Average Error: 11.8 → 11.7
Time: 23.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -4.8832649390149185 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - \left(\left(-b\right) \cdot \left(i \cdot a\right) + z \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \le 9.54049899235349 \cdot 10^{-144}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(y \cdot z\right) - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - \left(\left(-b\right) \cdot \left(i \cdot a\right) + \left(c \cdot z\right) \cdot b\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]
\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}\;i \le -4.8832649390149185 \cdot 10^{-28}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - \left(\left(-b\right) \cdot \left(i \cdot a\right) + z \cdot \left(b \cdot c\right)\right)\right)\\

\mathbf{elif}\;i \le 9.54049899235349 \cdot 10^{-144}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(y \cdot z\right) - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1553961 = x;
        double r1553962 = y;
        double r1553963 = z;
        double r1553964 = r1553962 * r1553963;
        double r1553965 = t;
        double r1553966 = a;
        double r1553967 = r1553965 * r1553966;
        double r1553968 = r1553964 - r1553967;
        double r1553969 = r1553961 * r1553968;
        double r1553970 = b;
        double r1553971 = c;
        double r1553972 = r1553971 * r1553963;
        double r1553973 = i;
        double r1553974 = r1553973 * r1553966;
        double r1553975 = r1553972 - r1553974;
        double r1553976 = r1553970 * r1553975;
        double r1553977 = r1553969 - r1553976;
        double r1553978 = j;
        double r1553979 = r1553971 * r1553965;
        double r1553980 = r1553973 * r1553962;
        double r1553981 = r1553979 - r1553980;
        double r1553982 = r1553978 * r1553981;
        double r1553983 = r1553977 + r1553982;
        return r1553983;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1553984 = i;
        double r1553985 = -4.8832649390149185e-28;
        bool r1553986 = r1553984 <= r1553985;
        double r1553987 = j;
        double r1553988 = t;
        double r1553989 = c;
        double r1553990 = r1553988 * r1553989;
        double r1553991 = y;
        double r1553992 = r1553991 * r1553984;
        double r1553993 = r1553990 - r1553992;
        double r1553994 = r1553987 * r1553993;
        double r1553995 = z;
        double r1553996 = r1553991 * r1553995;
        double r1553997 = a;
        double r1553998 = r1553988 * r1553997;
        double r1553999 = r1553996 - r1553998;
        double r1554000 = cbrt(r1553999);
        double r1554001 = r1554000 * r1554000;
        double r1554002 = x;
        double r1554003 = r1554001 * r1554002;
        double r1554004 = r1554000 * r1554003;
        double r1554005 = b;
        double r1554006 = -r1554005;
        double r1554007 = r1553984 * r1553997;
        double r1554008 = r1554006 * r1554007;
        double r1554009 = r1554005 * r1553989;
        double r1554010 = r1553995 * r1554009;
        double r1554011 = r1554008 + r1554010;
        double r1554012 = r1554004 - r1554011;
        double r1554013 = r1553994 + r1554012;
        double r1554014 = 9.54049899235349e-144;
        bool r1554015 = r1553984 <= r1554014;
        double r1554016 = r1554002 * r1553996;
        double r1554017 = r1554002 * r1553988;
        double r1554018 = r1554017 * r1553997;
        double r1554019 = r1554016 - r1554018;
        double r1554020 = r1553989 * r1553995;
        double r1554021 = r1554020 - r1554007;
        double r1554022 = r1554005 * r1554021;
        double r1554023 = r1554019 - r1554022;
        double r1554024 = r1553994 + r1554023;
        double r1554025 = r1554020 * r1554005;
        double r1554026 = r1554008 + r1554025;
        double r1554027 = r1554004 - r1554026;
        double r1554028 = r1554027 + r1553994;
        double r1554029 = r1554015 ? r1554024 : r1554028;
        double r1554030 = r1553986 ? r1554013 : r1554029;
        return r1554030;
}

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 i < -4.8832649390149185e-28

    1. Initial program 16.4

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

    3. Applied add-cube-cbrt16.6

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

    4. Applied associate-*r*16.6

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

    6. Applied sub-neg16.6

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

    7. Applied distribute-lft-in16.6

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

    8. Taylor expanded around inf 15.7

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

    if -4.8832649390149185e-28 < i < 9.54049899235349e-144

    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. Taylor expanded around inf 8.9

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

    if 9.54049899235349e-144 < i

    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 add-cube-cbrt12.8

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

    4. Applied associate-*r*12.8

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

    6. Applied sub-neg12.8

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

    7. Applied distribute-lft-in12.8

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

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -4.8832649390149185 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - \left(\left(-b\right) \cdot \left(i \cdot a\right) + z \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \le 9.54049899235349 \cdot 10^{-144}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(y \cdot z\right) - \left(x \cdot t\right) \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot x\right) - \left(\left(-b\right) \cdot \left(i \cdot a\right) + \left(c \cdot z\right) \cdot b\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 
(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)))))