Average Error: 12.4 → 11.1
Time: 26.7s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.672795493860766634501209364427778643557 \cdot 10^{-35}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j} \cdot \left(\sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j} \cdot \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j}\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;a \le 1.363075426981875327339653073768105985957 \cdot 10^{-173}:\\ \;\;\;\;\left(i \cdot a - c \cdot z\right) \cdot b + \left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(i \cdot j\right) \cdot \left(-y\right) + t \cdot \left(j \cdot c\right)\right)\right)\\ \mathbf{elif}\;a \le 2.77838378540003226799654426646560472166 \cdot 10^{-74}:\\ \;\;\;\;\left(\left(t \cdot c - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;a \le 30772525990492999025426432:\\ \;\;\;\;\left(i \cdot a - c \cdot z\right) \cdot b + \left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(i \cdot j\right) \cdot \left(-y\right) + t \cdot \left(j \cdot c\right)\right)\right)\\ \mathbf{elif}\;a \le 1.992368486632287830436354769032418169245 \cdot 10^{58}:\\ \;\;\;\;\left(\left(\left(y \cdot z - a \cdot t\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} + \left(t \cdot c - y \cdot i\right) \cdot j\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot c - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(c \cdot b\right) \cdot z\right)\\ \end{array}\]
\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 -1.672795493860766634501209364427778643557 \cdot 10^{-35}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j} \cdot \left(\sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j} \cdot \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j}\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\

\mathbf{elif}\;a \le 1.363075426981875327339653073768105985957 \cdot 10^{-173}:\\
\;\;\;\;\left(i \cdot a - c \cdot z\right) \cdot b + \left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(i \cdot j\right) \cdot \left(-y\right) + t \cdot \left(j \cdot c\right)\right)\right)\\

\mathbf{elif}\;a \le 2.77838378540003226799654426646560472166 \cdot 10^{-74}:\\
\;\;\;\;\left(\left(t \cdot c - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(c \cdot b\right) \cdot z\right)\\

\mathbf{elif}\;a \le 30772525990492999025426432:\\
\;\;\;\;\left(i \cdot a - c \cdot z\right) \cdot b + \left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(i \cdot j\right) \cdot \left(-y\right) + t \cdot \left(j \cdot c\right)\right)\right)\\

\mathbf{elif}\;a \le 1.992368486632287830436354769032418169245 \cdot 10^{58}:\\
\;\;\;\;\left(\left(\left(y \cdot z - a \cdot t\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} + \left(t \cdot c - y \cdot i\right) \cdot j\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r99268 = x;
        double r99269 = y;
        double r99270 = z;
        double r99271 = r99269 * r99270;
        double r99272 = t;
        double r99273 = a;
        double r99274 = r99272 * r99273;
        double r99275 = r99271 - r99274;
        double r99276 = r99268 * r99275;
        double r99277 = b;
        double r99278 = c;
        double r99279 = r99278 * r99270;
        double r99280 = i;
        double r99281 = r99280 * r99273;
        double r99282 = r99279 - r99281;
        double r99283 = r99277 * r99282;
        double r99284 = r99276 - r99283;
        double r99285 = j;
        double r99286 = r99278 * r99272;
        double r99287 = r99280 * r99269;
        double r99288 = r99286 - r99287;
        double r99289 = r99285 * r99288;
        double r99290 = r99284 + r99289;
        return r99290;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r99291 = a;
        double r99292 = -1.6727954938607666e-35;
        bool r99293 = r99291 <= r99292;
        double r99294 = x;
        double r99295 = y;
        double r99296 = z;
        double r99297 = r99295 * r99296;
        double r99298 = t;
        double r99299 = r99291 * r99298;
        double r99300 = r99297 - r99299;
        double r99301 = r99294 * r99300;
        double r99302 = c;
        double r99303 = r99298 * r99302;
        double r99304 = i;
        double r99305 = r99295 * r99304;
        double r99306 = r99303 - r99305;
        double r99307 = j;
        double r99308 = r99306 * r99307;
        double r99309 = cbrt(r99308);
        double r99310 = r99309 * r99309;
        double r99311 = r99309 * r99310;
        double r99312 = r99301 + r99311;
        double r99313 = b;
        double r99314 = r99304 * r99313;
        double r99315 = r99314 * r99291;
        double r99316 = r99313 * r99296;
        double r99317 = r99316 * r99302;
        double r99318 = r99315 - r99317;
        double r99319 = r99312 + r99318;
        double r99320 = 1.3630754269818753e-173;
        bool r99321 = r99291 <= r99320;
        double r99322 = r99304 * r99291;
        double r99323 = r99302 * r99296;
        double r99324 = r99322 - r99323;
        double r99325 = r99324 * r99313;
        double r99326 = r99304 * r99307;
        double r99327 = -r99295;
        double r99328 = r99326 * r99327;
        double r99329 = r99307 * r99302;
        double r99330 = r99298 * r99329;
        double r99331 = r99328 + r99330;
        double r99332 = r99301 + r99331;
        double r99333 = r99325 + r99332;
        double r99334 = 2.7783837854000323e-74;
        bool r99335 = r99291 <= r99334;
        double r99336 = r99308 + r99301;
        double r99337 = r99302 * r99313;
        double r99338 = r99337 * r99296;
        double r99339 = r99315 - r99338;
        double r99340 = r99336 + r99339;
        double r99341 = 3.0772525990493e+25;
        bool r99342 = r99291 <= r99341;
        double r99343 = 1.9923684866322878e+58;
        bool r99344 = r99291 <= r99343;
        double r99345 = cbrt(r99294);
        double r99346 = r99345 * r99345;
        double r99347 = r99300 * r99346;
        double r99348 = r99347 * r99345;
        double r99349 = r99348 + r99308;
        double r99350 = r99349 + r99318;
        double r99351 = r99344 ? r99350 : r99340;
        double r99352 = r99342 ? r99333 : r99351;
        double r99353 = r99335 ? r99340 : r99352;
        double r99354 = r99321 ? r99333 : r99353;
        double r99355 = r99293 ? r99319 : r99354;
        return r99355;
}

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 4 regimes

  2. if a < -1.6727954938607666e-35

    1. Initial program 16.1

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

    2. Simplified16.1

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

    3. Taylor expanded around inf 12.9

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

    4. Simplified11.9

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

    6. Applied add-cube-cbrt12.1

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

    7. Simplified12.1

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

    8. Simplified12.1

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

    if -1.6727954938607666e-35 < a < 1.3630754269818753e-173 or 2.7783837854000323e-74 < a < 3.0772525990493e+25

    1. Initial program 9.2

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

    2. Simplified9.2

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

    4. Applied sub-neg9.2

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

    5. Applied distribute-lft-in9.2

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

    6. Simplified8.9

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

    7. Simplified9.4

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

    if 1.3630754269818753e-173 < a < 2.7783837854000323e-74 or 1.9923684866322878e+58 < a

    1. Initial program 15.8

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

    2. Simplified15.8

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

    3. Taylor expanded around inf 14.2

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

    4. Simplified13.8

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

    5. Taylor expanded around inf 14.2

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

    6. Simplified14.2

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

    if 3.0772525990493e+25 < a < 1.9923684866322878e+58

    1. Initial program 11.6

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

    2. Simplified11.6

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

    3. Taylor expanded around inf 10.7

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

    4. Simplified9.1

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

    6. Applied add-cube-cbrt9.4

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

    7. Applied associate-*r*9.4

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

    8. Simplified9.4

      \[\leadsto \left(a \cdot \left(i \cdot b\right) - c \cdot \left(z \cdot b\right)\right) + \left(\color{blue}{\left(\left(y \cdot z - t \cdot a\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)} \cdot \sqrt[3]{x} + j \cdot \left(t \cdot c - i \cdot y\right)\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.672795493860766634501209364427778643557 \cdot 10^{-35}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j} \cdot \left(\sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j} \cdot \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot j}\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{elif}\;a \le 1.363075426981875327339653073768105985957 \cdot 10^{-173}:\\ \;\;\;\;\left(i \cdot a - c \cdot z\right) \cdot b + \left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(i \cdot j\right) \cdot \left(-y\right) + t \cdot \left(j \cdot c\right)\right)\right)\\ \mathbf{elif}\;a \le 2.77838378540003226799654426646560472166 \cdot 10^{-74}:\\ \;\;\;\;\left(\left(t \cdot c - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;a \le 30772525990492999025426432:\\ \;\;\;\;\left(i \cdot a - c \cdot z\right) \cdot b + \left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(i \cdot j\right) \cdot \left(-y\right) + t \cdot \left(j \cdot c\right)\right)\right)\\ \mathbf{elif}\;a \le 1.992368486632287830436354769032418169245 \cdot 10^{58}:\\ \;\;\;\;\left(\left(\left(y \cdot z - a \cdot t\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} + \left(t \cdot c - y \cdot i\right) \cdot j\right) + \left(\left(i \cdot b\right) \cdot a - \left(b \cdot z\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot c - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\left(i \cdot b\right) \cdot a - \left(c \cdot b\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(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)))))