Average Error: 12.1 → 12.6
Time: 45.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.510282121704738731660551701050045306425 \cdot 10^{-108}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(b \cdot \left(\sqrt[3]{c \cdot z - a \cdot i} \cdot \sqrt[3]{c \cdot z - a \cdot i}\right)\right) \cdot \sqrt[3]{c \cdot z - a \cdot i}\right) + j \cdot \left(t \cdot c - i \cdot y\right)\\ \mathbf{elif}\;x \le 2.801816886446554504036968501888911707507 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(t \cdot c - i \cdot y\right) + \left(z \cdot \left(\left(-b\right) \cdot c\right) + a \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot b\right) \cdot z + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + \left(j \cdot \left(t \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \end{array}\]
\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 -4.510282121704738731660551701050045306425 \cdot 10^{-108}:\\
\;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(b \cdot \left(\sqrt[3]{c \cdot z - a \cdot i} \cdot \sqrt[3]{c \cdot z - a \cdot i}\right)\right) \cdot \sqrt[3]{c \cdot z - a \cdot i}\right) + j \cdot \left(t \cdot c - i \cdot y\right)\\

\mathbf{elif}\;x \le 2.801816886446554504036968501888911707507 \cdot 10^{-147}:\\
\;\;\;\;j \cdot \left(t \cdot c - i \cdot y\right) + \left(z \cdot \left(\left(-b\right) \cdot c\right) + a \cdot \left(b \cdot i\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot b\right) \cdot z + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + \left(j \cdot \left(t \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\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 r4703602 = x;
        double r4703603 = y;
        double r4703604 = z;
        double r4703605 = r4703603 * r4703604;
        double r4703606 = t;
        double r4703607 = a;
        double r4703608 = r4703606 * r4703607;
        double r4703609 = r4703605 - r4703608;
        double r4703610 = r4703602 * r4703609;
        double r4703611 = b;
        double r4703612 = c;
        double r4703613 = r4703612 * r4703604;
        double r4703614 = i;
        double r4703615 = r4703614 * r4703607;
        double r4703616 = r4703613 - r4703615;
        double r4703617 = r4703611 * r4703616;
        double r4703618 = r4703610 - r4703617;
        double r4703619 = j;
        double r4703620 = r4703612 * r4703606;
        double r4703621 = r4703614 * r4703603;
        double r4703622 = r4703620 - r4703621;
        double r4703623 = r4703619 * r4703622;
        double r4703624 = r4703618 + r4703623;
        return r4703624;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4703625 = x;
        double r4703626 = -4.510282121704739e-108;
        bool r4703627 = r4703625 <= r4703626;
        double r4703628 = y;
        double r4703629 = z;
        double r4703630 = r4703628 * r4703629;
        double r4703631 = t;
        double r4703632 = a;
        double r4703633 = r4703631 * r4703632;
        double r4703634 = r4703630 - r4703633;
        double r4703635 = r4703634 * r4703625;
        double r4703636 = b;
        double r4703637 = c;
        double r4703638 = r4703637 * r4703629;
        double r4703639 = i;
        double r4703640 = r4703632 * r4703639;
        double r4703641 = r4703638 - r4703640;
        double r4703642 = cbrt(r4703641);
        double r4703643 = r4703642 * r4703642;
        double r4703644 = r4703636 * r4703643;
        double r4703645 = r4703644 * r4703642;
        double r4703646 = r4703635 - r4703645;
        double r4703647 = j;
        double r4703648 = r4703631 * r4703637;
        double r4703649 = r4703639 * r4703628;
        double r4703650 = r4703648 - r4703649;
        double r4703651 = r4703647 * r4703650;
        double r4703652 = r4703646 + r4703651;
        double r4703653 = 2.8018168864465545e-147;
        bool r4703654 = r4703625 <= r4703653;
        double r4703655 = -r4703636;
        double r4703656 = r4703655 * r4703637;
        double r4703657 = r4703629 * r4703656;
        double r4703658 = r4703636 * r4703639;
        double r4703659 = r4703632 * r4703658;
        double r4703660 = r4703657 + r4703659;
        double r4703661 = r4703651 + r4703660;
        double r4703662 = r4703637 * r4703636;
        double r4703663 = r4703662 * r4703629;
        double r4703664 = -r4703632;
        double r4703665 = r4703658 * r4703664;
        double r4703666 = r4703663 + r4703665;
        double r4703667 = r4703635 - r4703666;
        double r4703668 = r4703647 * r4703648;
        double r4703669 = -r4703647;
        double r4703670 = r4703669 * r4703649;
        double r4703671 = r4703668 + r4703670;
        double r4703672 = r4703667 + r4703671;
        double r4703673 = r4703654 ? r4703661 : r4703672;
        double r4703674 = r4703627 ? r4703652 : r4703673;
        return r4703674;
}

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 < -4.510282121704739e-108

    1. Initial program 8.1

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

    3. Applied add-cube-cbrt8.4

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

    4. Applied associate-*r*8.4

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

    if -4.510282121704739e-108 < x < 2.8018168864465545e-147

    1. Initial program 17.5

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

    3. Applied sub-neg17.5

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

    4. Applied distribute-lft-in17.5

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

    6. Applied associate-*r*17.3

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

    8. Applied distribute-rgt-neg-in17.3

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

    9. Applied associate-*r*17.1

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

    10. Taylor expanded around 0 17.8

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

    if 2.8018168864465545e-147 < x

    1. Initial program 9.6

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

    3. Applied sub-neg9.6

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

    4. Applied distribute-lft-in9.6

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

    6. Applied associate-*r*10.6

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

    8. Applied distribute-rgt-neg-in10.6

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

    9. Applied associate-*r*10.6

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

    11. Applied sub-neg10.6

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

    12. Applied distribute-rgt-in10.6

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

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.510282121704738731660551701050045306425 \cdot 10^{-108}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(b \cdot \left(\sqrt[3]{c \cdot z - a \cdot i} \cdot \sqrt[3]{c \cdot z - a \cdot i}\right)\right) \cdot \sqrt[3]{c \cdot z - a \cdot i}\right) + j \cdot \left(t \cdot c - i \cdot y\right)\\ \mathbf{elif}\;x \le 2.801816886446554504036968501888911707507 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(t \cdot c - i \cdot y\right) + \left(z \cdot \left(\left(-b\right) \cdot c\right) + a \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot b\right) \cdot z + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + \left(j \cdot \left(t \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(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)))))