Average Error: 12.2 → 13.1
Time: 32.2s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;c \le -5478662367150612676608:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right)\right) + \left(\left(\left(-y\right) \cdot j\right) \cdot i + j \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;c \le -6.535140165540710269045334632618486765212 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot c - i \cdot y\right) \cdot j + \left(z \cdot c - i \cdot a\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c\right) + \left(-j \cdot \left(i \cdot y\right)\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(\left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}}\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\\ \end{array}\]
\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}\;c \le -5478662367150612676608:\\
\;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right)\right) + \left(\left(\left(-y\right) \cdot j\right) \cdot i + j \cdot \left(t \cdot c\right)\right)\\

\mathbf{elif}\;c \le -6.535140165540710269045334632618486765212 \cdot 10^{-32}:\\
\;\;\;\;\left(t \cdot c - i \cdot y\right) \cdot j + \left(z \cdot c - i \cdot a\right) \cdot \left(-b\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3905020 = x;
        double r3905021 = y;
        double r3905022 = z;
        double r3905023 = r3905021 * r3905022;
        double r3905024 = t;
        double r3905025 = a;
        double r3905026 = r3905024 * r3905025;
        double r3905027 = r3905023 - r3905026;
        double r3905028 = r3905020 * r3905027;
        double r3905029 = b;
        double r3905030 = c;
        double r3905031 = r3905030 * r3905022;
        double r3905032 = i;
        double r3905033 = r3905032 * r3905025;
        double r3905034 = r3905031 - r3905033;
        double r3905035 = r3905029 * r3905034;
        double r3905036 = r3905028 - r3905035;
        double r3905037 = j;
        double r3905038 = r3905030 * r3905024;
        double r3905039 = r3905032 * r3905021;
        double r3905040 = r3905038 - r3905039;
        double r3905041 = r3905037 * r3905040;
        double r3905042 = r3905036 + r3905041;
        return r3905042;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3905043 = c;
        double r3905044 = -5.478662367150613e+21;
        bool r3905045 = r3905043 <= r3905044;
        double r3905046 = y;
        double r3905047 = z;
        double r3905048 = r3905046 * r3905047;
        double r3905049 = t;
        double r3905050 = a;
        double r3905051 = r3905049 * r3905050;
        double r3905052 = r3905048 - r3905051;
        double r3905053 = x;
        double r3905054 = r3905052 * r3905053;
        double r3905055 = r3905047 * r3905043;
        double r3905056 = i;
        double r3905057 = r3905056 * r3905050;
        double r3905058 = r3905055 - r3905057;
        double r3905059 = cbrt(r3905058);
        double r3905060 = r3905059 * r3905059;
        double r3905061 = b;
        double r3905062 = r3905060 * r3905061;
        double r3905063 = r3905059 * r3905062;
        double r3905064 = r3905054 - r3905063;
        double r3905065 = -r3905046;
        double r3905066 = j;
        double r3905067 = r3905065 * r3905066;
        double r3905068 = r3905067 * r3905056;
        double r3905069 = r3905049 * r3905043;
        double r3905070 = r3905066 * r3905069;
        double r3905071 = r3905068 + r3905070;
        double r3905072 = r3905064 + r3905071;
        double r3905073 = -6.53514016554071e-32;
        bool r3905074 = r3905043 <= r3905073;
        double r3905075 = r3905056 * r3905046;
        double r3905076 = r3905069 - r3905075;
        double r3905077 = r3905076 * r3905066;
        double r3905078 = -r3905061;
        double r3905079 = r3905058 * r3905078;
        double r3905080 = r3905077 + r3905079;
        double r3905081 = r3905066 * r3905075;
        double r3905082 = -r3905081;
        double r3905083 = r3905070 + r3905082;
        double r3905084 = cbrt(r3905060);
        double r3905085 = cbrt(r3905059);
        double r3905086 = r3905084 * r3905085;
        double r3905087 = r3905086 * r3905059;
        double r3905088 = r3905087 * r3905061;
        double r3905089 = r3905088 * r3905059;
        double r3905090 = r3905054 - r3905089;
        double r3905091 = r3905083 + r3905090;
        double r3905092 = r3905074 ? r3905080 : r3905091;
        double r3905093 = r3905045 ? r3905072 : r3905092;
        return r3905093;
}

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 c < -5.478662367150613e+21

    1. Initial program 16.7

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

    3. Applied add-cube-cbrt17.0

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

    4. Applied associate-*r*17.0

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

    6. Applied sub-neg17.0

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

    7. Applied distribute-rgt-in17.0

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

    9. Applied distribute-rgt-neg-in17.0

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

    10. Applied associate-*l*17.1

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

    if -5.478662367150613e+21 < c < -6.53514016554071e-32

    1. Initial program 10.3

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

    2. Taylor expanded around 0 23.3

      \[\leadsto \left(\color{blue}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if -6.53514016554071e-32 < c

    1. Initial program 11.2

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

    3. Applied add-cube-cbrt11.5

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

    4. Applied associate-*r*11.5

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

    6. Applied sub-neg11.5

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

    7. Applied distribute-rgt-in11.5

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

    9. Applied add-cube-cbrt11.5

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

    10. Applied cbrt-prod11.6

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

  4. Final simplification13.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;c \le -5478662367150612676608:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt[3]{z \cdot c - i \cdot a} \cdot \left(\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right)\right) + \left(\left(\left(-y\right) \cdot j\right) \cdot i + j \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;c \le -6.535140165540710269045334632618486765212 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot c - i \cdot y\right) \cdot j + \left(z \cdot c - i \cdot a\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c\right) + \left(-j \cdot \left(i \cdot y\right)\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(\left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}}\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b\right) \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(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)))))