Average Error: 12.4 → 13.0
Time: 27.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.7229977138183682 \cdot 10^{-105} \lor \neg \left(x \le 9.4020594270263231 \cdot 10^{-157}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;x \le -1.7229977138183682 \cdot 10^{-105} \lor \neg \left(x \le 9.4020594270263231 \cdot 10^{-157}\right):\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{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)}\\

\mathbf{else}:\\
\;\;\;\;\left(0 - b \cdot \left(c \cdot z - i \cdot a\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 r363 = x;
        double r364 = y;
        double r365 = z;
        double r366 = r364 * r365;
        double r367 = t;
        double r368 = a;
        double r369 = r367 * r368;
        double r370 = r366 - r369;
        double r371 = r363 * r370;
        double r372 = b;
        double r373 = c;
        double r374 = r373 * r365;
        double r375 = i;
        double r376 = r375 * r368;
        double r377 = r374 - r376;
        double r378 = r372 * r377;
        double r379 = r371 - r378;
        double r380 = j;
        double r381 = r373 * r367;
        double r382 = r375 * r364;
        double r383 = r381 - r382;
        double r384 = r380 * r383;
        double r385 = r379 + r384;
        return r385;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r386 = x;
        double r387 = -1.7229977138183682e-105;
        bool r388 = r386 <= r387;
        double r389 = 9.402059427026323e-157;
        bool r390 = r386 <= r389;
        double r391 = !r390;
        bool r392 = r388 || r391;
        double r393 = y;
        double r394 = z;
        double r395 = r393 * r394;
        double r396 = t;
        double r397 = a;
        double r398 = r396 * r397;
        double r399 = r395 - r398;
        double r400 = r386 * r399;
        double r401 = b;
        double r402 = c;
        double r403 = r402 * r394;
        double r404 = i;
        double r405 = r404 * r397;
        double r406 = r403 - r405;
        double r407 = r401 * r406;
        double r408 = r400 - r407;
        double r409 = j;
        double r410 = cbrt(r409);
        double r411 = r402 * r396;
        double r412 = r404 * r393;
        double r413 = r411 - r412;
        double r414 = cbrt(r413);
        double r415 = r410 * r414;
        double r416 = r409 * r413;
        double r417 = cbrt(r416);
        double r418 = r415 * r417;
        double r419 = r418 * r417;
        double r420 = r408 + r419;
        double r421 = 0.0;
        double r422 = r421 - r407;
        double r423 = r422 + r416;
        double r424 = r392 ? r420 : r423;
        return r424;
}

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 x < -1.7229977138183682e-105 or 9.402059427026323e-157 < x

    1. Initial program 9.5

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

    3. Applied add-cube-cbrt9.7

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

    5. Applied cbrt-prod9.7

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

    if -1.7229977138183682e-105 < x < 9.402059427026323e-157

    1. Initial program 17.6

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

    3. Applied add-cube-cbrt17.6

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

    4. Applied associate-*l*17.6

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

    5. Taylor expanded around 0 18.8

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

  4. Final simplification13.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.7229977138183682 \cdot 10^{-105} \lor \neg \left(x \le 9.4020594270263231 \cdot 10^{-157}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))))