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

Average Error: 19.07% → 9.35%

Time: 46.8s

Precision: binary64

Cost: 24584

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(t_1 + \left(c \cdot \left(a \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j\right)\right)\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, -c, t \cdot i\right), b, \mathsf{fma}\left(y, x \cdot z - i \cdot j, a \cdot \left(c \cdot j - x \cdot t\right)\right)\right)\\ \end{array} \]

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 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_3 (+ (* j (- (* a c) (* y i))) t_2)))
   (if (<= t_3 (- INFINITY))
     (+ (+ t_1 (- (* c (- (* a j) (* z b))) (* y (* i j)))) (* i (* t b)))
     (if (<= t_3 2e+291)
       (+ (- (* j (* a c)) (* j (* y i))) t_2)
       (fma
        (fma z (- c) (* t i))
        b
        (fma y (- (* x z) (* i j)) (* a (- (* c j) (* x t)))))))))

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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (j * ((a * c) - (y * i))) + t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (t_1 + ((c * ((a * j) - (z * b))) - (y * (i * j)))) + (i * (t * b));
	} else if (t_3 <= 2e+291) {
		tmp = ((j * (a * c)) - (j * (y * i))) + t_2;
	} else {
		tmp = fma(fma(z, -c, (t * i)), b, fma(y, ((x * z) - (i * j)), (a * ((c * j) - (x * t)))));
	}
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(t_1 + Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(y * Float64(i * j)))) + Float64(i * Float64(t * b)));
	elseif (t_3 <= 2e+291)
		tmp = Float64(Float64(Float64(j * Float64(a * c)) - Float64(j * Float64(y * i))) + t_2);
	else
		tmp = fma(fma(z, Float64(-c), Float64(t * i)), b, fma(y, Float64(Float64(x * z) - Float64(i * j)), Float64(a * Float64(Float64(c * j) - Float64(x * t)))));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(t$95$1 + N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+291], N[(N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(z * (-c) + N[(t * i), $MachinePrecision]), $MachinePrecision] * b + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	19.07%
Target	31.55%
Herbie	9.35%

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

Derivation

1. Split input into 3 regimes

2. 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)))) < -inf.0

   1. Initial program 100

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

   2. Simplified 100

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

      [Start] 100	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      +-commutative [=>] 100	\[ \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      fma-def [=>] 100	\[ \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      *-commutative [=>] 100	\[ \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]
      *-commutative [=>] 100	\[ \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Taylor expanded in c around 0 41.32

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

   if -inf.0 < (+.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)))) < 1.9999999999999999e291

   1. Initial program 1.27

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

   2. Simplified 1.27

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

      [Start] 1.27	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      sub-neg [=>] 1.27	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)} \]
      distribute-rgt-in [=>] 1.26	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]
      associate-+r+ [=>] 1.26	\[ \color{blue}{\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) + \left(-y \cdot i\right) \cdot j} \]
      *-commutative [=>] 1.26	\[ \left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) + \color{blue}{j \cdot \left(-y \cdot i\right)} \]
      cancel-sign-sub [<=] 1.26	\[ \color{blue}{\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) - \left(-j\right) \cdot \left(-y \cdot i\right)} \]
      associate-+r- [<=] 1.26	\[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j - \left(-j\right) \cdot \left(-y \cdot i\right)\right)} \]
      *-commutative [=>] 1.26	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j - \left(-j\right) \cdot \left(-y \cdot i\right)\right) \]
      cancel-sign-sub [=>] 1.26	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + j \cdot \left(-y \cdot i\right)\right)} \]
      *-commutative [<=] 1.26	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j + \color{blue}{\left(-y \cdot i\right) \cdot j}\right) \]
      distribute-rgt-in [<=] 1.27	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j \cdot \left(c \cdot a + \left(-y \cdot i\right)\right)} \]

   3. Applied egg-rr 1.26

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

   if 1.9999999999999999e291 < (+.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. Initial program 80.98

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

   2. Simplified 80.98

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

      [Start] 80.98	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      +-commutative [=>] 80.98	\[ \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      fma-def [=>] 80.98	\[ \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      *-commutative [=>] 80.98	\[ \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]
      *-commutative [=>] 80.98	\[ \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Taylor expanded in j around 0 80.98

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

   4. Simplified 40.63

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

      [Start] 80.98	\[ \left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]
      sub-neg [=>] 80.98	\[ \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \left(-\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]
      mul-1-neg [<=] 80.98	\[ \left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{-1 \cdot \left(\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]
      +-commutative [<=] 80.98	\[ \color{blue}{-1 \cdot \left(\left(c \cdot z - i \cdot t\right) \cdot b\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right)} \]
      associate-*r* [=>] 80.98	\[ \color{blue}{\left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right) \cdot b} + \left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right) \]
      neg-mul-1 [<=] 80.98	\[ \color{blue}{\left(-\left(c \cdot z - i \cdot t\right)\right)} \cdot b + \left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right) \]
      fma-def [=>] 80.98	\[ \color{blue}{\mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, \left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 9.35

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(c \cdot \left(a \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j\right)\right)\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, -c, t \cdot i\right), b, \mathsf{fma}\left(y, x \cdot z - i \cdot j, a \cdot \left(c \cdot j - x \cdot t\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	12.45%
Cost	5832

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_3 + t_2\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(t_1 + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_4 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 - \left(z \cdot \left(b \cdot c\right) + \left(a \cdot \left(x \cdot t\right) - y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 2
Error	10.56%
Cost	5832

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_3 + t_2\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(t_1 + \left(c \cdot \left(a \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j\right)\right)\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t_4 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 - \left(z \cdot \left(b \cdot c\right) + \left(a \cdot \left(x \cdot t\right) - y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	13.58%
Cost	5704

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(t_1 + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 4
Error	12.45%
Cost	5704

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_2 + \left(t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(t_1 + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 - \left(z \cdot \left(b \cdot c\right) + \left(a \cdot \left(x \cdot t\right) - y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	31.58%
Cost	2920

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := \left(y \cdot \left(x \cdot z\right) + t_1\right) - c \cdot \left(z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := \left(t_3 + t \cdot \left(b \cdot i\right)\right) + t_1\\ t_5 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_6 := t_3 + t_5\\ t_7 := \left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_5\\ \mathbf{if}\;x \leq -0.195:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-85}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-123}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-167}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-228}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-243}:\\ \;\;\;\;t_1 + t_5\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;t_1 - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+26}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Error	61.65%
Cost	2821

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.75 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-278}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 88000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+83} \lor \neg \left(i \leq 4.8 \cdot 10^{+152}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7
Error	37.23%
Cost	2793

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := \left(t_5 + t_1\right) - c \cdot \left(z \cdot b\right)\\ t_7 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_8 := t_5 + t_7\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-40}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;t_3 + t_7\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-86}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-158}:\\ \;\;\;\;t_4 + \left(t_2 - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-73}:\\ \;\;\;\;\left(t_1 - a \cdot \left(x \cdot t\right)\right) + t_7\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-38}:\\ \;\;\;\;t_3 - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+34} \lor \neg \left(t \leq 2.15 \cdot 10^{+138}\right):\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;t_4 + \left(t_2 + t \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 8
Error	61.01%
Cost	2689

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 2.75 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 10^{-278}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.25 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-244}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-51} \lor \neg \left(i \leq 4.8 \cdot 10^{+84}\right) \land i \leq 5.8 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 9
Error	31.96%
Cost	2656

\[\begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := \left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + \left(z \cdot \left(x \cdot y\right) + t_3\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := t_5 + t_3\\ t_7 := \left(t_5 + t \cdot \left(b \cdot i\right)\right) + t_2\\ \mathbf{if}\;j \leq -6.8 \cdot 10^{+104}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-39}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t_2\right) - t_1\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-97}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-216}:\\ \;\;\;\;\left(t_5 + c \cdot \left(a \cdot j\right)\right) - t_1\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-299}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-235}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{+37}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 10
Error	58.89%
Cost	2556

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_5 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-193}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-237}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-121}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 11
Error	59.3%
Cost	2553

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_5 := z \cdot \left(x \cdot y\right) - c \cdot \left(z \cdot b\right)\\ t_6 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+48}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-236}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-308}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-121}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+19} \lor \neg \left(a \leq 2.7 \cdot 10^{+72}\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 12
Error	61.99%
Cost	2029

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -9.8 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.46 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -9.4 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-279}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-50} \lor \neg \left(i \leq 8.2 \cdot 10^{+83}\right) \land i \leq 1.5 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Error	34.65%
Cost	2008

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(z \cdot b\right)\\ t_4 := \left(t_1 + c \cdot \left(a \cdot j\right)\right) - t_3\\ t_5 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_6 := t_5 + t_2\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+116}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{+82}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-38}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t_5\right) - t_3\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+204}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+264}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5 - z \cdot \left(b \cdot c - x \cdot y\right)\\ \end{array} \]

Alternative 14
Error	78.73%
Cost	1968

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_4 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+94}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 15
Error	60.1%
Cost	1764

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-259}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.3 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 16
Error	40.11%
Cost	1744

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+133}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-248}:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq 11500:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	33.3%
Cost	1744

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + t_3\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-240}:\\ \;\;\;\;t_1 + t_3\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 18
Error	78.85%
Cost	1508

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ t_4 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -1.12 \cdot 10^{+138}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.82 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 19
Error	62.59%
Cost	1500

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.65 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.95 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	37.82%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+160} \lor \neg \left(t \leq 1.65 \cdot 10^{+127}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \end{array} \]

Alternative 21
Error	79.33%
Cost	1376

\[\begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;i \leq -5.4 \cdot 10^{+69}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq -7.4 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-278}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 22
Error	65.21%
Cost	1368

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-180}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	78.51%
Cost	1176

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -1.66 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 38000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 24
Error	77.97%
Cost	980

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+136}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	78.06%
Cost	585

\[\begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-22} \lor \neg \left(a \leq 1.7 \cdot 10^{-112}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 26
Error	82.52%
Cost	452

\[\begin{array}{l} \mathbf{if}\;c \leq 9.5 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 27
Error	83.4%
Cost	320

\[a \cdot \left(c \cdot j\right) \]

Reproduce

herbie shell --seed 2023090 
(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)))))