Average Error: 12.3 → 12.0
Time: 31.9s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -2.734577024275635776606896347876237358818 \cdot 10^{-142}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + i \cdot \left(\left(-y\right) \cdot j\right)\right)\\ \mathbf{elif}\;i \le 3.189483550666528306044484300359716331537 \cdot 10^{-261}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(c \cdot \left(t \cdot j\right) + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot y\right) \cdot j\right)\\ \end{array}\]
\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}\;i \le -2.734577024275635776606896347876237358818 \cdot 10^{-142}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + i \cdot \left(\left(-y\right) \cdot j\right)\right)\\

\mathbf{elif}\;i \le 3.189483550666528306044484300359716331537 \cdot 10^{-261}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(c \cdot \left(t \cdot j\right) + \left(-i \cdot y\right) \cdot j\right)\\

\mathbf{else}:\\
\;\;\;\;\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) + \left(-i \cdot y\right) \cdot j\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r9237066 = x;
        double r9237067 = y;
        double r9237068 = z;
        double r9237069 = r9237067 * r9237068;
        double r9237070 = t;
        double r9237071 = a;
        double r9237072 = r9237070 * r9237071;
        double r9237073 = r9237069 - r9237072;
        double r9237074 = r9237066 * r9237073;
        double r9237075 = b;
        double r9237076 = c;
        double r9237077 = r9237076 * r9237068;
        double r9237078 = i;
        double r9237079 = r9237078 * r9237071;
        double r9237080 = r9237077 - r9237079;
        double r9237081 = r9237075 * r9237080;
        double r9237082 = r9237074 - r9237081;
        double r9237083 = j;
        double r9237084 = r9237076 * r9237070;
        double r9237085 = r9237078 * r9237067;
        double r9237086 = r9237084 - r9237085;
        double r9237087 = r9237083 * r9237086;
        double r9237088 = r9237082 + r9237087;
        return r9237088;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r9237089 = i;
        double r9237090 = -2.7345770242756358e-142;
        bool r9237091 = r9237089 <= r9237090;
        double r9237092 = x;
        double r9237093 = y;
        double r9237094 = z;
        double r9237095 = r9237093 * r9237094;
        double r9237096 = t;
        double r9237097 = a;
        double r9237098 = r9237096 * r9237097;
        double r9237099 = r9237095 - r9237098;
        double r9237100 = r9237092 * r9237099;
        double r9237101 = b;
        double r9237102 = c;
        double r9237103 = r9237102 * r9237094;
        double r9237104 = r9237089 * r9237097;
        double r9237105 = r9237103 - r9237104;
        double r9237106 = r9237101 * r9237105;
        double r9237107 = r9237100 - r9237106;
        double r9237108 = r9237102 * r9237096;
        double r9237109 = j;
        double r9237110 = r9237108 * r9237109;
        double r9237111 = -r9237093;
        double r9237112 = r9237111 * r9237109;
        double r9237113 = r9237089 * r9237112;
        double r9237114 = r9237110 + r9237113;
        double r9237115 = r9237107 + r9237114;
        double r9237116 = 3.1894835506665283e-261;
        bool r9237117 = r9237089 <= r9237116;
        double r9237118 = r9237096 * r9237109;
        double r9237119 = r9237102 * r9237118;
        double r9237120 = r9237089 * r9237093;
        double r9237121 = -r9237120;
        double r9237122 = r9237121 * r9237109;
        double r9237123 = r9237119 + r9237122;
        double r9237124 = r9237107 + r9237123;
        double r9237125 = r9237109 * r9237102;
        double r9237126 = r9237096 * r9237125;
        double r9237127 = r9237126 + r9237122;
        double r9237128 = r9237107 + r9237127;
        double r9237129 = r9237117 ? r9237124 : r9237128;
        double r9237130 = r9237091 ? r9237115 : r9237129;
        return r9237130;
}

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 i < -2.7345770242756358e-142

    1. Initial program 14.3

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

    3. Applied sub-neg14.3

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

    4. Applied distribute-rgt-in14.3

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

    6. Applied distribute-rgt-neg-in14.3

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

    7. Applied associate-*l*12.4

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

    if -2.7345770242756358e-142 < i < 3.1894835506665283e-261

    1. Initial program 10.0

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

    3. Applied sub-neg10.0

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

    4. Applied distribute-rgt-in10.0

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

    6. Applied associate-*l*10.6

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

    if 3.1894835506665283e-261 < i

    1. Initial program 12.0

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

    3. Applied sub-neg12.0

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

    4. Applied distribute-rgt-in12.0

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

    5. Taylor expanded around inf 12.4

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

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -2.734577024275635776606896347876237358818 \cdot 10^{-142}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + i \cdot \left(\left(-y\right) \cdot j\right)\right)\\ \mathbf{elif}\;i \le 3.189483550666528306044484300359716331537 \cdot 10^{-261}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(c \cdot \left(t \cdot j\right) + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot y\right) \cdot j\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(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)))))