Average Error: 11.9 → 10.8
Time: 25.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -8.906366522637092 \cdot 10^{-79}:\\ \;\;\;\;\sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)} \cdot \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - y \cdot i}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)}\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + \left(c \cdot z\right) \cdot b\right)\right)\\ \mathbf{elif}\;b \le -4.028168201093351 \cdot 10^{-290}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z\right) \cdot b + a \cdot \left(i \cdot \left(-b\right)\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;b \le 2.101267297331773 \cdot 10^{+110}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + z \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)} \cdot \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - y \cdot i}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)}\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + \left(c \cdot z\right) \cdot b\right)\right)\\ \end{array}\]
\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}\;b \le -8.906366522637092 \cdot 10^{-79}:\\
\;\;\;\;\sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)} \cdot \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - y \cdot i}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)}\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + \left(c \cdot z\right) \cdot b\right)\right)\\

\mathbf{elif}\;b \le -4.028168201093351 \cdot 10^{-290}:\\
\;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z\right) \cdot b + a \cdot \left(i \cdot \left(-b\right)\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\

\mathbf{elif}\;b \le 2.101267297331773 \cdot 10^{+110}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + z \cdot \left(c \cdot b\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)} \cdot \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - y \cdot i}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)}\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + \left(c \cdot z\right) \cdot b\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 r4317450 = x;
        double r4317451 = y;
        double r4317452 = z;
        double r4317453 = r4317451 * r4317452;
        double r4317454 = t;
        double r4317455 = a;
        double r4317456 = r4317454 * r4317455;
        double r4317457 = r4317453 - r4317456;
        double r4317458 = r4317450 * r4317457;
        double r4317459 = b;
        double r4317460 = c;
        double r4317461 = r4317460 * r4317452;
        double r4317462 = i;
        double r4317463 = r4317462 * r4317455;
        double r4317464 = r4317461 - r4317463;
        double r4317465 = r4317459 * r4317464;
        double r4317466 = r4317458 - r4317465;
        double r4317467 = j;
        double r4317468 = r4317460 * r4317454;
        double r4317469 = r4317462 * r4317451;
        double r4317470 = r4317468 - r4317469;
        double r4317471 = r4317467 * r4317470;
        double r4317472 = r4317466 + r4317471;
        return r4317472;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4317473 = b;
        double r4317474 = -8.906366522637092e-79;
        bool r4317475 = r4317473 <= r4317474;
        double r4317476 = j;
        double r4317477 = c;
        double r4317478 = t;
        double r4317479 = r4317477 * r4317478;
        double r4317480 = y;
        double r4317481 = i;
        double r4317482 = r4317480 * r4317481;
        double r4317483 = r4317479 - r4317482;
        double r4317484 = r4317476 * r4317483;
        double r4317485 = cbrt(r4317484);
        double r4317486 = cbrt(r4317476);
        double r4317487 = cbrt(r4317483);
        double r4317488 = r4317486 * r4317487;
        double r4317489 = r4317488 * r4317485;
        double r4317490 = r4317485 * r4317489;
        double r4317491 = z;
        double r4317492 = r4317480 * r4317491;
        double r4317493 = a;
        double r4317494 = r4317478 * r4317493;
        double r4317495 = r4317492 - r4317494;
        double r4317496 = x;
        double r4317497 = r4317495 * r4317496;
        double r4317498 = r4317481 * r4317493;
        double r4317499 = r4317473 * r4317498;
        double r4317500 = -r4317499;
        double r4317501 = r4317477 * r4317491;
        double r4317502 = r4317501 * r4317473;
        double r4317503 = r4317500 + r4317502;
        double r4317504 = r4317497 - r4317503;
        double r4317505 = r4317490 + r4317504;
        double r4317506 = -4.028168201093351e-290;
        bool r4317507 = r4317473 <= r4317506;
        double r4317508 = -r4317473;
        double r4317509 = r4317481 * r4317508;
        double r4317510 = r4317493 * r4317509;
        double r4317511 = r4317502 + r4317510;
        double r4317512 = r4317497 - r4317511;
        double r4317513 = r4317512 + r4317484;
        double r4317514 = 2.101267297331773e+110;
        bool r4317515 = r4317473 <= r4317514;
        double r4317516 = r4317477 * r4317473;
        double r4317517 = r4317491 * r4317516;
        double r4317518 = r4317500 + r4317517;
        double r4317519 = r4317497 - r4317518;
        double r4317520 = r4317484 + r4317519;
        double r4317521 = r4317515 ? r4317520 : r4317505;
        double r4317522 = r4317507 ? r4317513 : r4317521;
        double r4317523 = r4317475 ? r4317505 : r4317522;
        return r4317523;
}

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 b < -8.906366522637092e-79 or 2.101267297331773e+110 < b

    1. Initial program 7.7

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

    3. Applied sub-neg7.7

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

    4. Applied distribute-lft-in7.7

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

    6. Applied add-cube-cbrt8.0

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

    8. Applied cbrt-prod7.9

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

    if -8.906366522637092e-79 < b < -4.028168201093351e-290

    1. Initial program 15.6

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

    3. Applied sub-neg15.6

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

    4. Applied distribute-lft-in15.6

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

    5. Taylor expanded around inf 13.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    6. Simplified13.0

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

    if -4.028168201093351e-290 < b < 2.101267297331773e+110

    1. Initial program 13.8

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

    3. Applied sub-neg13.8

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

    4. Applied distribute-lft-in13.8

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

    5. Taylor expanded around inf 12.2

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

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.906366522637092 \cdot 10^{-79}:\\ \;\;\;\;\sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)} \cdot \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - y \cdot i}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)}\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + \left(c \cdot z\right) \cdot b\right)\right)\\ \mathbf{elif}\;b \le -4.028168201093351 \cdot 10^{-290}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z\right) \cdot b + a \cdot \left(i \cdot \left(-b\right)\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;b \le 2.101267297331773 \cdot 10^{+110}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + z \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)} \cdot \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - y \cdot i}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - y \cdot i\right)}\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(-b \cdot \left(i \cdot a\right)\right) + \left(c \cdot z\right) \cdot b\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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)))))