Average Error: 11.1 → 11.4
Time: 33.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.891701166498266 \cdot 10^{+24}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\ \mathbf{elif}\;x \le 9.508763394751354 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-a \cdot t\right) \cdot x\right) - \left(\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]
\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 -3.891701166498266 \cdot 10^{+24}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\

\mathbf{elif}\;x \le 9.508763394751354 \cdot 10^{+86}:\\
\;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-a \cdot t\right) \cdot x\right) - \left(\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r2423568 = x;
        double r2423569 = y;
        double r2423570 = z;
        double r2423571 = r2423569 * r2423570;
        double r2423572 = t;
        double r2423573 = a;
        double r2423574 = r2423572 * r2423573;
        double r2423575 = r2423571 - r2423574;
        double r2423576 = r2423568 * r2423575;
        double r2423577 = b;
        double r2423578 = c;
        double r2423579 = r2423578 * r2423570;
        double r2423580 = i;
        double r2423581 = r2423580 * r2423573;
        double r2423582 = r2423579 - r2423581;
        double r2423583 = r2423577 * r2423582;
        double r2423584 = r2423576 - r2423583;
        double r2423585 = j;
        double r2423586 = r2423578 * r2423572;
        double r2423587 = r2423580 * r2423569;
        double r2423588 = r2423586 - r2423587;
        double r2423589 = r2423585 * r2423588;
        double r2423590 = r2423584 + r2423589;
        return r2423590;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r2423591 = x;
        double r2423592 = -3.891701166498266e+24;
        bool r2423593 = r2423591 <= r2423592;
        double r2423594 = c;
        double r2423595 = t;
        double r2423596 = r2423594 * r2423595;
        double r2423597 = i;
        double r2423598 = y;
        double r2423599 = r2423597 * r2423598;
        double r2423600 = r2423596 - r2423599;
        double r2423601 = j;
        double r2423602 = r2423600 * r2423601;
        double r2423603 = z;
        double r2423604 = r2423598 * r2423603;
        double r2423605 = a;
        double r2423606 = r2423605 * r2423595;
        double r2423607 = r2423604 - r2423606;
        double r2423608 = r2423607 * r2423591;
        double r2423609 = b;
        double r2423610 = r2423603 * r2423594;
        double r2423611 = r2423597 * r2423605;
        double r2423612 = r2423610 - r2423611;
        double r2423613 = r2423609 * r2423612;
        double r2423614 = cbrt(r2423613);
        double r2423615 = cbrt(r2423612);
        double r2423616 = cbrt(r2423609);
        double r2423617 = r2423615 * r2423616;
        double r2423618 = r2423614 * r2423617;
        double r2423619 = r2423614 * r2423618;
        double r2423620 = r2423608 - r2423619;
        double r2423621 = r2423602 + r2423620;
        double r2423622 = 9.508763394751354e+86;
        bool r2423623 = r2423591 <= r2423622;
        double r2423624 = r2423603 * r2423591;
        double r2423625 = r2423598 * r2423624;
        double r2423626 = -r2423606;
        double r2423627 = r2423626 * r2423591;
        double r2423628 = r2423625 + r2423627;
        double r2423629 = r2423615 * r2423615;
        double r2423630 = r2423629 * r2423609;
        double r2423631 = r2423630 * r2423615;
        double r2423632 = r2423628 - r2423631;
        double r2423633 = r2423632 + r2423602;
        double r2423634 = r2423608 + r2423602;
        double r2423635 = r2423623 ? r2423633 : r2423634;
        double r2423636 = r2423593 ? r2423621 : r2423635;
        return r2423636;
}

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 < -3.891701166498266e+24

    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-cbrt7.5

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

    5. Applied cbrt-prod7.4

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

    if -3.891701166498266e+24 < x < 9.508763394751354e+86

    1. Initial program 12.7

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

    3. Applied add-cube-cbrt13.1

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

    4. Applied associate-*r*13.1

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

    6. Applied sub-neg13.1

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

    7. Applied distribute-rgt-in13.1

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

    9. Applied associate-*l*11.5

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

    if 9.508763394751354e+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 simplification11.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.891701166498266 \cdot 10^{+24}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{b}\right)\right)\right)\\ \mathbf{elif}\;x \le 9.508763394751354 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(-a \cdot t\right) \cdot x\right) - \left(\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(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)))))