Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.6 → 9.5

Time: 11.5s

Precision: binary64

Math

\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -1.071313390531877 \cdot 10^{+93}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -6.2850583882932655 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + \left(t \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.906034019089981 \cdot 10^{-187}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3.3836051240335285 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + \left(t \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.129092345516236 \cdot 10^{+60}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\right) + \left(j \cdot \left(a \cdot c\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2.6174748258182596 \cdot 10^{+284}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(t \cdot i - z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((double) (((double) (((double) (x * ((double) (((double) (y * z)) - ((double) (t * a)))))) - ((double) (b * ((double) (((double) (c * z)) - ((double) (t * i)))))))) + ((double) (j * ((double) (((double) (c * a)) - ((double) (y * i))))))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double VAR;
	if ((x <= -1.071313390531877e+93)) {
		VAR = ((double) (((double) (((double) (x * ((double) (((double) (y * z)) - ((double) (t * a)))))) + ((double) (((double) (i * ((double) (t * b)))) - ((double) (c * ((double) (z * b)))))))) + ((double) (j * ((double) (((double) (a * c)) - ((double) (y * i))))))));
	} else {
		double VAR_1;
		if ((x <= -6.2850583882932655e-273)) {
			VAR_1 = ((double) (((double) (j * ((double) (((double) (a * c)) - ((double) (y * i)))))) + ((double) (((double) (((double) (y * ((double) (x * z)))) - ((double) (a * ((double) (x * t)))))) + ((double) (((double) (t * ((double) (b * i)))) - ((double) (c * ((double) (z * b))))))))));
		} else {
			double VAR_2;
			if ((x <= 6.906034019089981e-187)) {
				VAR_2 = ((double) (((double) (j * ((double) (((double) (a * c)) - ((double) (y * i)))))) + ((double) (((double) (((double) (y * ((double) (x * z)))) - ((double) (t * ((double) (x * a)))))) + ((double) (b * ((double) (((double) (t * i)) - ((double) (z * c))))))))));
			} else {
				double VAR_3;
				if ((x <= 3.3836051240335285e-65)) {
					VAR_3 = ((double) (((double) (j * ((double) (((double) (a * c)) - ((double) (y * i)))))) + ((double) (((double) (((double) (y * ((double) (x * z)))) - ((double) (a * ((double) (x * t)))))) + ((double) (((double) (t * ((double) (b * i)))) - ((double) (c * ((double) (z * b))))))))));
				} else {
					double VAR_4;
					if ((x <= 2.129092345516236e+60)) {
						VAR_4 = ((double) (((double) (((double) (((double) (y * ((double) (x * z)))) - ((double) (a * ((double) (x * t)))))) + ((double) (((double) (i * ((double) (t * b)))) - ((double) (c * ((double) (z * b)))))))) + ((double) (((double) (j * ((double) (a * c)))) - ((double) (i * ((double) (y * j))))))));
					} else {
						double VAR_5;
						if ((x <= 2.6174748258182596e+284)) {
							VAR_5 = ((double) (((double) (j * ((double) (((double) (a * c)) - ((double) (y * i)))))) + ((double) (((double) (x * ((double) (((double) (y * z)) - ((double) (t * a)))))) + ((double) (((double) (((double) cbrt(b)) * ((double) cbrt(b)))) * ((double) (((double) cbrt(b)) * ((double) (((double) (t * i)) - ((double) (z * c))))))))))));
						} else {
							VAR_5 = ((double) (((double) (j * ((double) (((double) (a * c)) - ((double) (y * i)))))) + ((double) (((double) (((double) (y * ((double) (x * z)))) - ((double) (t * ((double) (x * a)))))) + ((double) (b * ((double) (((double) (t * i)) - ((double) (z * c))))))))));
						}
						VAR_4 = VAR_5;
					}
					VAR_3 = VAR_4;
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	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

Target

Original	12.6
Target	19.6
Herbie	9.5

\[\begin{array}{l} \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

1. Split input into 5 regimes

2. if x < -1.07131339053187692e93

   1. Initial program 8.6

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

   3. Applied sub-neg 8.6

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

   4. Applied distribute-lft-in 8.6

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

   5. Simplified 7.3

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

   6. Simplified 7.2

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

   if -1.07131339053187692e93 < x < -6.2850583882932655e-273 or 6.9060340190899813e-187 < x < 3.3836051240335285e-65

   1. Initial program 13.9

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

   3. Applied sub-neg 13.9

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

   4. Applied distribute-lft-in 13.9

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

   5. Simplified 12.4

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

   6. Simplified 10.8

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

   8. Applied sub-neg 10.8

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

   9. Applied distribute-lft-in 10.8

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

   10. Simplified 10.8

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

   11. Simplified 10.8

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

   13. Applied associate-*r* 9.8

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

   if -6.2850583882932655e-273 < x < 6.9060340190899813e-187 or 2.6174748258182596e284 < x

   1. Initial program 17.9

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

   3. Applied sub-neg 17.9

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

   4. Applied distribute-lft-in 17.9

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

   5. Simplified 15.2

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

   6. Simplified 11.9

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

   8. Applied associate-*r* 11.8

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

   if 3.3836051240335285e-65 < x < 2.12909234551623612e60

   1. Initial program 10.8

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

   3. Applied sub-neg 10.8

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

   4. Applied distribute-lft-in 10.8

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

   5. Simplified 10.6

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

   6. Simplified 10.4

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

   8. Applied sub-neg 10.4

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

   9. Applied distribute-lft-in 10.4

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

   10. Simplified 10.0

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

   11. Simplified 9.8

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

   13. Applied sub-neg 9.8

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

   14. Applied distribute-lft-in 9.8

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

   15. Simplified 10.3

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

   if 2.12909234551623612e60 < x < 2.6174748258182596e284

   1. Initial program 6.8

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

   3. Applied add-cube-cbrt 7.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]

   4. Applied associate-*l* 7.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(c \cdot z - t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]

   5. Simplified 7.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot \sqrt[3]{b}\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
3. Recombined 5 regimes into one program.

4. Final simplification 9.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.071313390531877 \cdot 10^{+93}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -6.2850583882932655 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + \left(t \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.906034019089981 \cdot 10^{-187}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3.3836051240335285 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + \left(t \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.129092345516236 \cdot 10^{+60}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\right) + \left(j \cdot \left(a \cdot c\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2.6174748258182596 \cdot 10^{+284}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(t \cdot i - z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(x \cdot z\right) - t \cdot \left(x \cdot a\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))