Average Error: 12.1 → 12.4
Time: 9.2s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot t - i \cdot y\right)\right)\]
\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)
↓
\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 \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot t - i \cdot y\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r89889 = x;
        double r89890 = y;
        double r89891 = z;
        double r89892 = r89890 * r89891;
        double r89893 = t;
        double r89894 = a;
        double r89895 = r89893 * r89894;
        double r89896 = r89892 - r89895;
        double r89897 = r89889 * r89896;
        double r89898 = b;
        double r89899 = c;
        double r89900 = r89899 * r89891;
        double r89901 = i;
        double r89902 = r89901 * r89894;
        double r89903 = r89900 - r89902;
        double r89904 = r89898 * r89903;
        double r89905 = r89897 - r89904;
        double r89906 = j;
        double r89907 = r89899 * r89893;
        double r89908 = r89901 * r89890;
        double r89909 = r89907 - r89908;
        double r89910 = r89906 * r89909;
        double r89911 = r89905 + r89910;
        return r89911;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r89912 = x;
        double r89913 = y;
        double r89914 = z;
        double r89915 = r89913 * r89914;
        double r89916 = t;
        double r89917 = a;
        double r89918 = r89916 * r89917;
        double r89919 = r89915 - r89918;
        double r89920 = r89912 * r89919;
        double r89921 = b;
        double r89922 = c;
        double r89923 = r89922 * r89914;
        double r89924 = i;
        double r89925 = r89924 * r89917;
        double r89926 = r89923 - r89925;
        double r89927 = r89921 * r89926;
        double r89928 = r89920 - r89927;
        double r89929 = j;
        double r89930 = cbrt(r89929);
        double r89931 = r89930 * r89930;
        double r89932 = r89922 * r89916;
        double r89933 = r89924 * r89913;
        double r89934 = r89932 - r89933;
        double r89935 = r89930 * r89934;
        double r89936 = r89931 * r89935;
        double r89937 = r89928 + r89936;
        return r89937;
}

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. Initial program 12.1

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

  3. Applied add-cube-cbrt12.4

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

  4. Applied associate-*l*12.4

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

  5. Final simplification12.4

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

Reproduce

herbie shell --seed 2019352 
(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)))))