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

Average Error: 12.3 → 18.9

Time: 42.0s

Precision: binary64

Cost: 9500

Math

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

↓

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(t_1 + j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right)\right) - \left(c \cdot \left(z \cdot b\right) + x \cdot \left(t \cdot a - z \cdot y\right)\right)\\ t_3 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_4 := c \cdot \left(a \cdot j\right)\\ t_5 := \left(y \cdot \left(z \cdot x\right) + b \cdot \left(i \cdot t - z \cdot c\right)\right) + \left(t_4 - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+145}:\\ \;\;\;\;\left(i \cdot \left(b \cdot t\right) - a \cdot \left(x \cdot t\right)\right) + t_3\\ \mathbf{elif}\;z \leq -1.462298553028206 \cdot 10^{+36}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -1.3360345713096714 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -5.706431800087509 \cdot 10^{-60}:\\ \;\;\;\;t_4 + \left(x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.269775795587896 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3206315369560735 \cdot 10^{-219}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{+154}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_3\\ \end{array} \]

FPCore

(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 (* j (- (* c a) (* y i))))
        (t_2
         (-
          (+ t_1 (* j (fma (- i) y (* y i))))
          (+ (* c (* z b)) (* x (- (* t a) (* z y))))))
        (t_3 (* z (- (* y x) (* c b))))
        (t_4 (* c (* a j)))
        (t_5
         (+
          (+ (* y (* z x)) (* b (- (* i t) (* z c))))
          (- t_4 (* i (* y j))))))
   (if (<= z -1e+145)
     (+ (- (* i (* b t)) (* a (* x t))) t_3)
     (if (<= z -1.462298553028206e+36)
       t_5
       (if (<= z -1.3360345713096714e+24)
         (* a (- (* c j) (* x t)))
         (if (<= z -5.706431800087509e-60)
           (+ t_4 (- (* x (- (* z y) (* t a))) (* b (- (* z c) (* i t)))))
           (if (<= z -7.269775795587896e-114)
             t_2
             (if (<= z 3.3206315369560735e-219)
               t_5
               (if (<= z 1e+110)
                 t_2
                 (if (<= z 1e+154) t_5 (+ t_1 t_3)))))))))))

C

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 = j * ((c * a) - (y * i));
	double t_2 = (t_1 + (j * fma(-i, y, (y * i)))) - ((c * (z * b)) + (x * ((t * a) - (z * y))));
	double t_3 = z * ((y * x) - (c * b));
	double t_4 = c * (a * j);
	double t_5 = ((y * (z * x)) + (b * ((i * t) - (z * c)))) + (t_4 - (i * (y * j)));
	double tmp;
	if (z <= -1e+145) {
		tmp = ((i * (b * t)) - (a * (x * t))) + t_3;
	} else if (z <= -1.462298553028206e+36) {
		tmp = t_5;
	} else if (z <= -1.3360345713096714e+24) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -5.706431800087509e-60) {
		tmp = t_4 + ((x * ((z * y) - (t * a))) - (b * ((z * c) - (i * t))));
	} else if (z <= -7.269775795587896e-114) {
		tmp = t_2;
	} else if (z <= 3.3206315369560735e-219) {
		tmp = t_5;
	} else if (z <= 1e+110) {
		tmp = t_2;
	} else if (z <= 1e+154) {
		tmp = t_5;
	} else {
		tmp = t_1 + t_3;
	}
	return tmp;
}

Julia

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(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(t_1 + Float64(j * fma(Float64(-i), y, Float64(y * i)))) - Float64(Float64(c * Float64(z * b)) + Float64(x * Float64(Float64(t * a) - Float64(z * y)))))
	t_3 = Float64(z * Float64(Float64(y * x) - Float64(c * b)))
	t_4 = Float64(c * Float64(a * j))
	t_5 = Float64(Float64(Float64(y * Float64(z * x)) + Float64(b * Float64(Float64(i * t) - Float64(z * c)))) + Float64(t_4 - Float64(i * Float64(y * j))))
	tmp = 0.0
	if (z <= -1e+145)
		tmp = Float64(Float64(Float64(i * Float64(b * t)) - Float64(a * Float64(x * t))) + t_3);
	elseif (z <= -1.462298553028206e+36)
		tmp = t_5;
	elseif (z <= -1.3360345713096714e+24)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= -5.706431800087509e-60)
		tmp = Float64(t_4 + Float64(Float64(x * Float64(Float64(z * y) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(i * t)))));
	elseif (z <= -7.269775795587896e-114)
		tmp = t_2;
	elseif (z <= 3.3206315369560735e-219)
		tmp = t_5;
	elseif (z <= 1e+110)
		tmp = t_2;
	elseif (z <= 1e+154)
		tmp = t_5;
	else
		tmp = Float64(t_1 + t_3);
	end
	return tmp
end

Wolfram

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[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(j * N[((-i) * y + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+145], N[(N[(N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[z, -1.462298553028206e+36], t$95$5, If[LessEqual[z, -1.3360345713096714e+24], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.706431800087509e-60], N[(t$95$4 + N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.269775795587896e-114], t$95$2, If[LessEqual[z, 3.3206315369560735e-219], t$95$5, If[LessEqual[z, 1e+110], t$95$2, If[LessEqual[z, 1e+154], t$95$5, N[(t$95$1 + t$95$3), $MachinePrecision]]]]]]]]]]]]]]

Target

Original	12.3
Target	19.9
Herbie	18.9

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

Derivation

1. Split input into 6 regimes

2. if z < -9.9999999999999999e144

   1. Initial program 22.6

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

   2. Simplified 22.5

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

   3. Taylor expanded in j around 0 28.8

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + i \cdot t\right) + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   4. Taylor expanded in z around 0 14.7

      \[\leadsto \color{blue}{\left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right) \cdot z + \left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} \]

   if -9.9999999999999999e144 < z < -1.4622985530282059e36 or -7.26977579558789633e-114 < z < 3.32063153695607348e-219 or 1e110 < z < 1.00000000000000004e154

   1. Initial program 11.2

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

   2. Taylor expanded in c around 0 10.5

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + c \cdot \left(a \cdot j\right)\right)} \]

   3. Taylor expanded in y around inf 20.4

      \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + c \cdot \left(a \cdot j\right)\right) \]

   if -1.4622985530282059e36 < z < -1.33603457130967135e24

   1. Initial program 6.2

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

   2. Simplified 6.2

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

   3. Taylor expanded in a around inf 46.3

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   if -1.33603457130967135e24 < z < -5.70643180008750853e-60

   1. Initial program 8.1

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

   2. Taylor expanded in c around inf 16.6

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

   if -5.70643180008750853e-60 < z < -7.26977579558789633e-114 or 3.32063153695607348e-219 < z < 1e110

   1. Initial program 9.7

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

   2. Applied egg-rr 9.7

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

   3. Taylor expanded in c around inf 18.6

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

   if 1.00000000000000004e154 < z

   1. Initial program 23.1

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

   2. Simplified 23.1

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

   3. Taylor expanded in t around 0 26.1

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   4. Simplified 15.2

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 18.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+145}:\\ \;\;\;\;\left(i \cdot \left(b \cdot t\right) - a \cdot \left(x \cdot t\right)\right) + z \cdot \left(y \cdot x - c \cdot b\right)\\ \mathbf{elif}\;z \leq -1.462298553028206 \cdot 10^{+36}:\\ \;\;\;\;\left(y \cdot \left(z \cdot x\right) + b \cdot \left(i \cdot t - z \cdot c\right)\right) + \left(c \cdot \left(a \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;z \leq -1.3360345713096714 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -5.706431800087509 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + \left(x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.269775795587896 \cdot 10^{-114}:\\ \;\;\;\;\left(j \cdot \left(c \cdot a - y \cdot i\right) + j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right)\right) - \left(c \cdot \left(z \cdot b\right) + x \cdot \left(t \cdot a - z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.3206315369560735 \cdot 10^{-219}:\\ \;\;\;\;\left(y \cdot \left(z \cdot x\right) + b \cdot \left(i \cdot t - z \cdot c\right)\right) + \left(c \cdot \left(a \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 10^{+110}:\\ \;\;\;\;\left(j \cdot \left(c \cdot a - y \cdot i\right) + j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right)\right) - \left(c \cdot \left(z \cdot b\right) + x \cdot \left(t \cdot a - z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 10^{+154}:\\ \;\;\;\;\left(y \cdot \left(z \cdot x\right) + b \cdot \left(i \cdot t - z \cdot c\right)\right) + \left(c \cdot \left(a \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot a - y \cdot i\right) + z \cdot \left(y \cdot x - c \cdot b\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	27.0
Cost	2932

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := t_1 + x \cdot \left(z \cdot y - t \cdot a\right)\\ t_3 := t_1 + z \cdot \left(y \cdot x - c \cdot b\right)\\ t_4 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+191}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{+145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2 \cdot 10^{+122}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.9160472348159035 \cdot 10^{-17}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c - i \cdot t\right)\\ \mathbf{elif}\;i \leq -1.1649663420556394 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9.617563749501432 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.73194100240974 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.5397573287959624 \cdot 10^{-274}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.503465461952706 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	27.9
Cost	2800

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := t_1 + z \cdot \left(y \cdot x - c \cdot b\right)\\ t_3 := t_1 + x \cdot \left(z \cdot y - t \cdot a\right)\\ t_4 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+191}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{+52}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.1649663420556394 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -9.617563749501432 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.73194100240974 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.5397573287959624 \cdot 10^{-274}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5.503465461952706 \cdot 10^{-143}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	20.6
Cost	2652

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ t_3 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_4 := t_2 + \left(t_3 - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\ t_5 := \left(y \cdot \left(z \cdot x\right) + b \cdot \left(i \cdot t - z \cdot c\right)\right) + \left(t_2 - i \cdot \left(y \cdot j\right)\right)\\ t_6 := j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-10}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -5.82887460802157 \cdot 10^{-113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.606431795178028 \cdot 10^{-185}:\\ \;\;\;\;t_6 + t_3\\ \mathbf{elif}\;t \leq -5.030513289134503 \cdot 10^{-240}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.431472627196643 \cdot 10^{-187}:\\ \;\;\;\;t_6 + t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+77}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(b \cdot t\right) - a \cdot \left(x \cdot t\right)\right) + t_1\\ \end{array} \]

Alternative 4
Error	20.7
Cost	2400

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_3 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_4 := b \cdot \left(z \cdot c - i \cdot t\right)\\ t_5 := \left(i \cdot \left(b \cdot t\right) - a \cdot \left(x \cdot t\right)\right) + t_3\\ t_6 := c \cdot \left(a \cdot j\right) + \left(t_2 - t_4\right)\\ t_7 := t_1 + t_2\\ \mathbf{if}\;z \leq -1.3360345713096714 \cdot 10^{+24}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -5.706431800087509 \cdot 10^{-60}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq -7.269775795587896 \cdot 10^{-114}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq -1.7761027916760283 \cdot 10^{-248}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq -1.031156176857762 \cdot 10^{-304}:\\ \;\;\;\;t_1 - t_4\\ \mathbf{elif}\;z \leq 5.453023361413947 \cdot 10^{-199}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 4.9174806281334267 \cdot 10^{-33}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 3.803142537374952 \cdot 10^{+27}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_3\\ \end{array} \]

Alternative 5
Error	37.2
Cost	2292

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_3 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_4 := i \cdot \left(b \cdot t - y \cdot j\right)\\ t_5 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -3331.8380148658634:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -5.941710389821897 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.022893654841392 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.3766155387778042 \cdot 10^{-284}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.6452059125117675 \cdot 10^{-175}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 2.2938574414215686 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 9.285848876553704 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 215248.01572976075:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Error	37.4
Cost	2160

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a\right) - c \cdot \left(z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_4 := z \cdot \left(y \cdot x\right) - a \cdot \left(x \cdot t\right)\\ t_5 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -3331.8380148658634:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -5.941710389821897 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.022893654841392 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.3766155387778042 \cdot 10^{-284}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.4420653061012436 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(y \cdot x - c \cdot b\right)\\ \mathbf{elif}\;i \leq 4.6452059125117675 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.1544951284490556 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 7
Error	28.7
Cost	2140

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right) + z \cdot \left(y \cdot x - c \cdot b\right)\\ t_2 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -3331.8380148658634:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.3303889520195468 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	17.4
Cost	2128

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right) + \left(x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\ t_2 := j \cdot \left(c \cdot a - y \cdot i\right) + z \cdot \left(y \cdot x - c \cdot b\right)\\ \mathbf{if}\;j \leq -1.45 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.197906133885462 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8.516471525243319 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 0.245:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	37.3
Cost	1896

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_2 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -3331.8380148658634:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -5.941710389821897 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.5803107494209144 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(c \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.6452059125117675 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.1544951284490556 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	40.5
Cost	1764

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.1397276728558034 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1264073672571058 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -1.2112672348344003 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 2.868552171499406 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;c \leq 2.336993443249 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 2.8468599944333282 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.3610271133017287 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	50.2
Cost	1704

\[\begin{array}{l} t_1 := b \cdot \left(c \cdot \left(-z\right)\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ t_3 := y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.258937198060099 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4569819325823891 \cdot 10^{-127}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;t \leq -1.270902376065161 \cdot 10^{-211}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 2.0694874784427928 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t \leq 1.614959524643835 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.339773048401518 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 12
Error	51.2
Cost	1704

\[\begin{array}{l} t_1 := i \cdot \left(j \cdot \left(-y\right)\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -4.258937198060099 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t \leq -1.4569819325823891 \cdot 10^{-127}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;t \leq -3.0272322467340635 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.270902376065161 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.0694874784427928 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 13
Error	49.8
Cost	1572

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7.045476593801986 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.193621889945078 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.0815248157294187 \cdot 10^{-165}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;a \leq 6.591320740820907 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.3470382499245108 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8901697065993674 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+186}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 14
Error	45.9
Cost	1440

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot x - c \cdot b\right)\\ t_2 := i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{+259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -7.973127329136852 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.7613521548414227 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.73194100240974 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]

Alternative 15
Error	37.4
Cost	1368

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(b \cdot t - y \cdot j\right)\\ t_3 := z \cdot \left(y \cdot x - c \cdot b\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.288406156393752 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.835919598754578 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2650819328810673 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.313468341353192 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.009934002820024 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	36.4
Cost	1368

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_3 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -3331.8380148658634:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -5.941710389821897 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.022893654841392 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.3766155387778042 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 215248.01572976075:\\ \;\;\;\;z \cdot \left(y \cdot x - c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	37.0
Cost	1104

\[\begin{array}{l} t_1 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -0.8027094991557209:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5.941710389821897 \cdot 10^{-93}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 215248.01572976075:\\ \;\;\;\;z \cdot \left(y \cdot x - c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	49.5
Cost	980

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := i \cdot \left(b \cdot t\right)\\ \mathbf{if}\;i \leq -75463.1874560175:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -5.941710389821897 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;i \leq 1.813535475963455 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	49.5
Cost	980

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := i \cdot \left(b \cdot t\right)\\ \mathbf{if}\;i \leq -75463.1874560175:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.7613521548414227 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.1198308881814245 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;i \leq 1.813535475963455 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	49.4
Cost	848

\[\begin{array}{l} t_1 := i \cdot \left(b \cdot t\right)\\ \mathbf{if}\;i \leq -75463.1874560175:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.7613521548414227 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;i \leq 1.0775734198761756 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 6.99441084117087 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	49.3
Cost	848

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4034179451798278 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq -1.7761027916760283 \cdot 10^{-248}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq 1.009934002820024 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	49.7
Cost	584

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	53.4
Cost	320

\[y \cdot \left(z \cdot x\right) \]

Reproduce

herbie shell --seed 2022228 
(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)))))