Average Error: 11.3 → 11.3
Time: 39.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.645805544531443 \cdot 10^{-232}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b}\right)\right)\\ \mathbf{elif}\;x \le 2.3221986550473696 \cdot 10^{-227}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - a \cdot t\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]
\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 -3.645805544531443 \cdot 10^{-232}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b}\right)\right)\\

\mathbf{elif}\;x \le 2.3221986550473696 \cdot 10^{-227}:\\
\;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - a \cdot t\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r9050151 = x;
        double r9050152 = y;
        double r9050153 = z;
        double r9050154 = r9050152 * r9050153;
        double r9050155 = t;
        double r9050156 = a;
        double r9050157 = r9050155 * r9050156;
        double r9050158 = r9050154 - r9050157;
        double r9050159 = r9050151 * r9050158;
        double r9050160 = b;
        double r9050161 = c;
        double r9050162 = r9050161 * r9050153;
        double r9050163 = i;
        double r9050164 = r9050163 * r9050156;
        double r9050165 = r9050162 - r9050164;
        double r9050166 = r9050160 * r9050165;
        double r9050167 = r9050159 - r9050166;
        double r9050168 = j;
        double r9050169 = r9050161 * r9050155;
        double r9050170 = r9050163 * r9050152;
        double r9050171 = r9050169 - r9050170;
        double r9050172 = r9050168 * r9050171;
        double r9050173 = r9050167 + r9050172;
        return r9050173;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r9050174 = x;
        double r9050175 = -3.645805544531443e-232;
        bool r9050176 = r9050174 <= r9050175;
        double r9050177 = c;
        double r9050178 = t;
        double r9050179 = r9050177 * r9050178;
        double r9050180 = i;
        double r9050181 = y;
        double r9050182 = r9050180 * r9050181;
        double r9050183 = r9050179 - r9050182;
        double r9050184 = j;
        double r9050185 = r9050183 * r9050184;
        double r9050186 = z;
        double r9050187 = r9050181 * r9050186;
        double r9050188 = a;
        double r9050189 = r9050188 * r9050178;
        double r9050190 = r9050187 - r9050189;
        double r9050191 = r9050190 * r9050174;
        double r9050192 = b;
        double r9050193 = r9050186 * r9050177;
        double r9050194 = r9050180 * r9050188;
        double r9050195 = r9050193 - r9050194;
        double r9050196 = r9050192 * r9050195;
        double r9050197 = cbrt(r9050196);
        double r9050198 = r9050197 * r9050197;
        double r9050199 = cbrt(r9050195);
        double r9050200 = cbrt(r9050199);
        double r9050201 = r9050199 * r9050199;
        double r9050202 = r9050201 * r9050192;
        double r9050203 = cbrt(r9050202);
        double r9050204 = r9050200 * r9050203;
        double r9050205 = r9050198 * r9050204;
        double r9050206 = r9050191 - r9050205;
        double r9050207 = r9050185 + r9050206;
        double r9050208 = 2.3221986550473696e-227;
        bool r9050209 = r9050174 <= r9050208;
        double r9050210 = -r9050192;
        double r9050211 = r9050210 * r9050195;
        double r9050212 = r9050211 + r9050185;
        double r9050213 = cbrt(r9050174);
        double r9050214 = r9050213 * r9050213;
        double r9050215 = r9050190 * r9050213;
        double r9050216 = r9050214 * r9050215;
        double r9050217 = r9050216 - r9050196;
        double r9050218 = r9050217 + r9050185;
        double r9050219 = r9050209 ? r9050212 : r9050218;
        double r9050220 = r9050176 ? r9050207 : r9050219;
        return r9050220;
}

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 < -3.645805544531443e-232

    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

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

    5. Applied add-cube-cbrt10.5

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

    6. Applied associate-*r*10.5

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

    7. Applied cbrt-prod10.5

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

    if -3.645805544531443e-232 < x < 2.3221986550473696e-227

    1. Initial program 16.7

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

    2. Taylor expanded around 0 15.3

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

    if 2.3221986550473696e-227 < x

    1. Initial program 10.1

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

    3. Applied add-cube-cbrt10.4

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

    4. Applied associate-*l*10.4

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

  4. Final simplification11.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.645805544531443 \cdot 10^{-232}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b}\right)\right)\\ \mathbf{elif}\;x \le 2.3221986550473696 \cdot 10^{-227}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - a \cdot t\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))))