Average Error: 12.0 → 12.3
Time: 31.7s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.462244819935999 \cdot 10^{-119}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{elif}\;b \le 6.409394434904169 \cdot 10^{-230}:\\ \;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(\left(j \cdot t\right) \cdot c - \left(y \cdot j\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot j\right) \cdot t - \left(y \cdot j\right) \cdot i\right) + \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - t \cdot a\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \end{array}\]
\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 -1.462244819935999 \cdot 10^{-119}:\\
\;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\

\mathbf{elif}\;b \le 6.409394434904169 \cdot 10^{-230}:\\
\;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(\left(j \cdot t\right) \cdot c - \left(y \cdot j\right) \cdot i\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(c \cdot j\right) \cdot t - \left(y \cdot j\right) \cdot i\right) + \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - t \cdot a\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(c \cdot z - i \cdot a\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 r3303425 = x;
        double r3303426 = y;
        double r3303427 = z;
        double r3303428 = r3303426 * r3303427;
        double r3303429 = t;
        double r3303430 = a;
        double r3303431 = r3303429 * r3303430;
        double r3303432 = r3303428 - r3303431;
        double r3303433 = r3303425 * r3303432;
        double r3303434 = b;
        double r3303435 = c;
        double r3303436 = r3303435 * r3303427;
        double r3303437 = i;
        double r3303438 = r3303437 * r3303430;
        double r3303439 = r3303436 - r3303438;
        double r3303440 = r3303434 * r3303439;
        double r3303441 = r3303433 - r3303440;
        double r3303442 = j;
        double r3303443 = r3303435 * r3303429;
        double r3303444 = r3303437 * r3303426;
        double r3303445 = r3303443 - r3303444;
        double r3303446 = r3303442 * r3303445;
        double r3303447 = r3303441 + r3303446;
        return r3303447;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3303448 = b;
        double r3303449 = -1.462244819935999e-119;
        bool r3303450 = r3303448 <= r3303449;
        double r3303451 = y;
        double r3303452 = z;
        double r3303453 = r3303451 * r3303452;
        double r3303454 = t;
        double r3303455 = a;
        double r3303456 = r3303454 * r3303455;
        double r3303457 = r3303453 - r3303456;
        double r3303458 = x;
        double r3303459 = r3303457 * r3303458;
        double r3303460 = c;
        double r3303461 = r3303460 * r3303452;
        double r3303462 = i;
        double r3303463 = r3303462 * r3303455;
        double r3303464 = r3303461 - r3303463;
        double r3303465 = r3303448 * r3303464;
        double r3303466 = r3303459 - r3303465;
        double r3303467 = r3303460 * r3303454;
        double r3303468 = r3303462 * r3303451;
        double r3303469 = r3303467 - r3303468;
        double r3303470 = cbrt(r3303469);
        double r3303471 = r3303470 * r3303470;
        double r3303472 = j;
        double r3303473 = r3303471 * r3303472;
        double r3303474 = r3303473 * r3303470;
        double r3303475 = r3303466 + r3303474;
        double r3303476 = 6.409394434904169e-230;
        bool r3303477 = r3303448 <= r3303476;
        double r3303478 = r3303472 * r3303454;
        double r3303479 = r3303478 * r3303460;
        double r3303480 = r3303451 * r3303472;
        double r3303481 = r3303480 * r3303462;
        double r3303482 = r3303479 - r3303481;
        double r3303483 = r3303459 + r3303482;
        double r3303484 = r3303460 * r3303472;
        double r3303485 = r3303484 * r3303454;
        double r3303486 = r3303485 - r3303481;
        double r3303487 = cbrt(r3303458);
        double r3303488 = r3303487 * r3303487;
        double r3303489 = r3303457 * r3303487;
        double r3303490 = r3303488 * r3303489;
        double r3303491 = r3303490 - r3303465;
        double r3303492 = r3303486 + r3303491;
        double r3303493 = r3303477 ? r3303483 : r3303492;
        double r3303494 = r3303450 ? r3303475 : r3303493;
        return r3303494;
}

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 < -1.462244819935999e-119

    1. Initial program 8.4

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

    3. Applied add-cube-cbrt8.6

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

    4. Applied associate-*r*8.6

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

    if -1.462244819935999e-119 < b < 6.409394434904169e-230

    1. Initial program 17.0

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

    3. Applied add-cube-cbrt17.3

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

    4. Applied associate-*l*17.3

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

    5. Taylor expanded around inf 16.6

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

    7. Applied associate-*r*16.5

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

    8. Taylor expanded around 0 17.8

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

    if 6.409394434904169e-230 < b

    1. Initial program 11.2

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

    3. Applied add-cube-cbrt11.4

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

    4. Applied associate-*l*11.4

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

    5. Taylor expanded around inf 11.0

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

    7. Applied add-cube-cbrt11.2

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

    8. Applied associate-*l*11.2

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

  4. Final simplification12.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.462244819935999 \cdot 10^{-119}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{elif}\;b \le 6.409394434904169 \cdot 10^{-230}:\\ \;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(\left(j \cdot t\right) \cdot c - \left(y \cdot j\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot j\right) \cdot t - \left(y \cdot j\right) \cdot i\right) + \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - t \cdot a\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 
(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)))))