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

Average Error: 12.0 → 4.6

Time: 1.5min

Precision: binary64

Cost: 44168

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot t_2\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right), \mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, t \cdot i\right), \mathsf{fma}\left(t_2, j, j \cdot \mathsf{fma}\left(y, -i, y \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
         (-
          (+ (+ (* y (* x z)) (* c (* a j))) (* t (- (* b i) (* x a))))
          (* c (* z b))))
        (t_2 (- (* a c) (* y i)))
        (t_3
         (+
          (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z))))
          (* j t_2))))
   (if (<= t_3 -2e+307)
     t_1
     (if (<= t_3 1e+300)
       (fma
        x
        (fma y z (* t (- a)))
        (fma b (fma z (- c) (* t i)) (fma t_2 j (* j (fma y (- i) (* y i))))))
       t_1))))

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 = (((y * (x * z)) + (c * (a * j))) + (t * ((b * i) - (x * a)))) - (c * (z * b));
	double t_2 = (a * c) - (y * i);
	double t_3 = ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))) + (j * t_2);
	double tmp;
	if (t_3 <= -2e+307) {
		tmp = t_1;
	} else if (t_3 <= 1e+300) {
		tmp = fma(x, fma(y, z, (t * -a)), fma(b, fma(z, -c, (t * i)), fma(t_2, j, (j * fma(y, -i, (y * i))))));
	} else {
		tmp = t_1;
	}
	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(Float64(Float64(Float64(y * Float64(x * z)) + Float64(c * Float64(a * j))) + Float64(t * Float64(Float64(b * i) - Float64(x * a)))) - Float64(c * Float64(z * b)))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * t_2))
	tmp = 0.0
	if (t_3 <= -2e+307)
		tmp = t_1;
	elseif (t_3 <= 1e+300)
		tmp = fma(x, fma(y, z, Float64(t * Float64(-a))), fma(b, fma(z, Float64(-c), Float64(t * i)), fma(t_2, j, Float64(j * fma(y, Float64(-i), Float64(y * i))))));
	else
		tmp = t_1;
	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[(N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+307], t$95$1, If[LessEqual[t$95$3, 1e+300], N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * (-c) + N[(t * i), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * j + N[(j * N[(y * (-i) + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Target

Original	12.0
Target	19.7
Herbie	4.6

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

Derivation

1. Split input into 2 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)))) < -1.99999999999999997e307 or 1.0000000000000001e300 < (+.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 59.3

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

   2. Simplified 59.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), \mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, t \cdot i\right), j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]
      Proof
      (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (fma.f64 y z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a t)))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (fma.f64 y z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 t a)))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) (*.f64 t a))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 z (neg.f64 c)) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z c))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c a)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 1 points increase in error, 1 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (neg.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 2 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.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))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in y around 0 49.6

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

   4. Taylor expanded in t around 0 20.4

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

   if -1.99999999999999997e307 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 1.0000000000000001e300

   1. Initial program 0.9

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

   2. Simplified 0.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), \mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, t \cdot i\right), j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]
      Proof
      (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (fma.f64 y z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a t)))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (fma.f64 y z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 t a)))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) (*.f64 t a))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 z (neg.f64 c)) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z c))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c a)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 1 points increase in error, 1 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (neg.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 2 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.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))))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 0.8

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), \mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, t \cdot i\right), \color{blue}{\mathsf{fma}\left(a \cdot c - y \cdot i, j, \mathsf{fma}\left(y, -i, y \cdot i\right) \cdot j\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 4.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -2 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;\left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right), \mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, t \cdot i\right), \mathsf{fma}\left(a \cdot c - y \cdot i, j, j \cdot \mathsf{fma}\left(y, -i, y \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.6
Cost	19208

\[\begin{array}{l} t_1 := \left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := a \cdot c - y \cdot i\\ t_4 := t_2 + j \cdot t_3\\ \mathbf{if}\;t_4 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq 10^{+300}:\\ \;\;\;\;t_2 + \left(\mathsf{fma}\left(t_3, j, j \cdot \mathsf{fma}\left(y, -i, y \cdot i\right)\right) + j \cdot 0\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	4.6
Cost	12680

\[\begin{array}{l} t_1 := \left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := t_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 10^{+300}:\\ \;\;\;\;t_2 + \left(j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	4.6
Cost	5832

\[\begin{array}{l} t_1 := \left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := t_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 10^{+300}:\\ \;\;\;\;t_2 + \left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	6.3
Cost	5704

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + t_3\\ \mathbf{if}\;t_4 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t_3 + \left(t_1 - t_2\right)\\ \mathbf{elif}\;t_4 \leq 10^{+300}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(y \cdot \left(x \cdot z\right) - t_2\right)\\ \end{array} \]

Alternative 5
Error	4.6
Cost	5704

\[\begin{array}{l} t_1 := \left(\left(y \cdot \left(x \cdot z\right) + c \cdot \left(a \cdot j\right)\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ t_2 := \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+300}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	34.7
Cost	4128

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := 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 \cdot \left(b \cdot i\right)\\ t_5 := i \cdot \left(t \cdot b\right)\\ t_6 := t_3 + t_5\\ t_7 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_8 := t_2 - a \cdot \left(x \cdot t\right)\\ t_9 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_10 := c \cdot \left(a \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ t_11 := t_5 + t_7\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;i \leq -7.579606184495105 \cdot 10^{-32}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;i \leq -6.258680621873061 \cdot 10^{-102}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;i \leq -1.5770449165296336 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - t_1\\ \mathbf{elif}\;i \leq -6.02205901245257 \cdot 10^{-212}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;i \leq -1.8398078227819646 \cdot 10^{-241}:\\ \;\;\;\;t_3 - t_1\\ \mathbf{elif}\;i \leq -1.3990373552139681 \cdot 10^{-263}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;i \leq -3.0211866819812733 \cdot 10^{-273}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;i \leq -4.857250175219709 \cdot 10^{-307}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 3.2294614518953356 \cdot 10^{-299}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq 7.158570323265279 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.496210992290998 \cdot 10^{-163}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;i \leq 1.4825294741095354 \cdot 10^{-126}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;i \leq 8.626675083141574 \cdot 10^{-98}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 9.663054486945432 \cdot 10^{-56}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.4842550662084083 \cdot 10^{-44}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;i \leq 10^{-17}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+71}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;i \leq 9.1 \cdot 10^{+89}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 10^{+142}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array} \]

Alternative 7
Error	35.3
Cost	3336

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_3 + t_1\\ t_5 := t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := t_3 - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{+147}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -4.1 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.579606184495105 \cdot 10^{-32}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -6.258680621873061 \cdot 10^{-102}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-116}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -5.42572184890903 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -1.8398078227819646 \cdot 10^{-241}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.3990373552139681 \cdot 10^{-263}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 8.159071889672203 \cdot 10^{-303}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 2.496210992290998 \cdot 10^{-163}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 2.4842550662084083 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 10^{-17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+71}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 9.1 \cdot 10^{+89}:\\ \;\;\;\;t_3 + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	26.7
Cost	3324

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := t_4 + \left(y \cdot \left(x \cdot z\right) - t_2\right)\\ t_6 := c \cdot \left(a \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ t_7 := i \cdot \left(t \cdot b\right)\\ t_8 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_9 := t_3 + t_8\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;t_7 + t_8\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+97}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{+61}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -7.579606184495105 \cdot 10^{-32}:\\ \;\;\;\;t_3 - t_2\\ \mathbf{elif}\;i \leq -6.258680621873061 \cdot 10^{-102}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-116}:\\ \;\;\;\;t_3 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 7.158570323265279 \cdot 10^{-295}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 4.526057038218826 \cdot 10^{-204}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq 1.4825294741095354 \cdot 10^{-126}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq 9.1 \cdot 10^{+89}:\\ \;\;\;\;t_4 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{+129}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+161}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+191}:\\ \;\;\;\;t_7 + \left(t_8 - t_2\right)\\ \mathbf{elif}\;i \leq 3.45 \cdot 10^{+239}:\\ \;\;\;\;t_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 9
Error	36.3
Cost	3072

\[\begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := i \cdot \left(t \cdot b\right) + t_4\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -3.9051270306434273 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -4.739656223881401 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.358781593698852 \cdot 10^{-204}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.661992453744347 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8708997919782233 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2869893976617917 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5256573529218883 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.4470941473621745 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.001281285823762 \cdot 10^{-166}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 6.282999355733142 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 3.244311648182292 \cdot 10^{-114}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 2.4505603108650445 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+152}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	30.4
Cost	3064

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_4 := c \cdot \left(a \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ t_5 := i \cdot \left(t \cdot b\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -7.579606184495105 \cdot 10^{-32}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -6.258680621873061 \cdot 10^{-102}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.5770449165296336 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - t_1\\ \mathbf{elif}\;i \leq -2.8400424731280784 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -7.622167211349627 \cdot 10^{-195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.8398078227819646 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t_1\\ \mathbf{elif}\;i \leq -1.3990373552139681 \cdot 10^{-263}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -3.0211866819812733 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq -4.857250175219709 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.4199436192674272 \cdot 10^{-217}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.496210992290998 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	34.5
Cost	2940

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 + t \cdot \left(b \cdot i\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ t_4 := t_1 + t_3\\ t_5 := t_3 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+97}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -2.247729045851862 \cdot 10^{-64}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -1.752012104723534 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.661992453744347 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.0970430927573293 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.628839411676377 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.244311648182292 \cdot 10^{-114}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.3585426713013636 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4505603108650445 \cdot 10^{-57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+44}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+140}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+140}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+168}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 12
Error	33.9
Cost	2804

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - c \cdot \left(z \cdot b\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ t_4 := t_3 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+97}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -3.9051270306434273 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.661992453744347 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.0970430927573293 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6364865714616326 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.244311648182292 \cdot 10^{-114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.4505603108650445 \cdot 10^{-57}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+88}:\\ \;\;\;\;t_1 + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+140}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+168}:\\ \;\;\;\;t_3 - \left(j \cdot \left(y \cdot i\right) - j \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 13
Error	27.3
Cost	2796

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + t_2\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := t_4 + \left(y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\right)\\ t_6 := i \cdot \left(t \cdot b\right) + \left(t_2 - y \cdot \left(i \cdot j\right)\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+161}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-14}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -3.085661659674361 \cdot 10^{-69}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -5.132787686709257 \cdot 10^{-138}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -3.0057152795389882 \cdot 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.0340946423759524 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5817435159544295 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.58815520457468 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;t_4 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 14
Error	26.0
Cost	2796

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := t_4 + \left(y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\right)\\ t_6 := i \cdot \left(t \cdot b\right) + \left(t_1 - y \cdot \left(i \cdot j\right)\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+161}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-14}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -3.085661659674361 \cdot 10^{-69}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c\right) - j \cdot \left(y \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -5.132787686709257 \cdot 10^{-138}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -9.880904296714906 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.841397507116138 \cdot 10^{-273}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_3\\ \mathbf{elif}\;y \leq 4.5817435159544295 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.58815520457468 \cdot 10^{-98}:\\ \;\;\;\;t_3 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;t_4 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 15
Error	33.9
Cost	2676

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - c \cdot \left(z \cdot b\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ t_4 := t_3 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+97}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -3.9051270306434273 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.661992453744347 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.0970430927573293 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6364865714616326 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.244311648182292 \cdot 10^{-114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.4505603108650445 \cdot 10^{-57}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+88}:\\ \;\;\;\;t_1 + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+140}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+168}:\\ \;\;\;\;t_1 + t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 16
Error	35.0
Cost	2544

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ t_3 := t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+97}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.9051270306434273 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.661992453744347 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.0970430927573293 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.628839411676377 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.244311648182292 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.3585426713013636 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4505603108650445 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+168}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 17
Error	23.3
Cost	2400

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b\right) + \left(t_1 - c \cdot \left(z \cdot b\right)\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6533703561405348 \cdot 10^{-74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.779114772841107 \cdot 10^{-279}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 4.610067618302939 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.4394045535856612 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 10^{+230}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	18.2
Cost	2392

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_3 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := t_3 + \left(t_2 - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+180}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 3.4230093734864167 \cdot 10^{-230}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.2855044980589127 \cdot 10^{-191}:\\ \;\;\;\;t_3 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;t_2 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	38.4
Cost	2292

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -3.108628862529143 \cdot 10^{-95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.2708285236269614 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -8.37891913980081 \cdot 10^{-226}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -4.019531645384025 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.06977029627003 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.746618925207967 \cdot 10^{-232}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.0763932211148114 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0619468743201336 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 20
Error	38.5
Cost	2292

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.108628862529143 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2708285236269614 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -8.37891913980081 \cdot 10^{-226}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -4.019531645384025 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.06977029627003 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.746618925207967 \cdot 10^{-232}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.0763932211148114 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.033142547375608 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5702632127589215 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 21
Error	38.1
Cost	2292

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.108628862529143 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2708285236269614 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -8.37891913980081 \cdot 10^{-226}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -2.33649682031079 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.127562696041552 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.0763932211148114 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.033142547375608 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0031436028793267 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.0200359214454824 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 22
Error	35.4
Cost	2280

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9051270306434273 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.661992453744347 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.0970430927573293 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.628839411676377 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.244311648182292 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4505603108650445 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	37.6
Cost	2028

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.108628862529143 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2708285236269614 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -8.37891913980081 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.33649682031079 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0619468743201336 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 24
Error	20.7
Cost	1876

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -8.432329714231381 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.849475139798119 \cdot 10^{-289}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 8.490458681914663 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + \left(t_1 - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 1.2292457760495205 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	23.0
Cost	1744

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.6533703561405348 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.779114772841107 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.610067618302939 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.4394045535856612 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	49.8
Cost	1704

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.76 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.792782575558686 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -8.609244473895712 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.1643240295784745 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.372747386723321 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -2.962139298764777 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.7300042845162944 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3282951898794946 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 27
Error	42.7
Cost	1632

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.500242956413021 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -6.02205901245257 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.4165439600742225 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq 1.6937845025127608 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.85466587929063 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 1.0222438476698148 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 3.1014477350049154 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2.5796844513676858 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 28
Error	37.4
Cost	1632

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.108628862529143 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.554055239134922 \cdot 10^{-163}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -3.1552899054244004 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.33649682031079 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0619468743201336 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 29
Error	49.1
Cost	1508

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_4 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.76 \cdot 10^{+86}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.792782575558686 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -8.609244473895712 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.307349209445984 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.0110487220691512 \cdot 10^{-274}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.7300042845162944 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6500990720552266 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.2629923005028118 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 30
Error	37.4
Cost	1500

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.2708285236269614 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.1552899054244004 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.33649682031079 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0619468743201336 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 31
Error	39.2
Cost	1368

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.500242956413021 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.003700074166939 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.5897938881394505 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq 7.85466587929063 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.740960880091683 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 32
Error	38.3
Cost	1236

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.927854784779411 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.823488177117566 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1686081789673257 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 33
Error	50.1
Cost	848

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.550236154038811 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.2589640073857886 \cdot 10^{-274}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 34
Error	50.1
Cost	584

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 110000000:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	49.9
Cost	584

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 18500000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 36
Error	53.5
Cost	320

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

Reproduce

herbie shell --seed 2022300 
(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)))))