Average Error: 11.7 → 12.0
Time: 58.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 1.405381109408611 \cdot 10^{-134}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + \left(\left(c \cdot j\right) \cdot t + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\left(c \cdot t\right) \cdot \sqrt[3]{j}\right) + \left(\left(-j\right) \cdot y\right) \cdot i\right)\\ \end{array}\]
\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}\;a \le 1.405381109408611 \cdot 10^{-134}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + \left(\left(c \cdot j\right) \cdot t + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\left(c \cdot t\right) \cdot \sqrt[3]{j}\right) + \left(\left(-j\right) \cdot y\right) \cdot i\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r11826498 = x;
        double r11826499 = y;
        double r11826500 = z;
        double r11826501 = r11826499 * r11826500;
        double r11826502 = t;
        double r11826503 = a;
        double r11826504 = r11826502 * r11826503;
        double r11826505 = r11826501 - r11826504;
        double r11826506 = r11826498 * r11826505;
        double r11826507 = b;
        double r11826508 = c;
        double r11826509 = r11826508 * r11826500;
        double r11826510 = i;
        double r11826511 = r11826510 * r11826503;
        double r11826512 = r11826509 - r11826511;
        double r11826513 = r11826507 * r11826512;
        double r11826514 = r11826506 - r11826513;
        double r11826515 = j;
        double r11826516 = r11826508 * r11826502;
        double r11826517 = r11826510 * r11826499;
        double r11826518 = r11826516 - r11826517;
        double r11826519 = r11826515 * r11826518;
        double r11826520 = r11826514 + r11826519;
        return r11826520;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r11826521 = a;
        double r11826522 = 1.405381109408611e-134;
        bool r11826523 = r11826521 <= r11826522;
        double r11826524 = x;
        double r11826525 = y;
        double r11826526 = z;
        double r11826527 = r11826525 * r11826526;
        double r11826528 = t;
        double r11826529 = r11826528 * r11826521;
        double r11826530 = r11826527 - r11826529;
        double r11826531 = r11826524 * r11826530;
        double r11826532 = b;
        double r11826533 = c;
        double r11826534 = r11826533 * r11826526;
        double r11826535 = i;
        double r11826536 = r11826521 * r11826535;
        double r11826537 = r11826534 - r11826536;
        double r11826538 = r11826532 * r11826537;
        double r11826539 = r11826531 - r11826538;
        double r11826540 = j;
        double r11826541 = r11826533 * r11826540;
        double r11826542 = r11826541 * r11826528;
        double r11826543 = -r11826540;
        double r11826544 = r11826535 * r11826525;
        double r11826545 = r11826543 * r11826544;
        double r11826546 = r11826542 + r11826545;
        double r11826547 = r11826539 + r11826546;
        double r11826548 = cbrt(r11826540);
        double r11826549 = r11826548 * r11826548;
        double r11826550 = r11826533 * r11826528;
        double r11826551 = r11826550 * r11826548;
        double r11826552 = r11826549 * r11826551;
        double r11826553 = r11826543 * r11826525;
        double r11826554 = r11826553 * r11826535;
        double r11826555 = r11826552 + r11826554;
        double r11826556 = r11826539 + r11826555;
        double r11826557 = r11826523 ? r11826547 : r11826556;
        return r11826557;
}

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 2 regimes

  2. if a < 1.405381109408611e-134

    1. Initial program 10.9

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

    3. Applied sub-neg10.9

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

    4. Applied distribute-lft-in10.9

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

    5. Taylor expanded around inf 11.1

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

    if 1.405381109408611e-134 < a

    1. Initial program 13.4

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

    3. Applied add-cube-cbrt13.6

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

    4. Applied associate-*l*13.6

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

    6. Applied sub-neg13.6

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

    7. Applied distribute-lft-in13.6

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

    8. Applied distribute-lft-in13.6

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

    9. Simplified14.2

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot t\right)\right) + \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 1.405381109408611 \cdot 10^{-134}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + \left(\left(c \cdot j\right) \cdot t + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\left(c \cdot t\right) \cdot \sqrt[3]{j}\right) + \left(\left(-j\right) \cdot y\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019107 
(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)))))