Average Error: 12.3 → 12.2
Time: 35.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.35838280615037666349340971153519687763 \cdot 10^{-188}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j\\ \mathbf{elif}\;b \le 9.95588474272539046952932324509302559692 \cdot 10^{-263}:\\ \;\;\;\;\left(t \cdot c - i \cdot y\right) \cdot j + \left(z \cdot y - t \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt{b} \cdot \left(\sqrt{b} \cdot \left(z \cdot c - i \cdot a\right)\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j\\ \end{array}\]
\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}\;b \le -3.35838280615037666349340971153519687763 \cdot 10^{-188}:\\
\;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j\\

\mathbf{elif}\;b \le 9.95588474272539046952932324509302559692 \cdot 10^{-263}:\\
\;\;\;\;\left(t \cdot c - i \cdot y\right) \cdot j + \left(z \cdot y - t \cdot a\right) \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4592098 = x;
        double r4592099 = y;
        double r4592100 = z;
        double r4592101 = r4592099 * r4592100;
        double r4592102 = t;
        double r4592103 = a;
        double r4592104 = r4592102 * r4592103;
        double r4592105 = r4592101 - r4592104;
        double r4592106 = r4592098 * r4592105;
        double r4592107 = b;
        double r4592108 = c;
        double r4592109 = r4592108 * r4592100;
        double r4592110 = i;
        double r4592111 = r4592110 * r4592103;
        double r4592112 = r4592109 - r4592111;
        double r4592113 = r4592107 * r4592112;
        double r4592114 = r4592106 - r4592113;
        double r4592115 = j;
        double r4592116 = r4592108 * r4592102;
        double r4592117 = r4592110 * r4592099;
        double r4592118 = r4592116 - r4592117;
        double r4592119 = r4592115 * r4592118;
        double r4592120 = r4592114 + r4592119;
        return r4592120;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4592121 = b;
        double r4592122 = -3.3583828061503767e-188;
        bool r4592123 = r4592121 <= r4592122;
        double r4592124 = x;
        double r4592125 = z;
        double r4592126 = y;
        double r4592127 = r4592125 * r4592126;
        double r4592128 = r4592124 * r4592127;
        double r4592129 = a;
        double r4592130 = t;
        double r4592131 = r4592124 * r4592130;
        double r4592132 = r4592129 * r4592131;
        double r4592133 = r4592128 - r4592132;
        double r4592134 = c;
        double r4592135 = r4592125 * r4592134;
        double r4592136 = i;
        double r4592137 = r4592136 * r4592129;
        double r4592138 = r4592135 - r4592137;
        double r4592139 = r4592121 * r4592138;
        double r4592140 = r4592133 - r4592139;
        double r4592141 = r4592130 * r4592134;
        double r4592142 = r4592136 * r4592126;
        double r4592143 = r4592141 - r4592142;
        double r4592144 = j;
        double r4592145 = r4592143 * r4592144;
        double r4592146 = r4592140 + r4592145;
        double r4592147 = 9.95588474272539e-263;
        bool r4592148 = r4592121 <= r4592147;
        double r4592149 = r4592130 * r4592129;
        double r4592150 = r4592127 - r4592149;
        double r4592151 = r4592150 * r4592124;
        double r4592152 = r4592145 + r4592151;
        double r4592153 = sqrt(r4592121);
        double r4592154 = r4592153 * r4592138;
        double r4592155 = r4592153 * r4592154;
        double r4592156 = r4592151 - r4592155;
        double r4592157 = r4592156 + r4592145;
        double r4592158 = r4592148 ? r4592152 : r4592157;
        double r4592159 = r4592123 ? r4592146 : r4592158;
        return r4592159;
}

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 b < -3.3583828061503767e-188

    1. Initial program 11.1

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

    2. Taylor expanded around inf 11.6

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

    if -3.3583828061503767e-188 < b < 9.95588474272539e-263

    1. Initial program 17.4

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

    2. Taylor expanded around 0 15.9

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

    if 9.95588474272539e-263 < b

    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-sqr-sqrt11.3

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

    4. Applied associate-*l*11.3

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.35838280615037666349340971153519687763 \cdot 10^{-188}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j\\ \mathbf{elif}\;b \le 9.95588474272539046952932324509302559692 \cdot 10^{-263}:\\ \;\;\;\;\left(t \cdot c - i \cdot y\right) \cdot j + \left(z \cdot y - t \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y - t \cdot a\right) \cdot x - \sqrt{b} \cdot \left(\sqrt{b} \cdot \left(z \cdot c - i \cdot a\right)\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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)))))