Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.0 → 5.6

Time: 1.6min

Precision: binary64

Cost: 5832

Math

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

↓

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

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

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 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - ((x * ((t * a) - (y * z))) - (b * ((a * i) - (z * c))));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (i * (a * b)) + ((t_1 + (c * ((t * j) - (z * b)))) - (i * (y * j)));
	} else if (t_3 <= 1e+300) {
		tmp = (t_1 - ((b * (z * c)) - (b * (a * i)))) + t_2;
	} else {
		tmp = ((a * ((b * i) - (x * t))) - (c * (z * b))) + (c * (t * j));
	}
	return tmp;
}

Java

public static 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)));
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - ((x * ((t * a) - (y * z))) - (b * ((a * i) - (z * c))));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (i * (a * b)) + ((t_1 + (c * ((t * j) - (z * b)))) - (i * (y * j)));
	} else if (t_3 <= 1e+300) {
		tmp = (t_1 - ((b * (z * c)) - (b * (a * i)))) + t_2;
	} else {
		tmp = ((a * ((b * i) - (x * t))) - (c * (z * b))) + (c * (t * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

↓

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 - ((x * ((t * a) - (y * z))) - (b * ((a * i) - (z * c))))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (i * (a * b)) + ((t_1 + (c * ((t * j) - (z * b)))) - (i * (y * j)))
	elif t_3 <= 1e+300:
		tmp = (t_1 - ((b * (z * c)) - (b * (a * i)))) + t_2
	else:
		tmp = ((a * ((b * i) - (x * t))) - (c * (z * b))) + (c * (t * j))
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) - Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(i * Float64(a * b)) + Float64(Float64(t_1 + Float64(c * Float64(Float64(t * j) - Float64(z * b)))) - Float64(i * Float64(y * j))));
	elseif (t_3 <= 1e+300)
		tmp = Float64(Float64(t_1 - Float64(Float64(b * Float64(z * c)) - Float64(b * Float64(a * i)))) + t_2);
	else
		tmp = Float64(Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) - Float64(c * Float64(z * b))) + Float64(c * Float64(t * j)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

↓

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 - ((x * ((t * a) - (y * z))) - (b * ((a * i) - (z * c))));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (i * (a * b)) + ((t_1 + (c * ((t * j) - (z * b)))) - (i * (y * j)));
	elseif (t_3 <= 1e+300)
		tmp = (t_1 - ((b * (z * c)) - (b * (a * i)))) + t_2;
	else
		tmp = ((a * ((b * i) - (x * t))) - (c * (z * b))) + (c * (t * j));
	end
	tmp_2 = 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+300], N[(N[(t$95$1 - N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	12.0
Target	16.1
Herbie	5.6

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

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

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

   3. Taylor expanded in c around 0 21.5

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

   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)))) < 1.0000000000000001e300

   1. Initial program 0.7

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

   2. Applied egg-rr 0.7

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

   if 1.0000000000000001e300 < (+.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 56.9

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

   2. Taylor expanded in c around inf 50.1

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

   3. Taylor expanded in y around 0 45.0

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

   4. Simplified 29.9

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} + c \cdot \left(t \cdot j\right) \]
      Proof
      (-.f64 (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 i b) (neg.f64 (*.f64 t x))))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (+.f64 (*.f64 i b) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 t x))))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 t x)) (*.f64 i b)))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (+.f64 (*.f64 -1 (*.f64 t x)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (*.f64 i b))))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (+.f64 (*.f64 -1 (*.f64 t x)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (*.f64 i b)))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 -1 (*.f64 t x)) (*.f64 -1 (*.f64 i b))))) (*.f64 c (*.f64 z b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 a (-.f64 (*.f64 -1 (*.f64 t x)) (*.f64 -1 (*.f64 i b)))) (*.f64 c (Rewrite<= *-commutative_binary64 (*.f64 b z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (*.f64 a (*.f64 -1 (*.f64 i b))))) (*.f64 c (*.f64 b z))): 3 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (*.f64 a (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 i b))))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a (*.f64 i b))))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (neg.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 a i) b)))) (*.f64 c (*.f64 b z))): 22 points increase in error, 17 points decrease in error
      (-.f64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (neg.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 i a)) b))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (neg.f64 (Rewrite<= associate-*r*_binary64 (*.f64 i (*.f64 a b))))) (*.f64 c (*.f64 b z))): 17 points increase in error, 23 points decrease in error
      (-.f64 (-.f64 (*.f64 a (*.f64 -1 (*.f64 t x))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 i (*.f64 a b))))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 a (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 t x)))) (*.f64 -1 (*.f64 i (*.f64 a b)))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a (*.f64 t x)))) (*.f64 -1 (*.f64 i (*.f64 a b)))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 a (*.f64 t x)))) (*.f64 -1 (*.f64 i (*.f64 a b)))) (*.f64 c (*.f64 b z))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate--l-_binary64 (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (+.f64 (*.f64 -1 (*.f64 i (*.f64 a b))) (*.f64 c (*.f64 b z))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 c (*.f64 b z)) (*.f64 -1 (*.f64 i (*.f64 a b)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (+.f64 (*.f64 c (*.f64 b z)) (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 i (*.f64 a b)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (Rewrite=> unsub-neg_binary64 (-.f64 (*.f64 c (*.f64 b z)) (*.f64 i (*.f64 a b))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (-.f64 (*.f64 c (Rewrite=> *-commutative_binary64 (*.f64 z b))) (*.f64 i (*.f64 a b)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (-.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 c z) b)) (*.f64 i (*.f64 a b)))): 24 points increase in error, 17 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (-.f64 (*.f64 (*.f64 c z) b) (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 i a) b)))): 23 points increase in error, 18 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (Rewrite=> distribute-rgt-out--_binary64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))): 2 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (*.f64 c z) (*.f64 i a)) b))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 5.6

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

Alternatives

Alternative 1
Error	5.2
Cost	5832

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

Alternative 2
Error	5.2
Cost	5704

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

Alternative 3
Error	23.8
Cost	3452

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := i \cdot \left(a \cdot b\right) + \left(\left(t_2 + z \cdot \left(x \cdot y\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := c \cdot \left(z \cdot b\right)\\ t_6 := \left(a \cdot \left(b \cdot i - x \cdot t\right) - t_5\right) + t_2\\ t_7 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_8 := t_4 + t_7\\ t_9 := t_2 + \left(t_7 - t_5\right)\\ t_10 := t_2 + \left(t_1 + y \cdot \left(x \cdot z\right)\right)\\ t_11 := t_1 + t_7\\ \mathbf{if}\;a \leq -169.63809670639523:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -2.603075684672899 \cdot 10^{-39}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;a \leq -2.1351396560312043 \cdot 10^{-59}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;a \leq -1.5776174293011505 \cdot 10^{-84}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -1.869930869973559 \cdot 10^{-180}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;a \leq -2.9033262989126225 \cdot 10^{-235}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;a \leq -5.211439362386129 \cdot 10^{-254}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;a \leq 5.905357376896127 \cdot 10^{-273}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;a \leq 1.2764714523461791 \cdot 10^{-228}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;a \leq 6.830563249519569 \cdot 10^{-163}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;a \leq 4.013682774704362 \cdot 10^{-91}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;a \leq 9.925884193903745 \cdot 10^{-70}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;a \leq 1.7516207686111942 \cdot 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.87639156326199 \cdot 10^{-32}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 4
Error	25.3
Cost	2664

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(z \cdot b\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + b \cdot \left(a \cdot i\right)\\ t_6 := c \cdot \left(t \cdot j\right)\\ t_7 := t_6 + \left(t_2 + y \cdot \left(x \cdot z\right)\right)\\ t_8 := t_6 + \left(t_1 - t_3\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+132}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{+76}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{+76}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2.307962160699151 \cdot 10^{-262}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i - x \cdot t\right) - t_3\right) + t_6\\ \mathbf{elif}\;j \leq 1.8782303385238037 \cdot 10^{-227}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;j \leq 6.486952100921755 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - t_3\\ \mathbf{elif}\;j \leq 2.9203025316786515 \cdot 10^{-82}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;j \leq 1.1535283192728654 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-19}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+97}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_4 - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 5
Error	22.6
Cost	2664

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_1 + t_2\\ t_4 := c \cdot \left(t \cdot j\right)\\ t_5 := c \cdot \left(z \cdot b\right)\\ t_6 := \left(a \cdot \left(b \cdot i - x \cdot t\right) - t_5\right) + t_4\\ t_7 := t_4 + \left(t_2 - t_5\right)\\ t_8 := j \cdot \left(t \cdot c - y \cdot i\right) + t_1\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq -6.620309217779688 \cdot 10^{-292}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.7852344413302353 \cdot 10^{-220}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x \leq 2.473278512771501 \cdot 10^{-159}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.1618552692232362 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.049677581530032 \cdot 10^{-98}:\\ \;\;\;\;t_4 + \left(t_1 + y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.3848080497166967 \cdot 10^{-10}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 10^{+210}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	23.6
Cost	2664

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ t_4 := c \cdot \left(z \cdot b\right)\\ t_5 := \left(a \cdot \left(b \cdot i - x \cdot t\right) - t_4\right) + t_3\\ t_6 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_7 := t_2 + t_6\\ t_8 := t_3 + \left(t_1 + y \cdot \left(x \cdot z\right)\right)\\ t_9 := t_1 + t_6\\ \mathbf{if}\;a \leq -169.63809670639523:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.603075684672899 \cdot 10^{-39}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq -2.1351396560312043 \cdot 10^{-59}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;a \leq -1.5776174293011505 \cdot 10^{-84}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -1.869930869973559 \cdot 10^{-180}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;a \leq -2.9033262989126225 \cdot 10^{-235}:\\ \;\;\;\;t_3 + \left(t_6 - t_4\right)\\ \mathbf{elif}\;a \leq -5.211439362386129 \cdot 10^{-254}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;a \leq 5.905357376896127 \cdot 10^{-273}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 1.2764714523461791 \cdot 10^{-228}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;a \leq 2.7285875550081638 \cdot 10^{-115}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 7
Error	18.9
Cost	2656

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := \left(t_4 + t_2\right) + t_3\\ t_6 := i \cdot \left(a \cdot b\right) + \left(\left(t_3 + z \cdot \left(x \cdot y\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{if}\;x \leq -1.8193897703541017 \cdot 10^{-87}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.2278762374241096 \cdot 10^{-241}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i - x \cdot t\right) - c \cdot \left(z \cdot b\right)\right) + t_3\\ \mathbf{elif}\;x \leq 4.325222157184275 \cdot 10^{-243}:\\ \;\;\;\;t_4 + \left(t_3 - y \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.7852344413302353 \cdot 10^{-220}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.430159834168625 \cdot 10^{-98}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+43}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+79}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 10^{+190}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 8
Error	19.0
Cost	2392

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(i \cdot j\right)\\ t_3 := c \cdot \left(z \cdot b\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := t_4 + t_1\\ t_6 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;b \leq -4.750584364274267 \cdot 10^{-82}:\\ \;\;\;\;t_5 + t_6\\ \mathbf{elif}\;b \leq -1.1282453790667103 \cdot 10^{-186}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i - x \cdot t\right) - t_3\right) + t_6\\ \mathbf{elif}\;b \leq 3.588879425984884 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t_1\\ \mathbf{elif}\;b \leq 2.464132117376915 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + \left(\left(t_6 + z \cdot \left(x \cdot y\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.563161195166431 \cdot 10^{-89}:\\ \;\;\;\;t_6 + \left(t_1 - t_3\right)\\ \mathbf{elif}\;b \leq 10^{+45}:\\ \;\;\;\;t_5 - t_2\\ \mathbf{else}:\\ \;\;\;\;t_4 + \left(t_6 - t_2\right)\\ \end{array} \]

Alternative 9
Error	34.4
Cost	2292

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 - t_1\\ t_4 := t_2 + b \cdot \left(a \cdot i\right)\\ t_5 := c \cdot \left(t \cdot j\right)\\ t_6 := t_5 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_7 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+36}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq -4.755065832622301 \cdot 10^{-142}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -1.6963385250109436 \cdot 10^{-188}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -6.620309217779688 \cdot 10^{-292}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.7852344413302353 \cdot 10^{-220}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.430159834168625 \cdot 10^{-98}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + t_5\\ \mathbf{elif}\;x \leq 8.811355858127044 \cdot 10^{-95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.9579333067035755 \cdot 10^{-21}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 10
Error	28.5
Cost	2268

\[\begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := \left(t_3 - t_1\right) + t_2\\ \mathbf{if}\;c \leq -3.4978269191383755 \cdot 10^{-37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.1952640768791891 \cdot 10^{-276}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5634318228014937 \cdot 10^{-289}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7.936736274580732 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - t_1\\ \mathbf{elif}\;c \leq 5.5967289579712696 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.6925660663371383 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.459466323462211 \cdot 10^{-87}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(x \cdot \left(y \cdot z - t \cdot a\right) - t_1\right)\\ \end{array} \]

Alternative 11
Error	24.8
Cost	2268

\[\begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 + b \cdot \left(a \cdot i\right)\\ t_4 := c \cdot \left(t \cdot j\right)\\ t_5 := t_4 + \left(b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\right)\\ t_6 := \left(a \cdot \left(b \cdot i - x \cdot t\right) - t_1\right) + t_4\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{+76}:\\ \;\;\;\;t_4 + \left(x \cdot \left(y \cdot z - t \cdot a\right) - t_1\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -6.084193083941334 \cdot 10^{-252}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 1.6427425562497738 \cdot 10^{-252}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-19}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 12
Error	16.7
Cost	2260

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b\right) + \left(\left(z \cdot \left(x \cdot y\right) + c \cdot \left(t \cdot j - z \cdot b\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := c \cdot \left(t \cdot j\right)\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_6 := t_5 + t_1\\ t_7 := y \cdot \left(i \cdot j\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+50}:\\ \;\;\;\;t_6 + t_4\\ \mathbf{elif}\;b \leq -3.85476219309804 \cdot 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.588879425984884 \cdot 10^{-241}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;b \leq 9.76106485467868 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 10^{+45}:\\ \;\;\;\;t_6 - t_7\\ \mathbf{elif}\;b \leq 10^{+75}:\\ \;\;\;\;t_3 + t_5\\ \mathbf{else}:\\ \;\;\;\;t_5 + \left(t_4 - t_7\right)\\ \end{array} \]

Alternative 13
Error	28.4
Cost	2136

\[\begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := \left(t_2 - t_1\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -3.4978269191383755 \cdot 10^{-37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.1952640768791891 \cdot 10^{-276}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5634318228014937 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.936736274580732 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - t_1\\ \mathbf{elif}\;c \leq 5.5967289579712696 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.6925660663371383 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Error	18.1
Cost	2132

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ t_4 := y \cdot \left(i \cdot j\right)\\ t_5 := i \cdot \left(a \cdot b\right) + \left(\left(t_3 + z \cdot \left(x \cdot y\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{+159}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;t_3 - \left(c \cdot \left(z \cdot b\right) + \left(x \cdot \left(t \cdot a - y \cdot z\right) - a \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.0176650394069758 \cdot 10^{+33}:\\ \;\;\;\;t_2 - t_4\\ \mathbf{elif}\;i \leq 2.4715888282504033 \cdot 10^{-124}:\\ \;\;\;\;t_2 + t_3\\ \mathbf{elif}\;i \leq 10^{+115}:\\ \;\;\;\;t_1 + \left(t_3 - t_4\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 15
Error	47.3
Cost	2028

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.8514820427532693 \cdot 10^{-57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.451226609144491 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4035844074091335 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 5.375874219219991 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6898939620020528 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.636667737072809 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4112128694166007 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 6.146030954035828 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	33.0
Cost	2016

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8.913066993881063 \cdot 10^{-279}:\\ \;\;\;\;t_3 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.7852344413302353 \cdot 10^{-220}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.022444851110695 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + t_1\\ \mathbf{elif}\;x \leq 2.9579333067035755 \cdot 10^{-21}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+43}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 17
Error	39.2
Cost	1896

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9500000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.2633080105738175 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -5.4833783709630996 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8632204061568728 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.25457933405912 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	38.2
Cost	1896

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;t \leq -949216412142553.5:\\ \;\;\;\;t \cdot \left(c \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2815621161928392 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.946945469783583 \cdot 10^{-112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.451226609144491 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.6048132912923183 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1164306929805162 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.3902348561814167 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5763279461209824 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 19
Error	33.3
Cost	1896

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ t_2 := c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.755065832622301 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6963385250109436 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8632204061568728 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.9579333067035755 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	32.8
Cost	1884

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.913066993881063 \cdot 10^{-279}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.7852344413302353 \cdot 10^{-220}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.022444851110695 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9579333067035755 \cdot 10^{-21}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	50.0
Cost	1772

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ t_4 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;x \leq -360000000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.1254576905826886 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6320581502893068 \cdot 10^{-43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq -2.5101639932064875 \cdot 10^{-73}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -1.5828537535046638 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.13356223835465 \cdot 10^{-210}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.491643854644261 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.440834538733288 \cdot 10^{-299}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.2527766474194893 \cdot 10^{-289}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.985982485224039 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2744387952937295 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 22
Error	41.9
Cost	1500

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.451226609144491 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4035844074091335 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 5.375874219219991 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6898939620020528 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 7.636667737072809 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	41.2
Cost	1500

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.451226609144491 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4035844074091335 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 5.008349248003336 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.9301300101262984 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	37.2
Cost	1500

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.505321751046605 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.700091429221239 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.5634318228014937 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.936736274580732 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5.5967289579712696 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 5.659894819030686 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.014823475551088 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	50.4
Cost	1244

\[\begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2538682004002647 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.984639106013461 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+253}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	41.1
Cost	1236

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.491643854644261 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7852344413302353 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 4.090534608541154 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.536239897257001 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	38.7
Cost	1236

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1164306929805162 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.3902348561814167 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.255702395946591 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 28
Error	38.5
Cost	1236

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.4332008552450565 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1164306929805162 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.3902348561814167 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.255702395946591 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 29
Error	38.5
Cost	1236

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -1.4332008552450565 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;t \leq 2.1164306929805162 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.3902348561814167 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.255702395946591 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 30
Error	39.6
Cost	1104

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2538682004002647 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.146030954035828 \cdot 10^{-110}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 31
Error	50.9
Cost	980

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3559921766095074 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 32
Error	50.7
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3559921766095074 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+253}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 33
Error	51.0
Cost	848

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.7301636798760958 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 34
Error	50.2
Cost	584

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -2.9827698676236503 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.014823475551088 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	53.4
Cost	320

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

Reproduce

herbie shell --seed 2022317 
(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)))))