r5252645 = r5252613 * r5252628;
        double r5252646 = -r5252617;
        double r5252647 = r5252645 * r5252646;
        double r5252648 = r5252644 + r5252647;
        double r5252649 = r5252648 - r5252638;
        double r5252650 = r5252624 + r5252649;
        double r5252651 = r5252613 * r5252630;
        double r5252652 = r5252624 + r5252651;
        double r5252653 = r5252642 ? r5252650 : r5252652;
        double r5252654 = r5252615 ? r5252640 : r5252653;
        return r5252654;
}

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 x < -6.2622282597039444e+72

    1. Initial program 7.2

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

    3. Applied add-cube-cbrt7.8

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

    4. Applied associate-*l*7.8

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

    6. Applied associate-*l*7.8

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

    if -6.2622282597039444e+72 < x < 7.708714260711597e+86

    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 add-cube-cbrt14.5

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

    4. Applied associate-*l*14.5

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

    6. Applied sub-neg14.5

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

    7. Applied distribute-lft-in14.5

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

    8. Applied distribute-lft-in14.5

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

    9. Simplified12.6

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

    10. Simplified12.5

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

    12. Applied associate-*r*10.5

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

    if 7.708714260711597e+86 < x

    1. Initial program 7.1

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

    2. Taylor expanded around 0 16.6

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

  4. Final simplification10.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.262228259703944418388054681956517640133 \cdot 10^{72}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{x} \cdot \left(\left(y \cdot z - t \cdot a\right) \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{elif}\;x \le 7.708714260711597468016611731654685252532 \cdot 10^{86}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(z \cdot \left(y \cdot x\right) + \left(x \cdot a\right) \cdot \left(-t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(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)))))