Average Error: 12.5 → 10.3
Time: 18.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -1.218516813516571829132864023880113981554 \cdot 10^{-215}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(x \cdot t\right) \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 64272744.59900391101837158203125:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -1.218516813516571829132864023880113981554 \cdot 10^{-215}:\\
\;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(x \cdot t\right) \cdot \left(-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}\;j \le 64272744.59900391101837158203125:\\
\;\;\;\;\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 \left(j \cdot y\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - \left(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 r81012 = x;
        double r81013 = y;
        double r81014 = z;
        double r81015 = r81013 * r81014;
        double r81016 = t;
        double r81017 = a;
        double r81018 = r81016 * r81017;
        double r81019 = r81015 - r81018;
        double r81020 = r81012 * r81019;
        double r81021 = b;
        double r81022 = c;
        double r81023 = r81022 * r81014;
        double r81024 = i;
        double r81025 = r81024 * r81017;
        double r81026 = r81023 - r81025;
        double r81027 = r81021 * r81026;
        double r81028 = r81020 - r81027;
        double r81029 = j;
        double r81030 = r81022 * r81016;
        double r81031 = r81024 * r81013;
        double r81032 = r81030 - r81031;
        double r81033 = r81029 * r81032;
        double r81034 = r81028 + r81033;
        return r81034;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r81035 = j;
        double r81036 = -1.2185168135165718e-215;
        bool r81037 = r81035 <= r81036;
        double r81038 = x;
        double r81039 = y;
        double r81040 = r81038 * r81039;
        double r81041 = z;
        double r81042 = r81040 * r81041;
        double r81043 = t;
        double r81044 = r81038 * r81043;
        double r81045 = a;
        double r81046 = -r81045;
        double r81047 = r81044 * r81046;
        double r81048 = r81042 + r81047;
        double r81049 = b;
        double r81050 = c;
        double r81051 = r81050 * r81041;
        double r81052 = i;
        double r81053 = r81052 * r81045;
        double r81054 = r81051 - r81053;
        double r81055 = r81049 * r81054;
        double r81056 = r81048 - r81055;
        double r81057 = r81050 * r81043;
        double r81058 = r81052 * r81039;
        double r81059 = r81057 - r81058;
        double r81060 = r81035 * r81059;
        double r81061 = r81056 + r81060;
        double r81062 = 64272744.59900391;
        bool r81063 = r81035 <= r81062;
        double r81064 = r81039 * r81041;
        double r81065 = r81043 * r81045;
        double r81066 = r81064 - r81065;
        double r81067 = r81038 * r81066;
        double r81068 = r81067 - r81055;
        double r81069 = r81035 * r81050;
        double r81070 = r81043 * r81069;
        double r81071 = r81035 * r81039;
        double r81072 = r81052 * r81071;
        double r81073 = -r81072;
        double r81074 = r81070 + r81073;
        double r81075 = r81068 + r81074;
        double r81076 = -r81065;
        double r81077 = r81038 * r81076;
        double r81078 = r81042 + r81077;
        double r81079 = r81049 * r81050;
        double r81080 = r81041 * r81079;
        double r81081 = -r81053;
        double r81082 = r81049 * r81081;
        double r81083 = r81080 + r81082;
        double r81084 = r81078 - r81083;
        double r81085 = r81084 + r81060;
        double r81086 = r81063 ? r81075 : r81085;
        double r81087 = r81037 ? r81061 : r81086;
        return r81087;
}

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 j < -1.2185168135165718e-215

    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*11.0

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

    8. Applied distribute-rgt-neg-in11.0

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

    9. Applied associate-*r*11.4

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

    if -1.2185168135165718e-215 < j < 64272744.59900391

    1. Initial program 16.2

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

    3. Applied sub-neg16.2

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

    4. Applied distribute-lft-in16.2

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

    5. Simplified13.2

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

    6. Simplified10.3

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

    if 64272744.59900391 < j

    1. Initial program 7.7

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

    3. Applied sub-neg7.7

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

    4. Applied distribute-lft-in7.7

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

    6. Applied associate-*r*7.9

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

    8. Applied sub-neg7.9

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

    9. Applied distribute-lft-in7.9

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

    10. Simplified8.0

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -1.218516813516571829132864023880113981554 \cdot 10^{-215}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + \left(x \cdot t\right) \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \le 64272744.59900391101837158203125:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + x \cdot \left(-t \cdot a\right)\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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)))))