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

Average Error: 12.0 → 5.5

Time: 1.2min

Precision: binary64

Cost: 11336

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(c, a \cdot j - z \cdot b, i \cdot \left(t \cdot b - y \cdot j\right)\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := \left(t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + t_3\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_3 + \left(t_2 + \left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (fma c (- (* a j) (* z b)) (* i (- (* t b) (* y j)))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ (+ t_2 (* b (- (* t i) (* z c)))) t_3)))
   (if (<= t_4 (- INFINITY))
     t_1
     (if (<= t_4 2e+304)
       (+ t_3 (+ t_2 (- (* b (* t i)) (* b (* z c)))))
       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 = fma(c, ((a * j) - (z * b)), (i * ((t * b) - (y * j))));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (t_2 + (b * ((t * i) - (z * c)))) + t_3;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_4 <= 2e+304) {
		tmp = t_3 + (t_2 + ((b * (t * i)) - (b * (z * c))));
	} 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 = fma(c, Float64(Float64(a * j) - Float64(z * b)), Float64(i * Float64(Float64(t * b) - Float64(y * j))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + t_3)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_4 <= 2e+304)
		tmp = Float64(t_3 + Float64(t_2 + Float64(Float64(b * Float64(t * i)) - Float64(b * Float64(z * c)))));
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$1, If[LessEqual[t$95$4, 2e+304], N[(t$95$3 + N[(t$95$2 + N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Target

Original	12.0
Target	19.7
Herbie	5.5

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

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)))) < -inf.0 or 1.9999999999999999e304 < (+.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 62.3

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

   2. Simplified 62.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), \mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, t \cdot i\right), j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]
      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)))))): 0 points increase in error, 0 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)))))): 1 points increase in error, 1 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 x around 0 56.6

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

   4. Simplified 26.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, j \cdot a - b \cdot z, i \cdot \left(b \cdot t - j \cdot y\right)\right)} \]
      Proof
      (fma.f64 c (-.f64 (*.f64 j a) (*.f64 b z)) (*.f64 i (-.f64 (*.f64 b t) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 a j)) (*.f64 b z)) (*.f64 i (-.f64 (*.f64 b t) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (-.f64 (*.f64 a j) (Rewrite=> *-commutative_binary64 (*.f64 z b))) (*.f64 i (-.f64 (*.f64 b t) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 a j) (neg.f64 (*.f64 z b)))) (*.f64 i (-.f64 (*.f64 b t) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 z b)))) (*.f64 i (-.f64 (*.f64 b t) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 t b)) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (-.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (*.f64 t b)))) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (-.f64 (neg.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 t b)))) (*.f64 j y)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (-.f64 (neg.f64 (*.f64 -1 (*.f64 t b))) (Rewrite<= *-commutative_binary64 (*.f64 y j))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 (*.f64 -1 (*.f64 t b))) (neg.f64 (*.f64 y j)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (*.f64 -1 (*.f64 t b)) (*.f64 y j)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (*.f64 i (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b))) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 c (+.f64 (*.f64 a j) (*.f64 -1 (*.f64 z b)))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b)))))): 2 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 c (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 z b)) (*.f64 a j)))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 c (*.f64 -1 (*.f64 z b))) (*.f64 c (*.f64 a j)))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))): 1 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 c (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 z b)))) (*.f64 c (*.f64 a j))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 c (*.f64 z b)))) (*.f64 c (*.f64 a j))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 c (*.f64 z b)))) (*.f64 c (*.f64 a j))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 -1 (*.f64 c (Rewrite<= *-commutative_binary64 (*.f64 b z)))) (*.f64 c (*.f64 a j))) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate--l+_binary64 (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (*.f64 i (+.f64 (*.f64 y j) (*.f64 -1 (*.f64 t b))))))): 0 points increase in error, 1 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (*.f64 i (+.f64 (*.f64 y j) (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 t b))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (*.f64 i (Rewrite=> unsub-neg_binary64 (-.f64 (*.f64 y j) (*.f64 t b)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 i (*.f64 y j)) (*.f64 i (*.f64 t b)))))): 1 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (-.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 i y) j)) (*.f64 i (*.f64 t b))))): 19 points increase in error, 12 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (-.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 y i)) j) (*.f64 i (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (-.f64 (*.f64 c (*.f64 a j)) (-.f64 (Rewrite<= associate-*r*_binary64 (*.f64 y (*.f64 i j))) (*.f64 i (*.f64 t b))))): 13 points increase in error, 27 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 c (*.f64 a j)) (*.f64 y (*.f64 i j))) (*.f64 i (*.f64 t b))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (+.f64 (-.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 c a) j)) (*.f64 y (*.f64 i j))) (*.f64 i (*.f64 t b)))): 20 points increase in error, 20 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (+.f64 (-.f64 (*.f64 (*.f64 c a) j) (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 y i) j))) (*.f64 i (*.f64 t b)))): 26 points increase in error, 15 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (+.f64 (Rewrite=> distribute-rgt-out--_binary64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) (*.f64 i (*.f64 t b)))): 2 points increase in error, 2 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 i (*.f64 t b)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 -1 (*.f64 c (*.f64 b z))) (*.f64 i (*.f64 t b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 i (*.f64 t b)) (*.f64 -1 (*.f64 c (*.f64 b z))))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 i (*.f64 t b)) (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 c (*.f64 b z))))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> unsub-neg_binary64 (-.f64 (*.f64 i (*.f64 t b)) (*.f64 c (*.f64 b z)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (*.f64 i (*.f64 t b)) (*.f64 c (Rewrite=> *-commutative_binary64 (*.f64 z b)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (*.f64 i (*.f64 t b)) (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 c z) b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 15 points increase in error, 12 points decrease in error
      (+.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (*.f64 i (*.f64 t b)) (*.f64 (neg.f64 (*.f64 c z)) b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 i t) b)) (*.f64 (neg.f64 (*.f64 c z)) b)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 9 points increase in error, 17 points decrease in error
      (+.f64 (+.f64 (*.f64 (*.f64 i t) b) (*.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 c z))) b)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 b (+.f64 (*.f64 i t) (*.f64 -1 (*.f64 c z))))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 1 points increase in error, 1 points decrease in error
      (+.f64 (*.f64 b (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 c z)) (*.f64 i t)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))): 0 points increase in error, 0 points decrease in error

   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)))) < 1.9999999999999999e304

   1. Initial program 0.8

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

   2. Applied egg-rr 0.8

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

4. Final simplification 5.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(c, a \cdot j - z \cdot b, i \cdot \left(t \cdot b - y \cdot j\right)\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, a \cdot j - z \cdot b, i \cdot \left(t \cdot b - y \cdot j\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	8.4
Cost	5832

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := \left(t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_2 + \left(t_1 + \left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 2
Error	8.4
Cost	5704

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 3
Error	22.8
Cost	3460

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_5 := \left(t_4 + y \cdot \left(x \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ t_6 := t_4 + t_2\\ t_7 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+120}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -2.815784963325257 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.0296737713101362 \cdot 10^{-51}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -5.542534147571649 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.2636757519280244 \cdot 10^{-84}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -2.296171259647786 \cdot 10^{-93}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -6.005723993579189 \cdot 10^{-108}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq -1.1098484556652816 \cdot 10^{-113}:\\ \;\;\;\;t_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq -5.681949481132866 \cdot 10^{-115}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -7.271542124392322 \cdot 10^{-143}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + \left(t_4 - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -9.22658146427795 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.795512306924226 \cdot 10^{-208}:\\ \;\;\;\;t_4 + t_7\\ \mathbf{elif}\;x \leq 8.309623005170098 \cdot 10^{-148}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.381780747057946 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + t_1\\ \mathbf{elif}\;x \leq 1.805462333997763 \cdot 10^{-45}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 2.971646240226075 \cdot 10^{-36}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 4
Error	34.0
Cost	2940

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := t_2 + c \cdot \left(a \cdot j\right)\\ t_4 := t_2 - c \cdot \left(z \cdot b\right)\\ t_5 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+100}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -270000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.1396697271264696 \cdot 10^{-68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.0603067942543728 \cdot 10^{-128}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6.464090258691645 \cdot 10^{-215}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.0940645339824377 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -6.10883249103892 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 5.741212834656993 \cdot 10^{-293}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 2.096419477269056 \cdot 10^{-241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.0783882770484756 \cdot 10^{-192}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.6901226030685482 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9.998702501700303 \cdot 10^{-140}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+86}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	34.7
Cost	2940

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - x \cdot \left(t \cdot a\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := t_3 + c \cdot \left(a \cdot j\right)\\ t_5 := t_3 - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -3.45 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+100}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -270000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.1396697271264696 \cdot 10^{-68}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.0603067942543728 \cdot 10^{-128}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -6.464090258691645 \cdot 10^{-215}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.0940645339824377 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -4.4287425669466105 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.741212834656993 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.096419477269056 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.0783882770484756 \cdot 10^{-192}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.6901226030685482 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9.998702501700303 \cdot 10^{-140}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 6
Error	28.5
Cost	2932

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_5 := t_4 + t_2\\ t_6 := t_4 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -65000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.156515502027743 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.0832217816906406 \cdot 10^{-145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.0662097359000225 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -3.8250971846137545 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.234441740500238 \cdot 10^{-306}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 5.741212834656993 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1843845280949329 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6414451524804885 \cdot 10^{-189}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.998702501700303 \cdot 10^{-140}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 10^{+68}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 10^{+255}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 7
Error	38.3
Cost	2688

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j\right) - i \cdot \left(y \cdot j\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_5 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3857101788273107 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -2.77964514299712 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -8.26336253650246 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.1022973167407394 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4476217894951346 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq -3.823361155573799 \cdot 10^{-259}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.193042958622137 \cdot 10^{-270}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 4.452969642898109 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.686901396142544 \cdot 10^{-132}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.503675578749619 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5981765252571477 \cdot 10^{-71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.0306629107245105 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-11}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	38.4
Cost	2688

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j\right) - i \cdot \left(y \cdot j\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3857101788273107 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -2.77964514299712 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -8.26336253650246 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.1022973167407394 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4476217894951346 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -3.823361155573799 \cdot 10^{-259}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.193042958622137 \cdot 10^{-270}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.452969642898109 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.686901396142544 \cdot 10^{-132}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.503675578749619 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5981765252571477 \cdot 10^{-71}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.0306629107245105 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-11}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 9
Error	36.3
Cost	2556

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right) - c \cdot \left(z \cdot b\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+174}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1450000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.139164463802876 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.26336253650246 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.060809211643969 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.4476217894951346 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.823361155573799 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.193042958622137 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.452969642898109 \cdot 10^{-205}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.513890016644629 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0616164595390893 \cdot 10^{-121}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.751918244086902 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9302894860037721 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	34.2
Cost	2412

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := t_2 + c \cdot \left(a \cdot j\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_6 := t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+168}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq -2.015904538487739 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.249104696147614 \cdot 10^{-253}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -3.735672417168185 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.7738763851245737 \cdot 10^{-297}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 3.2856248461059233 \cdot 10^{-271}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.8692483669332312 \cdot 10^{-165}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 9.078893762443148 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+78}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+124}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	21.8
Cost	2404

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := i \cdot \left(t \cdot b\right) + \left(t_3 - a \cdot \left(x \cdot t\right)\right)\\ t_5 := t_3 + t_1\\ \mathbf{if}\;x \leq -1 \cdot 10^{+120}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -2.815784963325257 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.34444296017272 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.681949481132866 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -7.271542124392322 \cdot 10^{-143}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8.610361923397159 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.971646240226075 \cdot 10^{-36}:\\ \;\;\;\;t_3 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{+215}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	38.0
Cost	2160

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_5 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3857101788273107 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -2.77964514299712 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -8.26336253650246 \cdot 10^{-168}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -8.436007912711337 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.7327115545772705 \cdot 10^{-233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.214693267148771 \cdot 10^{-218}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.751918244086902 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.9302894860037721 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0481872703280851 \cdot 10^{-49}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	39.5
Cost	2156

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -6 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{+17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.4576940292790353 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.6300513085196546 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -4.225481872424633 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.8713202595405874 \cdot 10^{-277}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.104335265601134 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.540095285173453 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.5468124381137387 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.02 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 14
Error	40.1
Cost	2028

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -6 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{+17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.4576940292790353 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.6300513085196546 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -4.225481872424633 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.8713202595405874 \cdot 10^{-277}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.104335265601134 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.540095285173453 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.5468124381137387 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.02 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 15
Error	25.0
Cost	2008

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := t_1 - c \cdot \left(z \cdot b\right)\\ t_3 := t_1 + c \cdot \left(a \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;i \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -6 \cdot 10^{+30}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.715857387106667 \cdot 10^{-138}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+27}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+127}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	22.4
Cost	1876

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t_3 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq -1.445775911834345 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 7.806923859089461 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3 - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 17
Error	45.9
Cost	1632

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.05 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.36 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -6.553073243773237 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq -6.492224026500633 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.209459849008553 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.6678058458061918 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	33.2
Cost	1620

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;j \leq -6.553073243773237 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.541162638779293 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -6.492224026500633 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4196016471039257 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.565923786395885 \cdot 10^{-106}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	37.5
Cost	1500

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.22 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -8.553132296568512 \cdot 10^{-154}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.541162638779293 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -6.492224026500633 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.4196016471039257 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8.377161805893925 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.346567626132523 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	49.6
Cost	1376

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.566356436984692 \cdot 10^{-38}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq -1.3061638971079957 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.352346715194776 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.8633127802503775 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.808505916982052 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	50.2
Cost	1376

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.0610151586592926 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.3061638971079957 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.352346715194776 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.8633127802503775 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.808505916982052 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	50.2
Cost	1376

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.0610151586592926 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.3061638971079957 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.352346715194776 \cdot 10^{-227}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.8633127802503775 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.808505916982052 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	42.4
Cost	1368

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.459962056747987 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.352346715194776 \cdot 10^{-227}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.8633127802503775 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 2.9528345737719788 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	38.3
Cost	1368

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.22 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -8.553132296568512 \cdot 10^{-154}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.541162638779293 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -6.492224026500633 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.209459849008553 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.649783196637432 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	49.5
Cost	1112

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.566356436984692 \cdot 10^{-38}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq -4.070269713407024 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.808505916982052 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Error	38.0
Cost	1104

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -480000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.492224026500633 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.209459849008553 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.649783196637432 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	49.9
Cost	848

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.4576940292790353 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.6300513085196546 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 28
Error	49.6
Cost	848

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -4.459962056747987 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 3.85 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 29
Error	49.5
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -4.459962056747987 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.437184667871764 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.808505916982052 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 30
Error	52.7
Cost	584

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -3.0000456250045086 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 10^{+110}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 31
Error	49.6
Cost	584

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -7.865854586409433 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 32
Error	53.6
Cost	320

\[i \cdot \left(t \cdot b\right) \]

Reproduce

herbie shell --seed 2022316 
(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)))))