Average Error: 12.1 → 12.1
Time: 10.9s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.88745775492739174 \cdot 10^{-157}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{elif}\;x \le 1.4823283017637211 \cdot 10^{-217}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot 0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \end{array}\]
\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 -2.88745775492739174 \cdot 10^{-157}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \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}\\

\mathbf{elif}\;x \le 1.4823283017637211 \cdot 10^{-217}:\\
\;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot 0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - 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 r128993 = x;
        double r128994 = y;
        double r128995 = z;
        double r128996 = r128994 * r128995;
        double r128997 = t;
        double r128998 = a;
        double r128999 = r128997 * r128998;
        double r129000 = r128996 - r128999;
        double r129001 = r128993 * r129000;
        double r129002 = b;
        double r129003 = c;
        double r129004 = r129003 * r128995;
        double r129005 = i;
        double r129006 = r129005 * r128998;
        double r129007 = r129004 - r129006;
        double r129008 = r129002 * r129007;
        double r129009 = r129001 - r129008;
        double r129010 = j;
        double r129011 = r129003 * r128997;
        double r129012 = r129005 * r128994;
        double r129013 = r129011 - r129012;
        double r129014 = r129010 * r129013;
        double r129015 = r129009 + r129014;
        return r129015;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r129016 = x;
        double r129017 = -2.8874577549273917e-157;
        bool r129018 = r129016 <= r129017;
        double r129019 = y;
        double r129020 = z;
        double r129021 = r129019 * r129020;
        double r129022 = t;
        double r129023 = a;
        double r129024 = r129022 * r129023;
        double r129025 = r129021 - r129024;
        double r129026 = r129016 * r129025;
        double r129027 = b;
        double r129028 = c;
        double r129029 = r129028 * r129020;
        double r129030 = i;
        double r129031 = r129030 * r129023;
        double r129032 = r129029 - r129031;
        double r129033 = r129027 * r129032;
        double r129034 = r129026 - r129033;
        double r129035 = j;
        double r129036 = r129028 * r129022;
        double r129037 = r129030 * r129019;
        double r129038 = r129036 - r129037;
        double r129039 = cbrt(r129038);
        double r129040 = r129039 * r129039;
        double r129041 = r129035 * r129040;
        double r129042 = r129041 * r129039;
        double r129043 = r129034 + r129042;
        double r129044 = 1.482328301763721e-217;
        bool r129045 = r129016 <= r129044;
        double r129046 = cbrt(r129016);
        double r129047 = r129046 * r129046;
        double r129048 = 0.0;
        double r129049 = r129047 * r129048;
        double r129050 = r129049 - r129033;
        double r129051 = r129035 * r129038;
        double r129052 = r129050 + r129051;
        double r129053 = cbrt(r129051);
        double r129054 = r129053 * r129053;
        double r129055 = r129054 * r129053;
        double r129056 = r129034 + r129055;
        double r129057 = r129045 ? r129052 : r129056;
        double r129058 = r129018 ? r129043 : r129057;
        return r129058;
}

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 < -2.8874577549273917e-157

    1. Initial program 9.3

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

    3. Applied add-cube-cbrt9.6

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

    4. Applied associate-*r*9.6

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

    if -2.8874577549273917e-157 < x < 1.482328301763721e-217

    1. Initial program 17.9

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

    3. Applied add-cube-cbrt17.9

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

    4. Applied associate-*l*17.9

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

    5. Taylor expanded around 0 17.3

      \[\leadsto \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if 1.482328301763721e-217 < x

    1. Initial program 10.8

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

    3. Applied add-cube-cbrt11.0

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

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.88745775492739174 \cdot 10^{-157}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{elif}\;x \le 1.4823283017637211 \cdot 10^{-217}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot 0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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)))))