Average Error: 12.0 → 11.0
Time: 31.2s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.013516326772894539133550704464714845769 \cdot 10^{57}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(x \cdot y\right) \cdot z + \left(-x\right) \cdot \left(t \cdot a\right)\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\left(z \cdot c - i \cdot a\right) \cdot \sqrt[3]{b}\right)\right)\\ \mathbf{elif}\;z \le 1.844173000389605873816137764003682175443 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(\sqrt{z} \cdot \left(x \cdot y\right)\right) \cdot \sqrt{z} + \left(-x\right) \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \end{array}\]
\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}\;z \le -5.013516326772894539133550704464714845769 \cdot 10^{57}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(x \cdot y\right) \cdot z + \left(-x\right) \cdot \left(t \cdot a\right)\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\left(z \cdot c - i \cdot a\right) \cdot \sqrt[3]{b}\right)\right)\\

\mathbf{elif}\;z \le 1.844173000389605873816137764003682175443 \cdot 10^{-169}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \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) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(\sqrt{z} \cdot \left(x \cdot y\right)\right) \cdot \sqrt{z} + \left(-x\right) \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c - 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 r4339083 = x;
        double r4339084 = y;
        double r4339085 = z;
        double r4339086 = r4339084 * r4339085;
        double r4339087 = t;
        double r4339088 = a;
        double r4339089 = r4339087 * r4339088;
        double r4339090 = r4339086 - r4339089;
        double r4339091 = r4339083 * r4339090;
        double r4339092 = b;
        double r4339093 = c;
        double r4339094 = r4339093 * r4339085;
        double r4339095 = i;
        double r4339096 = r4339095 * r4339088;
        double r4339097 = r4339094 - r4339096;
        double r4339098 = r4339092 * r4339097;
        double r4339099 = r4339091 - r4339098;
        double r4339100 = j;
        double r4339101 = r4339093 * r4339087;
        double r4339102 = r4339095 * r4339084;
        double r4339103 = r4339101 - r4339102;
        double r4339104 = r4339100 * r4339103;
        double r4339105 = r4339099 + r4339104;
        return r4339105;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4339106 = z;
        double r4339107 = -5.0135163267728945e+57;
        bool r4339108 = r4339106 <= r4339107;
        double r4339109 = j;
        double r4339110 = t;
        double r4339111 = c;
        double r4339112 = r4339110 * r4339111;
        double r4339113 = y;
        double r4339114 = i;
        double r4339115 = r4339113 * r4339114;
        double r4339116 = r4339112 - r4339115;
        double r4339117 = r4339109 * r4339116;
        double r4339118 = x;
        double r4339119 = r4339118 * r4339113;
        double r4339120 = r4339119 * r4339106;
        double r4339121 = -r4339118;
        double r4339122 = a;
        double r4339123 = r4339110 * r4339122;
        double r4339124 = r4339121 * r4339123;
        double r4339125 = r4339120 + r4339124;
        double r4339126 = b;
        double r4339127 = cbrt(r4339126);
        double r4339128 = r4339127 * r4339127;
        double r4339129 = r4339106 * r4339111;
        double r4339130 = r4339114 * r4339122;
        double r4339131 = r4339129 - r4339130;
        double r4339132 = r4339131 * r4339127;
        double r4339133 = r4339128 * r4339132;
        double r4339134 = r4339125 - r4339133;
        double r4339135 = r4339117 + r4339134;
        double r4339136 = 1.844173000389606e-169;
        bool r4339137 = r4339106 <= r4339136;
        double r4339138 = r4339113 * r4339106;
        double r4339139 = r4339138 - r4339123;
        double r4339140 = r4339118 * r4339139;
        double r4339141 = cbrt(r4339140);
        double r4339142 = r4339141 * r4339141;
        double r4339143 = r4339141 * r4339142;
        double r4339144 = r4339126 * r4339131;
        double r4339145 = r4339143 - r4339144;
        double r4339146 = r4339117 + r4339145;
        double r4339147 = sqrt(r4339106);
        double r4339148 = r4339147 * r4339119;
        double r4339149 = r4339148 * r4339147;
        double r4339150 = r4339149 + r4339124;
        double r4339151 = r4339150 - r4339144;
        double r4339152 = r4339117 + r4339151;
        double r4339153 = r4339137 ? r4339146 : r4339152;
        double r4339154 = r4339108 ? r4339135 : r4339153;
        return r4339154;
}

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 z < -5.0135163267728945e+57

    1. Initial program 18.0

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

    3. Applied sub-neg18.0

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

    4. Applied distribute-lft-in18.0

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

    6. Applied associate-*r*13.6

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

    8. Applied add-cube-cbrt13.9

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

    9. Applied associate-*l*13.9

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

    if -5.0135163267728945e+57 < z < 1.844173000389606e-169

    1. Initial program 9.4

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

    3. Applied add-cube-cbrt9.7

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

    if 1.844173000389606e-169 < z

    1. Initial program 13.2

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

    3. Applied sub-neg13.2

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

    4. Applied distribute-lft-in13.2

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

    6. Applied associate-*r*11.6

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

    8. Applied add-sqr-sqrt11.7

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

    9. Applied associate-*r*11.7

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

  4. Final simplification11.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.013516326772894539133550704464714845769 \cdot 10^{57}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(x \cdot y\right) \cdot z + \left(-x\right) \cdot \left(t \cdot a\right)\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\left(z \cdot c - i \cdot a\right) \cdot \sqrt[3]{b}\right)\right)\\ \mathbf{elif}\;z \le 1.844173000389605873816137764003682175443 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(\sqrt{z} \cdot \left(x \cdot y\right)\right) \cdot \sqrt{z} + \left(-x\right) \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))))