Average Error: 11.8 → 10.2
Time: 15.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4544251161.4776515960693359375 \lor \neg \left(a \le 1.713158425446813035880347350755354318048 \cdot 10^{57}\right):\\ \;\;\;\;\left(a \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} - \left(z \cdot \left(b \cdot c\right) + \left(-b\right) \cdot \left(i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -4544251161.4776515960693359375 \lor \neg \left(a \le 1.713158425446813035880347350755354318048 \cdot 10^{57}\right):\\
\;\;\;\;\left(a \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r81281 = x;
        double r81282 = y;
        double r81283 = z;
        double r81284 = r81282 * r81283;
        double r81285 = t;
        double r81286 = a;
        double r81287 = r81285 * r81286;
        double r81288 = r81284 - r81287;
        double r81289 = r81281 * r81288;
        double r81290 = b;
        double r81291 = c;
        double r81292 = r81291 * r81283;
        double r81293 = i;
        double r81294 = r81293 * r81286;
        double r81295 = r81292 - r81294;
        double r81296 = r81290 * r81295;
        double r81297 = r81289 - r81296;
        double r81298 = j;
        double r81299 = r81291 * r81285;
        double r81300 = r81293 * r81282;
        double r81301 = r81299 - r81300;
        double r81302 = r81298 * r81301;
        double r81303 = r81297 + r81302;
        return r81303;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r81304 = a;
        double r81305 = -4544251161.477652;
        bool r81306 = r81304 <= r81305;
        double r81307 = 1.713158425446813e+57;
        bool r81308 = r81304 <= r81307;
        double r81309 = !r81308;
        bool r81310 = r81306 || r81309;
        double r81311 = i;
        double r81312 = b;
        double r81313 = r81311 * r81312;
        double r81314 = r81304 * r81313;
        double r81315 = z;
        double r81316 = c;
        double r81317 = r81312 * r81316;
        double r81318 = r81315 * r81317;
        double r81319 = x;
        double r81320 = t;
        double r81321 = r81319 * r81320;
        double r81322 = r81304 * r81321;
        double r81323 = r81318 + r81322;
        double r81324 = r81314 - r81323;
        double r81325 = j;
        double r81326 = r81316 * r81320;
        double r81327 = y;
        double r81328 = r81311 * r81327;
        double r81329 = r81326 - r81328;
        double r81330 = r81325 * r81329;
        double r81331 = r81324 + r81330;
        double r81332 = r81327 * r81315;
        double r81333 = r81320 * r81304;
        double r81334 = r81332 - r81333;
        double r81335 = r81319 * r81334;
        double r81336 = cbrt(r81335);
        double r81337 = r81336 * r81336;
        double r81338 = r81337 * r81336;
        double r81339 = -r81312;
        double r81340 = r81311 * r81304;
        double r81341 = r81339 * r81340;
        double r81342 = r81318 + r81341;
        double r81343 = r81338 - r81342;
        double r81344 = r81343 + r81330;
        double r81345 = r81310 ? r81331 : r81344;
        return r81345;
}

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 < -4544251161.477652 or 1.713158425446813e+57 < a

    1. Initial program 18.2

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Taylor expanded around inf 11.8

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

    if -4544251161.477652 < a < 1.713158425446813e+57

    1. Initial program 8.7

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

    3. Applied add-cube-cbrt9.0

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

    4. Applied associate-*l*9.0

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

    6. Applied sub-neg9.0

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

    7. Applied distribute-lft-in9.0

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

    8. Applied distribute-lft-in9.0

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

    9. Simplified9.3

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

    10. Simplified9.2

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

    12. Applied add-cube-cbrt9.5

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

  4. Final simplification10.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4544251161.4776515960693359375 \lor \neg \left(a \le 1.713158425446813035880347350755354318048 \cdot 10^{57}\right):\\ \;\;\;\;\left(a \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} - \left(z \cdot \left(b \cdot c\right) + \left(-b\right) \cdot \left(i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019308 
(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)))))