Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.1 → 4.3

Time: 58.3s

Precision: binary64

Cost: 37256

Math

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

↓

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

↓

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j)))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ (+ t_2 (* b (- (* a i) (* z c)))) (* j (- (* t c) (* y i)))))
        (t_4 (* c (* z b))))
   (if (<= t_3 (- INFINITY))
     (- (+ (+ t_1 t_2) (* i (- (* a b) (* y j)))) t_4)
     (if (<= t_3 1e+307)
       (fma
        b
        (fma z (- c) (* a i))
        (fma x (fma y z (* t (- a))) (* j (fma i (- y) (* t c)))))
       (- (- (+ t_1 (* y (* x z))) (* i (- (* y j) (* a b)))) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = (t_2 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double t_4 = c * (z * b);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((t_1 + t_2) + (i * ((a * b) - (y * j)))) - t_4;
	} else if (t_3 <= 1e+307) {
		tmp = fma(b, fma(z, -c, (a * i)), fma(x, fma(y, z, (t * -a)), (j * fma(i, -y, (t * c)))));
	} else {
		tmp = ((t_1 + (y * (x * z))) - (i * ((y * j) - (a * b)))) - t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

↓

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	t_4 = Float64(c * Float64(z * b))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(t_1 + t_2) + Float64(i * Float64(Float64(a * b) - Float64(y * j)))) - t_4);
	elseif (t_3 <= 1e+307)
		tmp = fma(b, fma(z, Float64(-c), Float64(a * i)), fma(x, fma(y, z, Float64(t * Float64(-a))), Float64(j * fma(i, Float64(-y), Float64(t * c)))));
	else
		tmp = Float64(Float64(Float64(t_1 + Float64(y * Float64(x * z))) - Float64(i * Float64(Float64(y * j) - Float64(a * b)))) - t_4);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(t$95$1 + t$95$2), $MachinePrecision] + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[t$95$3, 1e+307], N[(b * N[(z * (-c) + N[(a * i), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision] + N[(j * N[(i * (-y) + N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(y * j), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]]]]]]]

Target

Original	12.1
Target	15.8
Herbie	4.3

\[\begin{array}{l} \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 64.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
      Proof
      (fma.f64 j (-.f64 (*.f64 t c) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c t)) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c t) (Rewrite<= *-commutative_binary64 (*.f64 i y))) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c t) (*.f64 i y)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (Rewrite<= *-commutative_binary64 (*.f64 i a)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c t) (*.f64 i y)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z)) (*.f64 i a))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))))): 1 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in i around -inf 24.2

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 9.99999999999999986e306

   1. Initial program 0.8

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

   2. Simplified 0.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)} \]
      Proof
      (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (fma.f64 z (neg.f64 c) (Rewrite<= *-commutative_binary64 (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 z (neg.f64 c)) (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 2 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z c))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a t)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 t a)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (fma.f64 i (neg.f64 y) (Rewrite<= *-commutative_binary64 (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= fma-def_binary64 (+.f64 (*.f64 i (neg.f64 y)) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i y))) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 i) y)) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 2 points increase in error, 1 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))): 0 points increase in error, 0 points decrease in error

   if 9.99999999999999986e306 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 62.9

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

   2. Simplified 62.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
      Proof
      (fma.f64 j (-.f64 (*.f64 t c) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c t)) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c t) (Rewrite<= *-commutative_binary64 (*.f64 i y))) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c t) (*.f64 i y)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (Rewrite<= *-commutative_binary64 (*.f64 i a)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c t) (*.f64 i y)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z)) (*.f64 i a))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))))): 1 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in i around -inf 26.8

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

   4. Taylor expanded in y around inf 17.4

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(y \cdot j - a \cdot b\right)\right) + \left(c \cdot \left(t \cdot j\right) + \color{blue}{y \cdot \left(z \cdot x\right)}\right)\right) - c \cdot \left(b \cdot z\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 4.3

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

Alternatives

Alternative 1
Error	3.9
Cost	5832

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

Alternative 2
Error	4.3
Cost	5832

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := \left(t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + t_3\\ t_5 := c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(\left(t_1 + t_2\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - t_5\\ \mathbf{elif}\;t_4 \leq 10^{+307}:\\ \;\;\;\;t_2 + \left(t_3 + \left(b \cdot \left(a \cdot i\right) - b \cdot \left(z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t_1 + y \cdot \left(x \cdot z\right)\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) - t_5\\ \end{array} \]

Alternative 3
Error	5.7
Cost	5704

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

Alternative 4
Error	3.9
Cost	5704

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

Alternative 5
Error	20.2
Cost	3444

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + i \cdot \left(a \cdot b\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := t_2 + t_4\\ t_6 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_7 := t_2 + t_6\\ t_8 := \left(x \cdot \left(y \cdot z\right) - x \cdot \left(t \cdot a\right)\right) + \left(t_6 - c \cdot \left(z \cdot b\right)\right)\\ t_9 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{-182}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t_4\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-253}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-189}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 10^{-133}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-80}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-61}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;t_9 + t_4\\ \end{array} \]

Alternative 6
Error	41.1
Cost	2952

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_6 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+82}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -0.0002:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-122}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-282}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-217}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-137}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+209}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7
Error	41.3
Cost	2952

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := y \cdot \left(x \cdot z\right)\\ t_5 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_6 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_7 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -0.00185:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-122}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-160}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-265}:\\ \;\;\;\;t_4 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-285}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-216}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-135}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-78}:\\ \;\;\;\;t_4 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-51}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-24}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+209}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 8
Error	24.4
Cost	2932

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + t_1\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + t_1\\ t_6 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_7 := t_6 + t_4\\ \mathbf{if}\;i \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.16 \cdot 10^{+67}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-223}:\\ \;\;\;\;t_6 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-281}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+46}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	24.0
Cost	2932

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + t_1\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + t_1\\ t_6 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_7 := t_6 + t_4\\ \mathbf{if}\;i \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+65}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-16}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-54}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-115}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-223}:\\ \;\;\;\;t_6 + t_1\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-279}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 9.8 \cdot 10^{-279}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	26.9
Cost	2800

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := z \cdot \left(b \cdot c\right)\\ t_5 := t \cdot \left(c \cdot j - x \cdot a\right) + t_1\\ t_6 := t_3 + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;i \leq -2.8 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{+63}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -5.1 \cdot 10^{-197}:\\ \;\;\;\;t_3 - t_4\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-301}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-278}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - t_4\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-80}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 11
Error	41.1
Cost	2688

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_6 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-5}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-123}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-160}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-298}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 10^{-281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-217}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-140}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-51}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-27}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 12
Error	41.3
Cost	2556

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -0.00185:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-229}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-216}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-141}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 13
Error	33.0
Cost	2544

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 - j \cdot \left(y \cdot i\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+105}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-101}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.02 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-245}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+31}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4 - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 14
Error	32.0
Cost	2412

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 - j \cdot \left(y \cdot i\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := t_5 + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+88}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-101}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-228}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{-253}:\\ \;\;\;\;t_5 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-202}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4 - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 15
Error	21.9
Cost	2404

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right) + t_1\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ t_6 := i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+105}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-100}:\\ \;\;\;\;t_2 + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-105}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-104}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 16
Error	37.4
Cost	2280

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+105}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-197}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	26.5
Cost	2272

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right) + t_4\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t_4\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;t_1 + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+179}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+208}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	50.5
Cost	2232

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_4 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{+188}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-125}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 3.65 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 19
Error	44.0
Cost	2160

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-155}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+245}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	43.9
Cost	2160

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-55}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-197}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 225000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	50.8
Cost	1968

\[\begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_3 := a \cdot \left(b \cdot i\right)\\ t_4 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+16}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	34.4
Cost	1884

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t_1 + b \cdot \left(a \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -4.25 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 23
Error	50.6
Cost	1836

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-9}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-183}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+147}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	50.5
Cost	1836

\[\begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_3 := a \cdot \left(b \cdot i\right)\\ t_4 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-109}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	49.9
Cost	1836

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ t_3 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;y \leq -8.9 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+21}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-54}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 26
Error	34.9
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.36:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.22:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 27
Error	24.7
Cost	1744

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -8.9 \cdot 10^{+105}:\\ \;\;\;\;t_3 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3 - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 28
Error	50.9
Cost	1704

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-30}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 29
Error	44.5
Cost	1632

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -95000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.58 \cdot 10^{-279}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 30
Error	40.8
Cost	1632

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-225}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 31
Error	38.2
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-49}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-197}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 32
Error	50.7
Cost	1572

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 33
Error	49.8
Cost	848

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 34
Error	50.2
Cost	848

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	53.7
Cost	320

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

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))