| Alternative 1 | |
|---|---|
| Accuracy | 88.6% |
| Cost | 5832 |
(FPCore (x y z t a b c i j) :precision binary64 (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))
(FPCore (x y z t a b c i j)
:precision binary64
(let* ((t_1 (* i (* t b)))
(t_2 (* x (- (* y z) (* t a))))
(t_3 (* j (- (* a c) (* y i))))
(t_4 (+ t_3 (+ t_2 (* b (- (* t i) (* z c)))))))
(if (<= t_4 -2e+307)
(+ (- t_1 (* a (* x t))) (* c (* a j)))
(if (<= t_4 2e+303)
(-
t_3
(- (+ (* b (fma c z (* t (- i)))) (* b (fma (- i) t (* t i)))) t_2))
(+ t_1 (* c (- (* a j) (* z b))))))))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) - (t * i)))) + (j * ((c * a) - (y * i)));
}
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
double t_1 = i * (t * b);
double t_2 = x * ((y * z) - (t * a));
double t_3 = j * ((a * c) - (y * i));
double t_4 = t_3 + (t_2 + (b * ((t * i) - (z * c))));
double tmp;
if (t_4 <= -2e+307) {
tmp = (t_1 - (a * (x * t))) + (c * (a * j));
} else if (t_4 <= 2e+303) {
tmp = t_3 - (((b * fma(c, z, (t * -i))) + (b * fma(-i, t, (t * i)))) - t_2);
} else {
tmp = t_1 + (c * ((a * j) - (z * b)));
}
return tmp;
}
function code(x, y, z, t, a, b, c, i, j) return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i)))) end
function code(x, y, z, t, a, b, c, i, j) t_1 = Float64(i * Float64(t * b)) t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a))) t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i))) t_4 = Float64(t_3 + Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))) tmp = 0.0 if (t_4 <= -2e+307) tmp = Float64(Float64(t_1 - Float64(a * Float64(x * t))) + Float64(c * Float64(a * j))); elseif (t_4 <= 2e+303) tmp = Float64(t_3 - Float64(Float64(Float64(b * fma(c, z, Float64(t * Float64(-i)))) + Float64(b * fma(Float64(-i), t, Float64(t * i)))) - t_2)); else tmp = Float64(t_1 + Float64(c * Float64(Float64(a * j) - Float64(z * b)))); end return tmp end
code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -2e+307], N[(N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+303], N[(t$95$3 - N[(N[(N[(b * N[(c * z + N[(t * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[((-i) * t + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]
\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}
t_1 := i \cdot \left(t \cdot b\right)\\
t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\
t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\
t_4 := t_3 + \left(t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\
\mathbf{if}\;t_4 \leq -2 \cdot 10^{+307}:\\
\;\;\;\;\left(t_1 - a \cdot \left(x \cdot t\right)\right) + c \cdot \left(a \cdot j\right)\\
\mathbf{elif}\;t_4 \leq 2 \cdot 10^{+303}:\\
\;\;\;\;t_3 - \left(\left(b \cdot \mathsf{fma}\left(c, z, t \cdot \left(-i\right)\right) + b \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right) - t_2\right)\\
\mathbf{else}:\\
\;\;\;\;t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\
\end{array}
| Original | 81.7% |
|---|---|
| Target | 69.5% |
| Herbie | 88.6% |
if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < -1.99999999999999997e307Initial program 2.4%
Simplified2.4%
[Start]2.4 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)
\] |
|---|---|
cancel-sign-sub [<=]2.4 | \[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)}
\] |
cancel-sign-sub-inv [=>]2.4 | \[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)}
\] |
*-commutative [=>]2.4 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)
\] |
remove-double-neg [=>]2.4 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right)
\] |
*-commutative [=>]2.4 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)
\] |
Taylor expanded in a around inf 20.6%
Simplified20.6%
[Start]20.6 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + c \cdot \left(a \cdot j\right)
\] |
|---|---|
*-commutative [=>]20.6 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + c \cdot \color{blue}{\left(j \cdot a\right)}
\] |
Taylor expanded in z around 0 39.2%
Simplified39.2%
[Start]39.2 | \[ \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right) + c \cdot \left(j \cdot a\right)
\] |
|---|---|
sub-neg [=>]39.2 | \[ \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right)} + c \cdot \left(j \cdot a\right)
\] |
*-lft-identity [<=]39.2 | \[ \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{1 \cdot \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)}\right) + c \cdot \left(j \cdot a\right)
\] |
metadata-eval [<=]39.2 | \[ \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(--1\right)} \cdot \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right) + c \cdot \left(j \cdot a\right)
\] |
cancel-sign-sub-inv [<=]39.2 | \[ \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right)} + c \cdot \left(j \cdot a\right)
\] |
distribute-lft-out-- [=>]39.2 | \[ \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right) - \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right)} + c \cdot \left(j \cdot a\right)
\] |
mul-1-neg [=>]39.2 | \[ -1 \cdot \left(a \cdot \left(t \cdot x\right) - \left(-\color{blue}{\left(-i \cdot \left(t \cdot b\right)\right)}\right)\right) + c \cdot \left(j \cdot a\right)
\] |
remove-double-neg [=>]39.2 | \[ -1 \cdot \left(a \cdot \left(t \cdot x\right) - \color{blue}{i \cdot \left(t \cdot b\right)}\right) + c \cdot \left(j \cdot a\right)
\] |
if -1.99999999999999997e307 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 2e303Initial program 98.8%
Simplified98.8%
[Start]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)
\] |
|---|---|
cancel-sign-sub [<=]98.8 | \[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)}
\] |
cancel-sign-sub-inv [=>]98.8 | \[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)}
\] |
*-commutative [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)
\] |
remove-double-neg [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right)
\] |
*-commutative [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)
\] |
Applied egg-rr98.8%
[Start]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
|---|---|
prod-diff [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{fma}\left(z, c, -i \cdot t\right) + \mathsf{fma}\left(-i, t, i \cdot t\right)\right)}\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
*-commutative [<=]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\mathsf{fma}\left(z, c, -\color{blue}{t \cdot i}\right) + \mathsf{fma}\left(-i, t, i \cdot t\right)\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
fma-neg [<=]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{\left(z \cdot c - t \cdot i\right)} + \mathsf{fma}\left(-i, t, i \cdot t\right)\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
distribute-rgt-in [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(z \cdot c - t \cdot i\right) \cdot b + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)}\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
*-commutative [<=]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{b \cdot \left(z \cdot c - t \cdot i\right)} + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
sub-neg [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \color{blue}{\left(z \cdot c + \left(-t \cdot i\right)\right)} + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
*-commutative [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{c \cdot z} + \left(-t \cdot i\right)\right) + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
fma-def [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \color{blue}{\mathsf{fma}\left(c, z, -t \cdot i\right)} + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
*-commutative [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \mathsf{fma}\left(c, z, -\color{blue}{i \cdot t}\right) + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
distribute-rgt-neg-in [=>]98.8 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \mathsf{fma}\left(c, z, \color{blue}{i \cdot \left(-t\right)}\right) + \mathsf{fma}\left(-i, t, i \cdot t\right) \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)
\] |
if 2e303 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) Initial program 7.0%
Simplified7.0%
[Start]7.0 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)
\] |
|---|---|
cancel-sign-sub [<=]7.0 | \[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)}
\] |
cancel-sign-sub-inv [=>]7.0 | \[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)}
\] |
*-commutative [=>]7.0 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)
\] |
remove-double-neg [=>]7.0 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right)
\] |
*-commutative [=>]7.0 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)
\] |
Taylor expanded in a around inf 21.7%
Simplified21.7%
[Start]21.7 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + c \cdot \left(a \cdot j\right)
\] |
|---|---|
*-commutative [=>]21.7 | \[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + c \cdot \color{blue}{\left(j \cdot a\right)}
\] |
Taylor expanded in b around inf 23.7%
Taylor expanded in c around 0 45.8%
Final simplification88.6%
| Alternative 1 | |
|---|---|
| Accuracy | 88.6% |
| Cost | 5832 |
| Alternative 2 | |
|---|---|
| Accuracy | 88.6% |
| Cost | 5704 |
| Alternative 3 | |
|---|---|
| Accuracy | 44.7% |
| Cost | 3205 |
| Alternative 4 | |
|---|---|
| Accuracy | 34.5% |
| Cost | 3080 |
| Alternative 5 | |
|---|---|
| Accuracy | 32.3% |
| Cost | 3080 |
| Alternative 6 | |
|---|---|
| Accuracy | 69.9% |
| Cost | 2920 |
| Alternative 7 | |
|---|---|
| Accuracy | 71.1% |
| Cost | 2788 |
| Alternative 8 | |
|---|---|
| Accuracy | 70.6% |
| Cost | 2788 |
| Alternative 9 | |
|---|---|
| Accuracy | 75.1% |
| Cost | 2784 |
| Alternative 10 | |
|---|---|
| Accuracy | 51.8% |
| Cost | 2676 |
| Alternative 11 | |
|---|---|
| Accuracy | 51.4% |
| Cost | 2676 |
| Alternative 12 | |
|---|---|
| Accuracy | 55.9% |
| Cost | 2664 |
| Alternative 13 | |
|---|---|
| Accuracy | 62.3% |
| Cost | 2660 |
| Alternative 14 | |
|---|---|
| Accuracy | 71.5% |
| Cost | 2657 |
| Alternative 15 | |
|---|---|
| Accuracy | 57.5% |
| Cost | 2532 |
| Alternative 16 | |
|---|---|
| Accuracy | 69.9% |
| Cost | 2524 |
| Alternative 17 | |
|---|---|
| Accuracy | 68.7% |
| Cost | 2524 |
| Alternative 18 | |
|---|---|
| Accuracy | 72.3% |
| Cost | 2524 |
| Alternative 19 | |
|---|---|
| Accuracy | 33.2% |
| Cost | 2420 |
| Alternative 20 | |
|---|---|
| Accuracy | 33.2% |
| Cost | 2420 |
| Alternative 21 | |
|---|---|
| Accuracy | 39.1% |
| Cost | 2420 |
| Alternative 22 | |
|---|---|
| Accuracy | 39.3% |
| Cost | 2420 |
| Alternative 23 | |
|---|---|
| Accuracy | 67.6% |
| Cost | 2392 |
| Alternative 24 | |
|---|---|
| Accuracy | 50.4% |
| Cost | 2280 |
| Alternative 25 | |
|---|---|
| Accuracy | 49.8% |
| Cost | 2280 |
| Alternative 26 | |
|---|---|
| Accuracy | 33.2% |
| Cost | 2156 |
| Alternative 27 | |
|---|---|
| Accuracy | 46.3% |
| Cost | 2148 |
| Alternative 28 | |
|---|---|
| Accuracy | 32.0% |
| Cost | 1632 |
| Alternative 29 | |
|---|---|
| Accuracy | 32.2% |
| Cost | 1500 |
| Alternative 30 | |
|---|---|
| Accuracy | 32.4% |
| Cost | 1500 |
| Alternative 31 | |
|---|---|
| Accuracy | 19.7% |
| Cost | 913 |
| Alternative 32 | |
|---|---|
| Accuracy | 19.8% |
| Cost | 912 |
| Alternative 33 | |
|---|---|
| Accuracy | 33.2% |
| Cost | 841 |
| Alternative 34 | |
|---|---|
| Accuracy | 17.5% |
| Cost | 585 |
| Alternative 35 | |
|---|---|
| Accuracy | 17.2% |
| Cost | 584 |
| Alternative 36 | |
|---|---|
| Accuracy | 29.6% |
| Cost | 576 |
| Alternative 37 | |
|---|---|
| Accuracy | 16.3% |
| Cost | 320 |
herbie shell --seed 2023151
(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)))))