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

Average Accuracy: 80.9% → 87.2%

Time: 59.7s

Precision: binary64

Cost: 12552

Math

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

↓

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+302}:\\ \;\;\;\;\left(\left(t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - t_4\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + t_1\right) - \left(i \cdot \left(y \cdot j - t \cdot b\right) + i \cdot \mathsf{fma}\left(-b, t, t \cdot b\right)\right)\right) - t_4\\ \end{array} \]

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 (* c (* a j)))
        (t_2 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_3 (+ t_2 (* j (- (* a c) (* y i)))))
        (t_4 (* c (* z b))))
   (if (<= t_3 -1e+302)
     (- (+ (- t_1 (* x (- (* t a) (* y z)))) (* i (- (* t b) (* y j)))) t_4)
     (if (<= t_3 INFINITY)
       (+ (- (* j (* a c)) (* j (* y i))) t_2)
       (-
        (-
         (+ (* y (* x z)) t_1)
         (+ (* i (- (* y j) (* t b))) (* i (fma (- b) t (* t b)))))
        t_4)))))

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 = c * (a * j);
	double t_2 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double t_4 = c * (z * b);
	double tmp;
	if (t_3 <= -1e+302) {
		tmp = ((t_1 - (x * ((t * a) - (y * z)))) + (i * ((t * b) - (y * j)))) - t_4;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = ((j * (a * c)) - (j * (y * i))) + t_2;
	} else {
		tmp = (((y * (x * z)) + t_1) - ((i * ((y * j) - (t * b))) + (i * fma(-b, t, (t * b))))) - t_4;
	}
	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(c * Float64(a * j))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_4 = Float64(c * Float64(z * b))
	tmp = 0.0
	if (t_3 <= -1e+302)
		tmp = Float64(Float64(Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(i * Float64(Float64(t * b) - Float64(y * j)))) - t_4);
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(Float64(j * Float64(a * c)) - Float64(j * Float64(y * i))) + t_2);
	else
		tmp = Float64(Float64(Float64(Float64(y * Float64(x * z)) + t_1) - Float64(Float64(i * Float64(Float64(y * j) - Float64(t * b))) + Float64(i * fma(Float64(-b), t, Float64(t * b))))) - t_4);
	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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+302], N[(N[(N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(N[(i * N[(N[(y * j), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[((-b) * t + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]]]]]]]

Target

Original	80.9%
Target	69.0%
Herbie	87.2%

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

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)))) < -1.0000000000000001e302

   1. Initial program 7.9%

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

   2. Simplified 7.9%

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

      [Start] 7.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      +-commutative [=>] 7.9	\[ \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      fma-def [=>] 7.9	\[ \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      *-commutative [=>] 7.9	\[ \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]
      *-commutative [=>] 7.9	\[ \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Taylor expanded in i around -inf 64.0%

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

   if -1.0000000000000001e302 < (+.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 89.9%

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

   2. Simplified 89.9%

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

      [Start] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      sub-neg [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)} \]
      distribute-rgt-in [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]
      associate-+r+ [=>] 89.9	\[ \color{blue}{\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) + \left(-y \cdot i\right) \cdot j} \]
      *-commutative [=>] 89.9	\[ \left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) + \color{blue}{j \cdot \left(-y \cdot i\right)} \]
      cancel-sign-sub [<=] 89.9	\[ \color{blue}{\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) - \left(-j\right) \cdot \left(-y \cdot i\right)} \]
      associate-+r- [<=] 89.9	\[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j - \left(-j\right) \cdot \left(-y \cdot i\right)\right)} \]
      *-commutative [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j - \left(-j\right) \cdot \left(-y \cdot i\right)\right) \]
      cancel-sign-sub [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + j \cdot \left(-y \cdot i\right)\right)} \]
      *-commutative [<=] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j + \color{blue}{\left(-y \cdot i\right) \cdot j}\right) \]
      distribute-rgt-in [<=] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j \cdot \left(c \cdot a + \left(-y \cdot i\right)\right)} \]

   3. Applied egg-rr 89.9%

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

      [Start] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]
      sub-neg [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \color{blue}{\left(a \cdot c + \left(-y \cdot i\right)\right)} \]
      distribute-rgt-in [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\left(\left(a \cdot c\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]
      +-commutative [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\left(\left(-y \cdot i\right) \cdot j + \left(a \cdot c\right) \cdot j\right)} \]
      distribute-rgt-neg-in [=>] 89.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j + \left(a \cdot c\right) \cdot j\right) \]

   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. Initial program 0.0%

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

   2. Simplified 0.0%

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

      [Start] 0.0	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      +-commutative [=>] 0.0	\[ \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      fma-def [=>] 0.0	\[ \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      *-commutative [=>] 0.0	\[ \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]
      *-commutative [=>] 0.0	\[ \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Taylor expanded in i around -inf 33.4%

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

   4. Taylor expanded in y around inf 69.9%

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

   5. Applied egg-rr 70.0%

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

      [Start] 69.9	\[ \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      prod-diff [=>] 70.0	\[ \left(-1 \cdot \left(i \cdot \color{blue}{\left(\mathsf{fma}\left(y, j, -b \cdot t\right) + \mathsf{fma}\left(-b, t, b \cdot t\right)\right)}\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      *-commutative [<=] 70.0	\[ \left(-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(y, j, -\color{blue}{t \cdot b}\right) + \mathsf{fma}\left(-b, t, b \cdot t\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      fma-neg [<=] 69.9	\[ \left(-1 \cdot \left(i \cdot \left(\color{blue}{\left(y \cdot j - t \cdot b\right)} + \mathsf{fma}\left(-b, t, b \cdot t\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      distribute-rgt-in [=>] 70.0	\[ \left(-1 \cdot \color{blue}{\left(\left(y \cdot j - t \cdot b\right) \cdot i + \mathsf{fma}\left(-b, t, b \cdot t\right) \cdot i\right)} + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      *-commutative [<=] 70.0	\[ \left(-1 \cdot \left(\color{blue}{i \cdot \left(y \cdot j - t \cdot b\right)} + \mathsf{fma}\left(-b, t, b \cdot t\right) \cdot i\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      +-commutative [=>] 70.0	\[ \left(-1 \cdot \color{blue}{\left(\mathsf{fma}\left(-b, t, b \cdot t\right) \cdot i + i \cdot \left(y \cdot j - t \cdot b\right)\right)} + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      *-commutative [<=] 70.0	\[ \left(-1 \cdot \left(\mathsf{fma}\left(-b, t, \color{blue}{t \cdot b}\right) \cdot i + i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -1 \cdot 10^{+302}:\\ \;\;\;\;\left(\left(c \cdot \left(a \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) - \left(i \cdot \left(y \cdot j - t \cdot b\right) + i \cdot \mathsf{fma}\left(-b, t, t \cdot b\right)\right)\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	87.9%
Cost	5833

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+305} \lor \neg \left(t_2 \leq \infty\right):\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + t_1\\ \end{array} \]

Alternative 2
Accuracy	87.2%
Cost	5832

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := t_3 + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_5 := c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+302}:\\ \;\;\;\;\left(\left(t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\right) + t_2\right) - t_5\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + t_1\right) + t_2\right) - t_5\\ \end{array} \]

Alternative 3
Accuracy	86.5%
Cost	5705

\[\begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+305} \lor \neg \left(t_1 \leq \infty\right):\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) - i \cdot \left(y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	87.9%
Cost	5705

\[\begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+305} \lor \neg \left(t_1 \leq \infty\right):\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	47.9%
Cost	2809

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right) + c \cdot \left(a \cdot j\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-190}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+29} \lor \neg \left(y \leq 5.8 \cdot 10^{+51}\right) \land y \leq 1.05 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	68.5%
Cost	2652

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_2 - \left(z \cdot \left(b \cdot c\right) + \left(x \cdot \left(t \cdot a\right) - x \cdot \left(y \cdot z\right)\right)\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_5 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+17}:\\ \;\;\;\;t_5 + t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-300}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + t_1\right) - i \cdot \left(y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-216}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5 + t_2\\ \end{array} \]

Alternative 7
Accuracy	64.1%
Cost	2404

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right) + t_3\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + \left(t_2 - y \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-272}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-268}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-240}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t_3\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-191}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-121}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 0.46:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \]

Alternative 8
Accuracy	52.8%
Cost	2272

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-225}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Accuracy	65.1%
Cost	2272

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right) + t_3\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ t_6 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -0.0135:\\ \;\;\;\;t_6 + t_2\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-135}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-307}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + t_2\right) - i \cdot \left(y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-268}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-233}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-217}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-7}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6 + t_3\\ \end{array} \]

Alternative 10
Accuracy	39.6%
Cost	2160

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-110}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-156}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Accuracy	41.1%
Cost	2160

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_5 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-247}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-218}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-147}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+21}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Accuracy	41.1%
Cost	2160

\[\begin{array}{l} t_1 := a \cdot j - z \cdot b\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_6 := c \cdot t_1\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-8}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-175}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-247}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-218}:\\ \;\;\;\;\frac{c}{\frac{1}{t_1}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-148}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-113}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+19}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 13
Accuracy	44.4%
Cost	2148

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right) + c \cdot \left(a \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -32000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Accuracy	63.3%
Cost	2140

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;t_4 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4 + t_1\\ \end{array} \]

Alternative 15
Accuracy	63.5%
Cost	2140

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right) + t_2\\ t_5 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;t_5 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-296}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-268}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-216}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-46}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5 + t_1\\ \end{array} \]

Alternative 16
Accuracy	61.7%
Cost	2008

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+16}:\\ \;\;\;\;t_3 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-217}:\\ \;\;\;\;t_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + t_1\\ \end{array} \]

Alternative 17
Accuracy	41.3%
Cost	1764

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 18
Accuracy	41.9%
Cost	1764

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Accuracy	41.5%
Cost	1764

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-8}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 20
Accuracy	30.0%
Cost	1500

\[\begin{array}{l} t_1 := \left(x \cdot a\right) \cdot \left(-t\right)\\ t_2 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Accuracy	39.7%
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 90000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 22
Accuracy	20.6%
Cost	1308

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;a \leq -1.56 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Accuracy	38.1%
Cost	1236

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 96000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Accuracy	36.0%
Cost	1104

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-293}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 3350000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Accuracy	21.2%
Cost	1044

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+197}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+284}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Accuracy	21.4%
Cost	1044

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+194}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{+297}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 27
Accuracy	21.8%
Cost	912

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 19000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+193}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Accuracy	19.8%
Cost	649

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-145} \lor \neg \left(t \leq 4.8 \cdot 10^{-116}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 29
Accuracy	16.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq 3.9 \cdot 10^{+160} \lor \neg \left(c \leq 1.06 \cdot 10^{+297}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 30
Accuracy	17.1%
Cost	452

\[\begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+63}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 31
Accuracy	16.2%
Cost	320

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

Reproduce

herbie shell --seed 2023130 
(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)))))