Average Error: 12.4 → 10.1
Time: 20.2s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -3.533433425377577084162084627135294593078 \cdot 10^{-69}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 7.683957053609646520320388725480686187382 \cdot 10^{-152}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(j \cdot i\right) \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \le 4.578744244050201741536238422863270325902 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{z \cdot \left(b \cdot c\right)} \cdot \sqrt[3]{z \cdot \left(b \cdot c\right)}\right) \cdot \sqrt[3]{z \cdot \left(b \cdot c\right)} + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -3.533433425377577084162084627135294593078 \cdot 10^{-69}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{elif}\;j \le 7.683957053609646520320388725480686187382 \cdot 10^{-152}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(j \cdot i\right) \cdot \left(-y\right)\right)\\

\mathbf{elif}\;j \le 4.578744244050201741536238422863270325902 \cdot 10^{-35}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r101110 = x;
        double r101111 = y;
        double r101112 = z;
        double r101113 = r101111 * r101112;
        double r101114 = t;
        double r101115 = a;
        double r101116 = r101114 * r101115;
        double r101117 = r101113 - r101116;
        double r101118 = r101110 * r101117;
        double r101119 = b;
        double r101120 = c;
        double r101121 = r101120 * r101112;
        double r101122 = i;
        double r101123 = r101122 * r101115;
        double r101124 = r101121 - r101123;
        double r101125 = r101119 * r101124;
        double r101126 = r101118 - r101125;
        double r101127 = j;
        double r101128 = r101120 * r101114;
        double r101129 = r101122 * r101111;
        double r101130 = r101128 - r101129;
        double r101131 = r101127 * r101130;
        double r101132 = r101126 + r101131;
        return r101132;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r101133 = j;
        double r101134 = -3.533433425377577e-69;
        bool r101135 = r101133 <= r101134;
        double r101136 = x;
        double r101137 = y;
        double r101138 = z;
        double r101139 = r101137 * r101138;
        double r101140 = t;
        double r101141 = a;
        double r101142 = r101140 * r101141;
        double r101143 = r101139 - r101142;
        double r101144 = r101136 * r101143;
        double r101145 = b;
        double r101146 = c;
        double r101147 = r101145 * r101146;
        double r101148 = r101138 * r101147;
        double r101149 = i;
        double r101150 = r101145 * r101149;
        double r101151 = -r101141;
        double r101152 = r101150 * r101151;
        double r101153 = r101148 + r101152;
        double r101154 = r101144 - r101153;
        double r101155 = r101146 * r101140;
        double r101156 = r101149 * r101137;
        double r101157 = r101155 - r101156;
        double r101158 = r101133 * r101157;
        double r101159 = r101154 + r101158;
        double r101160 = 7.683957053609647e-152;
        bool r101161 = r101133 <= r101160;
        double r101162 = r101149 * r101141;
        double r101163 = -r101162;
        double r101164 = r101145 * r101163;
        double r101165 = r101148 + r101164;
        double r101166 = r101144 - r101165;
        double r101167 = r101133 * r101146;
        double r101168 = r101140 * r101167;
        double r101169 = r101133 * r101149;
        double r101170 = -r101137;
        double r101171 = r101169 * r101170;
        double r101172 = r101168 + r101171;
        double r101173 = r101166 + r101172;
        double r101174 = 4.578744244050202e-35;
        bool r101175 = r101133 <= r101174;
        double r101176 = r101136 * r101139;
        double r101177 = r101136 * r101140;
        double r101178 = r101141 * r101177;
        double r101179 = -r101178;
        double r101180 = r101176 + r101179;
        double r101181 = r101146 * r101138;
        double r101182 = r101181 - r101162;
        double r101183 = r101145 * r101182;
        double r101184 = r101180 - r101183;
        double r101185 = r101184 + r101158;
        double r101186 = cbrt(r101148);
        double r101187 = r101186 * r101186;
        double r101188 = r101187 * r101186;
        double r101189 = r101188 + r101164;
        double r101190 = r101144 - r101189;
        double r101191 = r101190 + r101158;
        double r101192 = r101175 ? r101185 : r101191;
        double r101193 = r101161 ? r101173 : r101192;
        double r101194 = r101135 ? r101159 : r101193;
        return r101194;
}

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 4 regimes

  2. if j < -3.533433425377577e-69

    1. Initial program 8.0

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

    3. Applied sub-neg8.0

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

    4. Applied distribute-lft-in8.0

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

    5. Simplified8.0

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

    7. Applied distribute-rgt-neg-in8.0

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

    8. Applied associate-*r*8.6

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

    if -3.533433425377577e-69 < j < 7.683957053609647e-152

    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. Using strategy rm

    3. Applied sub-neg17.4

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

    4. Applied distribute-lft-in17.4

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

    5. Simplified17.4

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

    7. Applied sub-neg17.4

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

    8. Applied distribute-lft-in17.4

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

    9. Simplified14.0

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

    11. Applied distribute-rgt-neg-in14.0

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

    12. Applied associate-*r*10.8

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

    if 7.683957053609647e-152 < j < 4.578744244050202e-35

    1. Initial program 12.9

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

    3. Applied sub-neg12.9

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

    4. Applied distribute-lft-in12.9

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

    5. Simplified13.5

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

    if 4.578744244050202e-35 < j

    1. Initial program 8.2

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

    3. Applied sub-neg8.2

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

    4. Applied distribute-lft-in8.2

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

    5. Simplified8.5

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

    7. Applied add-cube-cbrt8.6

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(\sqrt[3]{z \cdot \left(b \cdot c\right)} \cdot \sqrt[3]{z \cdot \left(b \cdot c\right)}\right) \cdot \sqrt[3]{z \cdot \left(b \cdot c\right)}} + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -3.533433425377577084162084627135294593078 \cdot 10^{-69}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 7.683957053609646520320388725480686187382 \cdot 10^{-152}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(j \cdot i\right) \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \le 4.578744244050201741536238422863270325902 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{z \cdot \left(b \cdot c\right)} \cdot \sqrt[3]{z \cdot \left(b \cdot c\right)}\right) \cdot \sqrt[3]{z \cdot \left(b \cdot c\right)} + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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)))))