Average Error: 12.3 → 12.2
Time: 8.7s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.6945330208330025 \cdot 10^{-225}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;b \le 1.72525044162472135 \cdot 10^{-266}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + {\left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;b \le -3.6945330208330025 \cdot 10^{-225}:\\
\;\;\;\;\left(\left(\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)\\

\mathbf{elif}\;b \le 1.72525044162472135 \cdot 10^{-266}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + {\left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\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 r94062 = x;
        double r94063 = y;
        double r94064 = z;
        double r94065 = r94063 * r94064;
        double r94066 = t;
        double r94067 = a;
        double r94068 = r94066 * r94067;
        double r94069 = r94065 - r94068;
        double r94070 = r94062 * r94069;
        double r94071 = b;
        double r94072 = c;
        double r94073 = r94072 * r94064;
        double r94074 = i;
        double r94075 = r94074 * r94067;
        double r94076 = r94073 - r94075;
        double r94077 = r94071 * r94076;
        double r94078 = r94070 - r94077;
        double r94079 = j;
        double r94080 = r94072 * r94066;
        double r94081 = r94074 * r94063;
        double r94082 = r94080 - r94081;
        double r94083 = r94079 * r94082;
        double r94084 = r94078 + r94083;
        return r94084;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r94085 = b;
        double r94086 = -3.6945330208330025e-225;
        bool r94087 = r94085 <= r94086;
        double r94088 = x;
        double r94089 = y;
        double r94090 = r94088 * r94089;
        double r94091 = z;
        double r94092 = r94090 * r94091;
        double r94093 = t;
        double r94094 = a;
        double r94095 = r94093 * r94094;
        double r94096 = -r94095;
        double r94097 = r94088 * r94096;
        double r94098 = r94092 + r94097;
        double r94099 = c;
        double r94100 = r94099 * r94091;
        double r94101 = i;
        double r94102 = r94101 * r94094;
        double r94103 = r94100 - r94102;
        double r94104 = r94085 * r94103;
        double r94105 = r94098 - r94104;
        double r94106 = j;
        double r94107 = r94099 * r94093;
        double r94108 = r94101 * r94089;
        double r94109 = r94107 - r94108;
        double r94110 = r94106 * r94109;
        double r94111 = r94105 + r94110;
        double r94112 = 1.7252504416247213e-266;
        bool r94113 = r94085 <= r94112;
        double r94114 = r94089 * r94091;
        double r94115 = r94088 * r94114;
        double r94116 = r94115 + r94097;
        double r94117 = 0.0;
        double r94118 = r94116 - r94117;
        double r94119 = r94118 + r94110;
        double r94120 = -1.0;
        double r94121 = r94088 * r94093;
        double r94122 = r94094 * r94121;
        double r94123 = r94120 * r94122;
        double r94124 = 1.0;
        double r94125 = pow(r94123, r94124);
        double r94126 = r94115 + r94125;
        double r94127 = r94126 - r94104;
        double r94128 = r94127 + r94110;
        double r94129 = r94113 ? r94119 : r94128;
        double r94130 = r94087 ? r94111 : r94129;
        return r94130;
}

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 < -3.6945330208330025e-225

    1. Initial program 10.9

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

    3. Applied sub-neg10.9

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

    4. Applied distribute-lft-in10.9

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

    6. Applied associate-*r*10.9

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

    if -3.6945330208330025e-225 < b < 1.7252504416247213e-266

    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. Taylor expanded around 0 16.6

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

    if 1.7252504416247213e-266 < b

    1. Initial program 11.9

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

    3. Applied sub-neg11.9

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

    4. Applied distribute-lft-in11.9

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

    6. Applied pow111.9

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + x \cdot \color{blue}{{\left(-t \cdot a\right)}^{1}}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    7. Applied pow111.9

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + \color{blue}{{x}^{1}} \cdot {\left(-t \cdot a\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    8. Applied pow-prod-down11.9

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + \color{blue}{{\left(x \cdot \left(-t \cdot a\right)\right)}^{1}}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    9. Simplified12.2

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + {\color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)}}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.6945330208330025 \cdot 10^{-225}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;b \le 1.72525044162472135 \cdot 10^{-266}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - 0\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + {\left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 
(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)))))