Average Error: 12.1 → 12.2
Time: 10.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.6638058677896054 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \le 3.5355044355755603 \cdot 10^{-198}:\\ \;\;\;\;\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot \left(\sqrt{x} \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -5.6638058677896054 \cdot 10^{-176}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\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)\\

\mathbf{elif}\;x \le 3.5355044355755603 \cdot 10^{-198}:\\
\;\;\;\;\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt{x} \cdot \left(\sqrt{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)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r100559 = x;
        double r100560 = y;
        double r100561 = z;
        double r100562 = r100560 * r100561;
        double r100563 = t;
        double r100564 = a;
        double r100565 = r100563 * r100564;
        double r100566 = r100562 - r100565;
        double r100567 = r100559 * r100566;
        double r100568 = b;
        double r100569 = c;
        double r100570 = r100569 * r100561;
        double r100571 = i;
        double r100572 = r100571 * r100564;
        double r100573 = r100570 - r100572;
        double r100574 = r100568 * r100573;
        double r100575 = r100567 - r100574;
        double r100576 = j;
        double r100577 = r100569 * r100563;
        double r100578 = r100571 * r100560;
        double r100579 = r100577 - r100578;
        double r100580 = r100576 * r100579;
        double r100581 = r100575 + r100580;
        return r100581;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r100582 = x;
        double r100583 = -5.6638058677896054e-176;
        bool r100584 = r100582 <= r100583;
        double r100585 = y;
        double r100586 = z;
        double r100587 = r100585 * r100586;
        double r100588 = t;
        double r100589 = a;
        double r100590 = r100588 * r100589;
        double r100591 = r100587 - r100590;
        double r100592 = r100582 * r100591;
        double r100593 = b;
        double r100594 = cbrt(r100593);
        double r100595 = c;
        double r100596 = r100595 * r100586;
        double r100597 = i;
        double r100598 = r100597 * r100589;
        double r100599 = r100596 - r100598;
        double r100600 = cbrt(r100599);
        double r100601 = r100594 * r100600;
        double r100602 = r100593 * r100599;
        double r100603 = cbrt(r100602);
        double r100604 = r100601 * r100603;
        double r100605 = r100604 * r100603;
        double r100606 = r100592 - r100605;
        double r100607 = j;
        double r100608 = r100595 * r100588;
        double r100609 = r100597 * r100585;
        double r100610 = r100608 - r100609;
        double r100611 = r100607 * r100610;
        double r100612 = r100606 + r100611;
        double r100613 = 3.53550443557556e-198;
        bool r100614 = r100582 <= r100613;
        double r100615 = 0.0;
        double r100616 = r100615 - r100602;
        double r100617 = r100616 + r100611;
        double r100618 = sqrt(r100582);
        double r100619 = r100618 * r100591;
        double r100620 = r100618 * r100619;
        double r100621 = r100620 - r100602;
        double r100622 = r100621 + r100611;
        double r100623 = r100614 ? r100617 : r100622;
        double r100624 = r100584 ? r100612 : r100623;
        return r100624;
}

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 < -5.6638058677896054e-176

    1. Initial program 10.1

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

    3. Applied add-cube-cbrt10.4

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

    5. Applied cbrt-prod10.3

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

    if -5.6638058677896054e-176 < x < 3.53550443557556e-198

    1. Initial program 16.4

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

    2. Taylor expanded around 0 16.5

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

    if 3.53550443557556e-198 < x

    1. Initial program 11.0

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

    3. Applied add-sqr-sqrt11.1

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

    4. Applied associate-*l*11.1

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.6638058677896054 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{b} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \le 3.5355044355755603 \cdot 10^{-198}:\\ \;\;\;\;\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot \left(\sqrt{x} \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))