Average Error: 12.3 → 9.7
Time: 36.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -0.01018236418344508308064799706471603712998:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;j \le 6.630197526137251571160185503510114222161 \cdot 10^{136}:\\ \;\;\;\;\left(t \cdot \left(j \cdot c\right) - i \cdot \left(y \cdot j\right)\right) + \left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b} \cdot \left(\sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b} \cdot \sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]
\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}\;j \le -0.01018236418344508308064799706471603712998:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\

\mathbf{elif}\;j \le 6.630197526137251571160185503510114222161 \cdot 10^{136}:\\
\;\;\;\;\left(t \cdot \left(j \cdot c\right) - i \cdot \left(y \cdot j\right)\right) + \left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b} \cdot \left(\sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b} \cdot \sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b}\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 r4979197 = x;
        double r4979198 = y;
        double r4979199 = z;
        double r4979200 = r4979198 * r4979199;
        double r4979201 = t;
        double r4979202 = a;
        double r4979203 = r4979201 * r4979202;
        double r4979204 = r4979200 - r4979203;
        double r4979205 = r4979197 * r4979204;
        double r4979206 = b;
        double r4979207 = c;
        double r4979208 = r4979207 * r4979199;
        double r4979209 = i;
        double r4979210 = r4979209 * r4979202;
        double r4979211 = r4979208 - r4979210;
        double r4979212 = r4979206 * r4979211;
        double r4979213 = r4979205 - r4979212;
        double r4979214 = j;
        double r4979215 = r4979207 * r4979201;
        double r4979216 = r4979209 * r4979198;
        double r4979217 = r4979215 - r4979216;
        double r4979218 = r4979214 * r4979217;
        double r4979219 = r4979213 + r4979218;
        return r4979219;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4979220 = j;
        double r4979221 = -0.010182364183445083;
        bool r4979222 = r4979220 <= r4979221;
        double r4979223 = c;
        double r4979224 = t;
        double r4979225 = r4979223 * r4979224;
        double r4979226 = i;
        double r4979227 = y;
        double r4979228 = r4979226 * r4979227;
        double r4979229 = r4979225 - r4979228;
        double r4979230 = r4979229 * r4979220;
        double r4979231 = x;
        double r4979232 = z;
        double r4979233 = r4979232 * r4979227;
        double r4979234 = r4979231 * r4979233;
        double r4979235 = a;
        double r4979236 = r4979231 * r4979224;
        double r4979237 = r4979235 * r4979236;
        double r4979238 = r4979234 - r4979237;
        double r4979239 = r4979223 * r4979232;
        double r4979240 = r4979235 * r4979226;
        double r4979241 = r4979239 - r4979240;
        double r4979242 = b;
        double r4979243 = r4979241 * r4979242;
        double r4979244 = r4979238 - r4979243;
        double r4979245 = r4979230 + r4979244;
        double r4979246 = 6.630197526137252e+136;
        bool r4979247 = r4979220 <= r4979246;
        double r4979248 = r4979220 * r4979223;
        double r4979249 = r4979224 * r4979248;
        double r4979250 = r4979227 * r4979220;
        double r4979251 = r4979226 * r4979250;
        double r4979252 = r4979249 - r4979251;
        double r4979253 = r4979224 * r4979235;
        double r4979254 = r4979233 - r4979253;
        double r4979255 = r4979254 * r4979231;
        double r4979256 = r4979255 - r4979243;
        double r4979257 = r4979252 + r4979256;
        double r4979258 = cbrt(r4979243);
        double r4979259 = r4979258 * r4979258;
        double r4979260 = r4979258 * r4979259;
        double r4979261 = r4979255 - r4979260;
        double r4979262 = r4979261 + r4979230;
        double r4979263 = r4979247 ? r4979257 : r4979262;
        double r4979264 = r4979222 ? r4979245 : r4979263;
        return r4979264;
}

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 j < -0.010182364183445083

    1. Initial program 8.1

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

    2. Taylor expanded around inf 8.0

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

    if -0.010182364183445083 < j < 6.630197526137252e+136

    1. Initial program 14.1

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

    2. Taylor expanded around inf 10.5

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

    if 6.630197526137252e+136 < j

    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-cbrt7.0

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

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -0.01018236418344508308064799706471603712998:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;j \le 6.630197526137251571160185503510114222161 \cdot 10^{136}:\\ \;\;\;\;\left(t \cdot \left(j \cdot c\right) - i \cdot \left(y \cdot j\right)\right) + \left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b} \cdot \left(\sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b} \cdot \sqrt[3]{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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)))))