Average Error: 12.1 → 14.8
Time: 45.5s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.172860284485528595047591965528966099206 \cdot 10^{-300}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(z \cdot \left(c \cdot b\right) + \left(\left(-b\right) \cdot i\right) \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \le 2.083254038277545593791520267293058213879 \cdot 10^{-77}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot \left(b \cdot z\right) + \left(-b\right) \cdot \left(i \cdot a\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \le 1.940099898116223542085668982122560115368 \cdot 10^{81}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(i \cdot \left(\left(-a\right) \cdot b\right) + z \cdot \left(c \cdot b\right)\right)\right) + \left(\left(t \cdot c\right) \cdot j + j \cdot \left(-y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(-z \cdot \left(c \cdot b\right)\right) + b \cdot \left(i \cdot a\right)\right)\\ \end{array}\]
\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}\;y \le -2.172860284485528595047591965528966099206 \cdot 10^{-300}:\\
\;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(z \cdot \left(c \cdot b\right) + \left(\left(-b\right) \cdot i\right) \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\

\mathbf{elif}\;y \le 2.083254038277545593791520267293058213879 \cdot 10^{-77}:\\
\;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot \left(b \cdot z\right) + \left(-b\right) \cdot \left(i \cdot a\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\

\mathbf{elif}\;y \le 1.940099898116223542085668982122560115368 \cdot 10^{81}:\\
\;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(i \cdot \left(\left(-a\right) \cdot b\right) + z \cdot \left(c \cdot b\right)\right)\right) + \left(\left(t \cdot c\right) \cdot j + j \cdot \left(-y \cdot i\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(-z \cdot \left(c \cdot b\right)\right) + b \cdot \left(i \cdot a\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 r5018903 = x;
        double r5018904 = y;
        double r5018905 = z;
        double r5018906 = r5018904 * r5018905;
        double r5018907 = t;
        double r5018908 = a;
        double r5018909 = r5018907 * r5018908;
        double r5018910 = r5018906 - r5018909;
        double r5018911 = r5018903 * r5018910;
        double r5018912 = b;
        double r5018913 = c;
        double r5018914 = r5018913 * r5018905;
        double r5018915 = i;
        double r5018916 = r5018915 * r5018908;
        double r5018917 = r5018914 - r5018916;
        double r5018918 = r5018912 * r5018917;
        double r5018919 = r5018911 - r5018918;
        double r5018920 = j;
        double r5018921 = r5018913 * r5018907;
        double r5018922 = r5018915 * r5018904;
        double r5018923 = r5018921 - r5018922;
        double r5018924 = r5018920 * r5018923;
        double r5018925 = r5018919 + r5018924;
        return r5018925;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r5018926 = y;
        double r5018927 = -2.1728602844855286e-300;
        bool r5018928 = r5018926 <= r5018927;
        double r5018929 = z;
        double r5018930 = r5018929 * r5018926;
        double r5018931 = t;
        double r5018932 = a;
        double r5018933 = r5018931 * r5018932;
        double r5018934 = r5018930 - r5018933;
        double r5018935 = x;
        double r5018936 = r5018934 * r5018935;
        double r5018937 = c;
        double r5018938 = b;
        double r5018939 = r5018937 * r5018938;
        double r5018940 = r5018929 * r5018939;
        double r5018941 = -r5018938;
        double r5018942 = i;
        double r5018943 = r5018941 * r5018942;
        double r5018944 = r5018943 * r5018932;
        double r5018945 = r5018940 + r5018944;
        double r5018946 = r5018936 - r5018945;
        double r5018947 = j;
        double r5018948 = r5018931 * r5018937;
        double r5018949 = r5018926 * r5018942;
        double r5018950 = r5018948 - r5018949;
        double r5018951 = r5018947 * r5018950;
        double r5018952 = r5018946 + r5018951;
        double r5018953 = 2.0832540382775456e-77;
        bool r5018954 = r5018926 <= r5018953;
        double r5018955 = r5018938 * r5018929;
        double r5018956 = r5018937 * r5018955;
        double r5018957 = r5018942 * r5018932;
        double r5018958 = r5018941 * r5018957;
        double r5018959 = r5018956 + r5018958;
        double r5018960 = r5018936 - r5018959;
        double r5018961 = r5018960 + r5018951;
        double r5018962 = 1.9400998981162235e+81;
        bool r5018963 = r5018926 <= r5018962;
        double r5018964 = -r5018932;
        double r5018965 = r5018964 * r5018938;
        double r5018966 = r5018942 * r5018965;
        double r5018967 = r5018966 + r5018940;
        double r5018968 = r5018936 - r5018967;
        double r5018969 = r5018948 * r5018947;
        double r5018970 = -r5018949;
        double r5018971 = r5018947 * r5018970;
        double r5018972 = r5018969 + r5018971;
        double r5018973 = r5018968 + r5018972;
        double r5018974 = -r5018940;
        double r5018975 = r5018938 * r5018957;
        double r5018976 = r5018974 + r5018975;
        double r5018977 = r5018951 + r5018976;
        double r5018978 = r5018963 ? r5018973 : r5018977;
        double r5018979 = r5018954 ? r5018961 : r5018978;
        double r5018980 = r5018928 ? r5018952 : r5018979;
        return r5018980;
}

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 4 regimes

  2. if y < -2.1728602844855286e-300

    1. Initial program 12.6

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

    3. Applied sub-neg12.6

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

    4. Applied distribute-lft-in12.6

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

    5. Taylor expanded around inf 13.2

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

    7. Applied distribute-rgt-neg-in13.2

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

    8. Applied associate-*r*13.0

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

    if -2.1728602844855286e-300 < y < 2.0832540382775456e-77

    1. Initial program 9.1

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

    3. Applied sub-neg9.1

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

    4. Applied distribute-lft-in9.1

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

    5. Taylor expanded around inf 8.8

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

    7. Applied associate-*r*10.0

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

    if 2.0832540382775456e-77 < y < 1.9400998981162235e+81

    1. Initial program 9.0

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

    3. Applied sub-neg9.0

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

    4. Applied distribute-lft-in9.0

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

    5. Taylor expanded around inf 9.1

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

    6. Taylor expanded around inf 9.7

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \color{blue}{-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    7. Simplified9.9

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

    9. Applied sub-neg9.9

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

    10. Applied distribute-rgt-in9.9

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

    if 1.9400998981162235e+81 < y

    1. Initial program 19.5

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

    3. Applied sub-neg19.5

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

    4. Applied distribute-lft-in19.5

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

    5. Taylor expanded around inf 21.0

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

    6. Taylor expanded around 0 35.6

      \[\leadsto \left(\color{blue}{0} - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification14.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.172860284485528595047591965528966099206 \cdot 10^{-300}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(z \cdot \left(c \cdot b\right) + \left(\left(-b\right) \cdot i\right) \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \le 2.083254038277545593791520267293058213879 \cdot 10^{-77}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot \left(b \cdot z\right) + \left(-b\right) \cdot \left(i \cdot a\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \le 1.940099898116223542085668982122560115368 \cdot 10^{81}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \left(i \cdot \left(\left(-a\right) \cdot b\right) + z \cdot \left(c \cdot b\right)\right)\right) + \left(\left(t \cdot c\right) \cdot j + j \cdot \left(-y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(-z \cdot \left(c \cdot b\right)\right) + b \cdot \left(i \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(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)))))