Average Error: 11.9 → 12.1
Time: 30.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -7.257505336466529 \cdot 10^{-204}:\\ \;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot c\right) \cdot j + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \mathbf{elif}\;b \le 4.532812091876448 \cdot 10^{-184}:\\ \;\;\;\;\left(t \cdot c - y \cdot i\right) \cdot j + \left(y \cdot z - t \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot c\right) \cdot j + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \end{array}\]
\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 -7.257505336466529 \cdot 10^{-204}:\\
\;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot c\right) \cdot j + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\

\mathbf{elif}\;b \le 4.532812091876448 \cdot 10^{-184}:\\
\;\;\;\;\left(t \cdot c - y \cdot i\right) \cdot j + \left(y \cdot z - t \cdot a\right) \cdot x\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot c\right) \cdot j + \left(-i \cdot \left(y \cdot j\right)\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 r3043321 = x;
        double r3043322 = y;
        double r3043323 = z;
        double r3043324 = r3043322 * r3043323;
        double r3043325 = t;
        double r3043326 = a;
        double r3043327 = r3043325 * r3043326;
        double r3043328 = r3043324 - r3043327;
        double r3043329 = r3043321 * r3043328;
        double r3043330 = b;
        double r3043331 = c;
        double r3043332 = r3043331 * r3043323;
        double r3043333 = i;
        double r3043334 = r3043333 * r3043326;
        double r3043335 = r3043332 - r3043334;
        double r3043336 = r3043330 * r3043335;
        double r3043337 = r3043329 - r3043336;
        double r3043338 = j;
        double r3043339 = r3043331 * r3043325;
        double r3043340 = r3043333 * r3043322;
        double r3043341 = r3043339 - r3043340;
        double r3043342 = r3043338 * r3043341;
        double r3043343 = r3043337 + r3043342;
        return r3043343;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3043344 = b;
        double r3043345 = -7.257505336466529e-204;
        bool r3043346 = r3043344 <= r3043345;
        double r3043347 = y;
        double r3043348 = z;
        double r3043349 = r3043347 * r3043348;
        double r3043350 = t;
        double r3043351 = a;
        double r3043352 = r3043350 * r3043351;
        double r3043353 = r3043349 - r3043352;
        double r3043354 = cbrt(r3043353);
        double r3043355 = cbrt(r3043354);
        double r3043356 = r3043355 * r3043355;
        double r3043357 = r3043356 * r3043355;
        double r3043358 = r3043357 * r3043354;
        double r3043359 = x;
        double r3043360 = r3043358 * r3043359;
        double r3043361 = r3043354 * r3043360;
        double r3043362 = c;
        double r3043363 = r3043348 * r3043362;
        double r3043364 = i;
        double r3043365 = r3043364 * r3043351;
        double r3043366 = r3043363 - r3043365;
        double r3043367 = r3043344 * r3043366;
        double r3043368 = r3043361 - r3043367;
        double r3043369 = r3043350 * r3043362;
        double r3043370 = j;
        double r3043371 = r3043369 * r3043370;
        double r3043372 = r3043347 * r3043370;
        double r3043373 = r3043364 * r3043372;
        double r3043374 = -r3043373;
        double r3043375 = r3043371 + r3043374;
        double r3043376 = r3043368 + r3043375;
        double r3043377 = 4.532812091876448e-184;
        bool r3043378 = r3043344 <= r3043377;
        double r3043379 = r3043347 * r3043364;
        double r3043380 = r3043369 - r3043379;
        double r3043381 = r3043380 * r3043370;
        double r3043382 = r3043353 * r3043359;
        double r3043383 = r3043381 + r3043382;
        double r3043384 = r3043378 ? r3043383 : r3043376;
        double r3043385 = r3043346 ? r3043376 : r3043384;
        return r3043385;
}

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 b < -7.257505336466529e-204 or 4.532812091876448e-184 < b

    1. Initial program 10.2

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

    3. Applied add-cube-cbrt10.5

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

    4. Applied associate-*r*10.5

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

    6. Applied sub-neg10.5

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

    7. Applied distribute-rgt-in10.5

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

    8. Taylor expanded around -inf 10.7

      \[\leadsto \left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)}\right)\]

    9. Simplified10.7

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

    11. Applied add-cube-cbrt10.8

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

    if -7.257505336466529e-204 < b < 4.532812091876448e-184

    1. Initial program 17.1

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

    2. Taylor expanded around 0 16.3

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{0}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.257505336466529 \cdot 10^{-204}:\\ \;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot c\right) \cdot j + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \mathbf{elif}\;b \le 4.532812091876448 \cdot 10^{-184}:\\ \;\;\;\;\left(t \cdot c - y \cdot i\right) \cdot j + \left(y \cdot z - t \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot z - t \cdot a}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot c\right) \cdot j + \left(-i \cdot \left(y \cdot j\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019132 
(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)))))