Average Error: 11.9 → 9.3
Time: 14.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -4.4898681204567659 \cdot 10^{122}:\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 4.2792569441990407 \cdot 10^{99}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-\left(i \cdot j\right) \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;j \le -4.4898681204567659 \cdot 10^{122}:\\
\;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{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)\\

\mathbf{elif}\;j \le 4.2792569441990407 \cdot 10^{99}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-\left(i \cdot j\right) \cdot y\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r119009 = x;
        double r119010 = y;
        double r119011 = z;
        double r119012 = r119010 * r119011;
        double r119013 = t;
        double r119014 = a;
        double r119015 = r119013 * r119014;
        double r119016 = r119012 - r119015;
        double r119017 = r119009 * r119016;
        double r119018 = b;
        double r119019 = c;
        double r119020 = r119019 * r119011;
        double r119021 = i;
        double r119022 = r119021 * r119014;
        double r119023 = r119020 - r119022;
        double r119024 = r119018 * r119023;
        double r119025 = r119017 - r119024;
        double r119026 = j;
        double r119027 = r119019 * r119013;
        double r119028 = r119021 * r119010;
        double r119029 = r119027 - r119028;
        double r119030 = r119026 * r119029;
        double r119031 = r119025 + r119030;
        return r119031;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r119032 = j;
        double r119033 = -4.489868120456766e+122;
        bool r119034 = r119032 <= r119033;
        double r119035 = x;
        double r119036 = y;
        double r119037 = z;
        double r119038 = r119036 * r119037;
        double r119039 = t;
        double r119040 = a;
        double r119041 = r119039 * r119040;
        double r119042 = r119038 - r119041;
        double r119043 = r119035 * r119042;
        double r119044 = cbrt(r119043);
        double r119045 = r119044 * r119044;
        double r119046 = r119045 * r119044;
        double r119047 = b;
        double r119048 = c;
        double r119049 = r119048 * r119037;
        double r119050 = i;
        double r119051 = r119050 * r119040;
        double r119052 = r119049 - r119051;
        double r119053 = r119047 * r119052;
        double r119054 = r119046 - r119053;
        double r119055 = r119048 * r119039;
        double r119056 = r119050 * r119036;
        double r119057 = r119055 - r119056;
        double r119058 = r119032 * r119057;
        double r119059 = r119054 + r119058;
        double r119060 = 4.2792569441990407e+99;
        bool r119061 = r119032 <= r119060;
        double r119062 = r119043 - r119053;
        double r119063 = r119039 * r119032;
        double r119064 = r119063 * r119048;
        double r119065 = r119050 * r119032;
        double r119066 = r119065 * r119036;
        double r119067 = -r119066;
        double r119068 = r119064 + r119067;
        double r119069 = r119062 + r119068;
        double r119070 = r119047 * r119048;
        double r119071 = r119037 * r119070;
        double r119072 = -r119051;
        double r119073 = r119072 * r119047;
        double r119074 = r119071 + r119073;
        double r119075 = r119043 - r119074;
        double r119076 = r119075 + r119058;
        double r119077 = r119061 ? r119069 : r119076;
        double r119078 = r119034 ? r119059 : r119077;
        return r119078;
}

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 j < -4.489868120456766e+122

    1. Initial program 6.1

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

    3. Applied add-cube-cbrt6.3

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

    if -4.489868120456766e+122 < j < 4.2792569441990407e+99

    1. Initial program 13.4

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

    3. Applied sub-neg13.4

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

    4. Applied distribute-lft-in13.4

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

    5. Simplified11.8

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

    6. Simplified10.1

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

    8. Applied associate-*r*10.1

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

    10. Applied associate-*r*10.0

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

    if 4.2792569441990407e+99 < j

    1. Initial program 6.1

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

    3. Applied sub-neg6.1

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

    4. Applied distribute-lft-in6.1

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

    5. Simplified6.6

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

    6. Simplified6.6

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

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -4.4898681204567659 \cdot 10^{122}:\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 4.2792569441990407 \cdot 10^{99}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-\left(i \cdot j\right) \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))))