Average Error: 12.5 → 9.0
Time: 24.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -3.558679195290626040559800458140671253204 \lor \neg \left(j \le 4.784801129022457779255706995671921542182 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \end{array}\]
\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 -3.558679195290626040559800458140671253204 \lor \neg \left(j \le 4.784801129022457779255706995671921542182 \cdot 10^{-23}\right):\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\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 r81378 = x;
        double r81379 = y;
        double r81380 = z;
        double r81381 = r81379 * r81380;
        double r81382 = t;
        double r81383 = a;
        double r81384 = r81382 * r81383;
        double r81385 = r81381 - r81384;
        double r81386 = r81378 * r81385;
        double r81387 = b;
        double r81388 = c;
        double r81389 = r81388 * r81380;
        double r81390 = i;
        double r81391 = r81390 * r81383;
        double r81392 = r81389 - r81391;
        double r81393 = r81387 * r81392;
        double r81394 = r81386 - r81393;
        double r81395 = j;
        double r81396 = r81388 * r81382;
        double r81397 = r81390 * r81379;
        double r81398 = r81396 - r81397;
        double r81399 = r81395 * r81398;
        double r81400 = r81394 + r81399;
        return r81400;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r81401 = j;
        double r81402 = -3.558679195290626;
        bool r81403 = r81401 <= r81402;
        double r81404 = 4.784801129022458e-23;
        bool r81405 = r81401 <= r81404;
        double r81406 = !r81405;
        bool r81407 = r81403 || r81406;
        double r81408 = x;
        double r81409 = y;
        double r81410 = z;
        double r81411 = r81409 * r81410;
        double r81412 = t;
        double r81413 = a;
        double r81414 = r81412 * r81413;
        double r81415 = r81411 - r81414;
        double r81416 = r81408 * r81415;
        double r81417 = b;
        double r81418 = c;
        double r81419 = r81417 * r81418;
        double r81420 = r81410 * r81419;
        double r81421 = i;
        double r81422 = r81421 * r81413;
        double r81423 = -r81422;
        double r81424 = r81417 * r81423;
        double r81425 = r81420 + r81424;
        double r81426 = r81416 - r81425;
        double r81427 = r81418 * r81412;
        double r81428 = r81421 * r81409;
        double r81429 = r81427 - r81428;
        double r81430 = r81401 * r81429;
        double r81431 = r81426 + r81430;
        double r81432 = r81408 * r81410;
        double r81433 = cbrt(r81409);
        double r81434 = r81433 * r81433;
        double r81435 = r81432 * r81434;
        double r81436 = r81435 * r81433;
        double r81437 = r81408 * r81412;
        double r81438 = r81413 * r81437;
        double r81439 = -r81438;
        double r81440 = r81436 + r81439;
        double r81441 = r81418 * r81410;
        double r81442 = r81441 - r81422;
        double r81443 = r81417 * r81442;
        double r81444 = r81440 - r81443;
        double r81445 = r81401 * r81418;
        double r81446 = r81412 * r81445;
        double r81447 = r81401 * r81409;
        double r81448 = r81421 * r81447;
        double r81449 = -r81448;
        double r81450 = r81446 + r81449;
        double r81451 = r81444 + r81450;
        double r81452 = r81407 ? r81431 : r81451;
        return r81452;
}

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 j < -3.558679195290626 or 4.784801129022458e-23 < j

    1. Initial program 7.6

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

    3. Applied sub-neg7.6

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

    4. Applied distribute-lft-in7.6

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

    5. Simplified7.8

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

    if -3.558679195290626 < j < 4.784801129022458e-23

    1. Initial program 15.9

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

    3. Applied sub-neg15.9

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

    4. Applied distribute-lft-in15.9

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

    5. Simplified15.9

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

    6. Simplified15.8

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

    8. Applied associate-*r*15.3

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

    10. Applied add-cube-cbrt15.5

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

    11. Applied associate-*r*15.5

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

    13. Applied sub-neg15.5

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

    14. Applied distribute-lft-in15.5

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

    15. Simplified13.0

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

    16. Simplified9.8

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

  4. Final simplification9.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -3.558679195290626040559800458140671253204 \lor \neg \left(j \le 4.784801129022457779255706995671921542182 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)))))