Average Error: 12.3 → 10.7
Time: 8.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -1.76023307603761202409938293253843061099 \cdot 10^{58}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(\sqrt[3]{x \cdot \left(-t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(-t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(-t \cdot a\right)}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{elif}\;j \le 1.516551054990740022970306969909426253394 \cdot 10^{61}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot c\right) \cdot t + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{elif}\;j \le 2.85640851406350578387766548712466692209 \cdot 10^{304}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot c\right) \cdot t + j \cdot \left(-i \cdot y\right)\right)\\ \end{array}\]
\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}\;j \le -1.76023307603761202409938293253843061099 \cdot 10^{58}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(\sqrt[3]{x \cdot \left(-t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(-t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(-t \cdot a\right)}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\

\mathbf{elif}\;j \le 1.516551054990740022970306969909426253394 \cdot 10^{61}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot c\right) \cdot t + j \cdot \left(-i \cdot y\right)\right)\\

\mathbf{elif}\;j \le 2.85640851406350578387766548712466692209 \cdot 10^{304}:\\
\;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot c\right) \cdot t + j \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 r99477 = x;
        double r99478 = y;
        double r99479 = z;
        double r99480 = r99478 * r99479;
        double r99481 = t;
        double r99482 = a;
        double r99483 = r99481 * r99482;
        double r99484 = r99480 - r99483;
        double r99485 = r99477 * r99484;
        double r99486 = b;
        double r99487 = c;
        double r99488 = r99487 * r99479;
        double r99489 = i;
        double r99490 = r99489 * r99482;
        double r99491 = r99488 - r99490;
        double r99492 = r99486 * r99491;
        double r99493 = r99485 - r99492;
        double r99494 = j;
        double r99495 = r99487 * r99481;
        double r99496 = r99489 * r99478;
        double r99497 = r99495 - r99496;
        double r99498 = r99494 * r99497;
        double r99499 = r99493 + r99498;
        return r99499;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r99500 = j;
        double r99501 = -1.760233076037612e+58;
        bool r99502 = r99500 <= r99501;
        double r99503 = x;
        double r99504 = y;
        double r99505 = z;
        double r99506 = r99504 * r99505;
        double r99507 = r99503 * r99506;
        double r99508 = t;
        double r99509 = a;
        double r99510 = r99508 * r99509;
        double r99511 = -r99510;
        double r99512 = r99503 * r99511;
        double r99513 = cbrt(r99512);
        double r99514 = r99513 * r99513;
        double r99515 = r99514 * r99513;
        double r99516 = r99507 + r99515;
        double r99517 = b;
        double r99518 = c;
        double r99519 = r99518 * r99505;
        double r99520 = i;
        double r99521 = r99520 * r99509;
        double r99522 = r99519 - r99521;
        double r99523 = r99517 * r99522;
        double r99524 = r99516 - r99523;
        double r99525 = r99518 * r99508;
        double r99526 = r99500 * r99525;
        double r99527 = r99520 * r99504;
        double r99528 = -r99527;
        double r99529 = r99500 * r99528;
        double r99530 = r99526 + r99529;
        double r99531 = r99524 + r99530;
        double r99532 = 1.51655105499074e+61;
        bool r99533 = r99500 <= r99532;
        double r99534 = r99507 + r99512;
        double r99535 = r99534 - r99523;
        double r99536 = r99500 * r99518;
        double r99537 = r99536 * r99508;
        double r99538 = r99537 + r99529;
        double r99539 = r99535 + r99538;
        double r99540 = 2.856408514063506e+304;
        bool r99541 = r99500 <= r99540;
        double r99542 = r99503 * r99504;
        double r99543 = r99542 * r99505;
        double r99544 = r99543 + r99512;
        double r99545 = r99544 - r99523;
        double r99546 = r99545 + r99530;
        double r99547 = r99541 ? r99546 : r99539;
        double r99548 = r99533 ? r99539 : r99547;
        double r99549 = r99502 ? r99531 : r99548;
        return r99549;
}

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 j < -1.760233076037612e+58

    1. Initial program 7.8

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

    3. Applied sub-neg7.8

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

    4. Applied distribute-lft-in7.8

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

    6. Applied sub-neg7.8

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

    7. Applied distribute-lft-in7.8

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

    9. Applied add-cube-cbrt7.9

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

    if -1.760233076037612e+58 < j < 1.51655105499074e+61 or 2.856408514063506e+304 < j

    1. Initial program 14.2

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

    3. Applied sub-neg14.2

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

    4. Applied distribute-lft-in14.2

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

    6. Applied sub-neg14.2

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

    7. Applied distribute-lft-in14.2

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

    9. Applied associate-*r*12.1

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

    if 1.51655105499074e+61 < j < 2.856408514063506e+304

    1. Initial program 6.5

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

    3. Applied sub-neg6.5

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

    4. Applied distribute-lft-in6.5

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

    6. Applied sub-neg6.5

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

    7. Applied distribute-lft-in6.5

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

    9. Applied associate-*r*5.9

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -1.76023307603761202409938293253843061099 \cdot 10^{58}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(\sqrt[3]{x \cdot \left(-t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(-t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(-t \cdot a\right)}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{elif}\;j \le 1.516551054990740022970306969909426253394 \cdot 10^{61}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot c\right) \cdot t + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{elif}\;j \le 2.85640851406350578387766548712466692209 \cdot 10^{304}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot c\right) \cdot t + j \cdot \left(-i \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))))