Average Error: 11.8 → 13.6
Time: 7.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le 4.4754383724291455 \cdot 10^{27} \lor \neg \left(j \le 1.55117453921864358 \cdot 10^{172}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot t\right) \cdot c + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left(\left(c \cdot t\right) \cdot \left(c \cdot t\right) - \left(i \cdot y\right) \cdot \left(i \cdot y\right)\right)}{c \cdot t + i \cdot y}\\ \end{array}\]
\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 4.4754383724291455 \cdot 10^{27} \lor \neg \left(j \le 1.55117453921864358 \cdot 10^{172}\right):\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot t\right) \cdot c + j \cdot \left(-i \cdot y\right)\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) + \frac{j \cdot \left(\left(c \cdot t\right) \cdot \left(c \cdot t\right) - \left(i \cdot y\right) \cdot \left(i \cdot y\right)\right)}{c \cdot t + i \cdot y}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double VAR;
	if (((j <= 4.4754383724291455e+27) || !(j <= 1.5511745392186436e+172))) {
		VAR = (((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (((j * t) * c) + (j * -(i * y))));
	} else {
		VAR = (((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) * (c * t)) - ((i * y) * (i * y)))) / ((c * t) + (i * y))));
	}
	return VAR;
}

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 2 regimes

  2. if j < 4.4754383724291455e+27 or 1.5511745392186436e+172 < j

    1. Initial program 12.4

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

    3. Applied sub-neg12.4

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

    4. Applied distribute-lft-in12.4

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

    6. Applied *-commutative12.4

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

    7. Applied associate-*r*12.3

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

    if 4.4754383724291455e+27 < j < 1.5511745392186436e+172

    1. Initial program 7.5

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

    3. Applied flip--18.0

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

    4. Applied associate-*r/24.7

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\frac{j \cdot \left(\left(c \cdot t\right) \cdot \left(c \cdot t\right) - \left(i \cdot y\right) \cdot \left(i \cdot y\right)\right)}{c \cdot t + i \cdot y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification13.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le 4.4754383724291455 \cdot 10^{27} \lor \neg \left(j \le 1.55117453921864358 \cdot 10^{172}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(j \cdot t\right) \cdot c + j \cdot \left(-i \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left(\left(c \cdot t\right) \cdot \left(c \cdot t\right) - \left(i \cdot y\right) \cdot \left(i \cdot y\right)\right)}{c \cdot t + i \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020071 
(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)))))