Average Error: 11.8 → 10.6
Time: 36.9s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.048171832402189 \cdot 10^{+43}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{elif}\;x \le 1.4835629551870247 \cdot 10^{+117}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \end{array}\]
\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}\;x \le -3.048171832402189 \cdot 10^{+43}:\\
\;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - 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}\;x \le 1.4835629551870247 \cdot 10^{+117}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3494310 = x;
        double r3494311 = y;
        double r3494312 = z;
        double r3494313 = r3494311 * r3494312;
        double r3494314 = t;
        double r3494315 = a;
        double r3494316 = r3494314 * r3494315;
        double r3494317 = r3494313 - r3494316;
        double r3494318 = r3494310 * r3494317;
        double r3494319 = b;
        double r3494320 = c;
        double r3494321 = r3494320 * r3494312;
        double r3494322 = i;
        double r3494323 = r3494322 * r3494315;
        double r3494324 = r3494321 - r3494323;
        double r3494325 = r3494319 * r3494324;
        double r3494326 = r3494318 - r3494325;
        double r3494327 = j;
        double r3494328 = r3494320 * r3494314;
        double r3494329 = r3494322 * r3494311;
        double r3494330 = r3494328 - r3494329;
        double r3494331 = r3494327 * r3494330;
        double r3494332 = r3494326 + r3494331;
        return r3494332;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3494333 = x;
        double r3494334 = -3.048171832402189e+43;
        bool r3494335 = r3494333 <= r3494334;
        double r3494336 = y;
        double r3494337 = z;
        double r3494338 = r3494336 * r3494337;
        double r3494339 = a;
        double r3494340 = t;
        double r3494341 = r3494339 * r3494340;
        double r3494342 = r3494338 - r3494341;
        double r3494343 = r3494342 * r3494333;
        double r3494344 = b;
        double r3494345 = c;
        double r3494346 = r3494337 * r3494345;
        double r3494347 = i;
        double r3494348 = r3494347 * r3494339;
        double r3494349 = r3494346 - r3494348;
        double r3494350 = r3494344 * r3494349;
        double r3494351 = r3494343 - r3494350;
        double r3494352 = r3494345 * r3494340;
        double r3494353 = r3494347 * r3494336;
        double r3494354 = r3494352 - r3494353;
        double r3494355 = cbrt(r3494354);
        double r3494356 = r3494355 * r3494355;
        double r3494357 = j;
        double r3494358 = r3494356 * r3494357;
        double r3494359 = r3494358 * r3494355;
        double r3494360 = r3494351 + r3494359;
        double r3494361 = 1.4835629551870247e+117;
        bool r3494362 = r3494333 <= r3494361;
        double r3494363 = r3494333 * r3494338;
        double r3494364 = r3494333 * r3494340;
        double r3494365 = r3494364 * r3494339;
        double r3494366 = r3494363 - r3494365;
        double r3494367 = r3494366 - r3494350;
        double r3494368 = r3494357 * r3494354;
        double r3494369 = r3494367 + r3494368;
        double r3494370 = cbrt(r3494368);
        double r3494371 = r3494370 * r3494370;
        double r3494372 = r3494371 * r3494370;
        double r3494373 = r3494351 + r3494372;
        double r3494374 = r3494362 ? r3494369 : r3494373;
        double r3494375 = r3494335 ? r3494360 : r3494374;
        return r3494375;
}

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 x < -3.048171832402189e+43

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt7.0

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

    4. Applied associate-*r*7.0

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

    if -3.048171832402189e+43 < x < 1.4835629551870247e+117

    1. Initial program 13.6

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

    3. Applied add-cube-cbrt13.8

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

    4. Applied associate-*l*13.8

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

    5. Taylor expanded around -inf 11.9

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

    if 1.4835629551870247e+117 < x

    1. Initial program 6.9

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

    3. Applied add-cube-cbrt7.1

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

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.048171832402189 \cdot 10^{+43}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{elif}\;x \le 1.4835629551870247 \cdot 10^{+117}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019134 
(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)))))