Average Error: 11.6 → 11.4
Time: 34.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.6583099023676616 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + i \cdot \left(j \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;x \le 2.3530021940861816 \cdot 10^{-72}:\\ \;\;\;\;\left(\left(i \cdot a - z \cdot c\right) \cdot b - a \cdot \left(x \cdot t\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + i \cdot \left(j \cdot \left(-y\right)\right)\right)\\ \end{array}\]
\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 -4.6583099023676616 \cdot 10^{-141}:\\
\;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + i \cdot \left(j \cdot \left(-y\right)\right)\right)\\

\mathbf{elif}\;x \le 2.3530021940861816 \cdot 10^{-72}:\\
\;\;\;\;\left(\left(i \cdot a - z \cdot c\right) \cdot b - a \cdot \left(x \cdot t\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3869907 = x;
        double r3869908 = y;
        double r3869909 = z;
        double r3869910 = r3869908 * r3869909;
        double r3869911 = t;
        double r3869912 = a;
        double r3869913 = r3869911 * r3869912;
        double r3869914 = r3869910 - r3869913;
        double r3869915 = r3869907 * r3869914;
        double r3869916 = b;
        double r3869917 = c;
        double r3869918 = r3869917 * r3869909;
        double r3869919 = i;
        double r3869920 = r3869919 * r3869912;
        double r3869921 = r3869918 - r3869920;
        double r3869922 = r3869916 * r3869921;
        double r3869923 = r3869915 - r3869922;
        double r3869924 = j;
        double r3869925 = r3869917 * r3869911;
        double r3869926 = r3869919 * r3869908;
        double r3869927 = r3869925 - r3869926;
        double r3869928 = r3869924 * r3869927;
        double r3869929 = r3869923 + r3869928;
        return r3869929;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3869930 = x;
        double r3869931 = -4.6583099023676616e-141;
        bool r3869932 = r3869930 <= r3869931;
        double r3869933 = y;
        double r3869934 = z;
        double r3869935 = r3869933 * r3869934;
        double r3869936 = a;
        double r3869937 = t;
        double r3869938 = r3869936 * r3869937;
        double r3869939 = r3869935 - r3869938;
        double r3869940 = r3869939 * r3869930;
        double r3869941 = b;
        double r3869942 = c;
        double r3869943 = r3869934 * r3869942;
        double r3869944 = i;
        double r3869945 = r3869944 * r3869936;
        double r3869946 = r3869943 - r3869945;
        double r3869947 = r3869941 * r3869946;
        double r3869948 = r3869940 - r3869947;
        double r3869949 = j;
        double r3869950 = r3869937 * r3869949;
        double r3869951 = r3869950 * r3869942;
        double r3869952 = -r3869933;
        double r3869953 = r3869949 * r3869952;
        double r3869954 = r3869944 * r3869953;
        double r3869955 = r3869951 + r3869954;
        double r3869956 = r3869948 + r3869955;
        double r3869957 = 2.3530021940861816e-72;
        bool r3869958 = r3869930 <= r3869957;
        double r3869959 = r3869945 - r3869943;
        double r3869960 = r3869959 * r3869941;
        double r3869961 = r3869930 * r3869937;
        double r3869962 = r3869936 * r3869961;
        double r3869963 = r3869960 - r3869962;
        double r3869964 = r3869942 * r3869937;
        double r3869965 = r3869944 * r3869933;
        double r3869966 = r3869964 - r3869965;
        double r3869967 = r3869966 * r3869949;
        double r3869968 = r3869963 + r3869967;
        double r3869969 = r3869958 ? r3869968 : r3869956;
        double r3869970 = r3869932 ? r3869956 : r3869969;
        return r3869970;
}

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 < -4.6583099023676616e-141 or 2.3530021940861816e-72 < x

    1. Initial program 8.6

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

    3. Applied sub-neg8.6

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

    4. Applied distribute-rgt-in8.6

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

    6. Applied distribute-rgt-neg-in8.6

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

    7. Applied associate-*l*9.0

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

    9. Applied associate-*l*8.9

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

    if -4.6583099023676616e-141 < x < 2.3530021940861816e-72

    1. Initial program 15.9

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

    2. Taylor expanded around inf 14.2

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

    3. Simplified14.9

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

  4. Final simplification11.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.6583099023676616 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + i \cdot \left(j \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;x \le 2.3530021940861816 \cdot 10^{-72}:\\ \;\;\;\;\left(\left(i \cdot a - z \cdot c\right) \cdot b - a \cdot \left(x \cdot t\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + i \cdot \left(j \cdot \left(-y\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(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)))))