Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.2 → 5.3

Time: 1.1min

Precision: binary64

Cost: 11976

Math

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

↓

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

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

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 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = (t * c) - (y * i);
	double t_4 = t_2 + (j * t_3);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((i * ((a * b) - (y * j))) + ((c * (t * j)) + t_1)) - (c * (z * b));
	} else if (t_4 <= 1e+307) {
		tmp = fma(j, t_3, t_2);
	} else {
		tmp = ((y * (x * z)) - (a * (x * t))) + (c * ((t * j) - (z * b)));
	}
	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(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(Float64(t * c) - Float64(y * i))
	t_4 = Float64(t_2 + Float64(j * t_3))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) + Float64(Float64(c * Float64(t * j)) + t_1)) - Float64(c * Float64(z * b)));
	elseif (t_4 <= 1e+307)
		tmp = fma(j, t_3, t_2);
	else
		tmp = Float64(Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(x * t))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+307], N[(j * t$95$3 + t$95$2), $MachinePrecision], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	12.2
Target	16.0
Herbie	5.3

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

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)))))): 2 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 21.1

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

   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 0.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
      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)))))): 2 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

   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 63.1

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

   2. Simplified 63.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right)} \]
      Proof
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 a i) (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 i a)) (*.f64 c z)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 i a) (neg.f64 (*.f64 c z)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (*.f64 c z)) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c t)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 c t) (Rewrite<= *-commutative_binary64 (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (neg.f64 i) y) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i 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 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i 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 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (*.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.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
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 1 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 0 41.7

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

   4. Simplified 41.7

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

   5. Taylor expanded in z around 0 28.6

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

4. Final simplification 5.3

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

Alternatives

Alternative 1
Error	4.9
Cost	5832

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

Alternative 2
Error	5.3
Cost	5832

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

Alternative 3
Error	6.0
Cost	5704

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

Alternative 4
Error	4.9
Cost	5704

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

Alternative 5
Error	45.7
Cost	2688

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-150}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-157}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-237}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-163}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	35.8
Cost	2676

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{-15}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -3.75 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-117}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-303}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 10^{-259}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-165}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3200000:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+128}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Error	26.3
Cost	2668

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ t_4 := t_2 + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-234}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	39.2
Cost	2556

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_5 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-16}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-37}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+106}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 9
Error	39.1
Cost	2556

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_5 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-15}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 340:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 10
Error	38.0
Cost	2544

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-196}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-244}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-191}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	24.8
Cost	2404

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_3 + t_2\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{elif}\;x \leq -122000000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-179}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 12
Error	39.1
Cost	2292

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 22000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 13
Error	29.6
Cost	2272

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-273}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+110}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	20.7
Cost	2256

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -5500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-304}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-272}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(j \cdot \left(t \cdot c\right) - j \cdot \left(y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	43.0
Cost	2160

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+98}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-48}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	44.3
Cost	2160

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_5 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -3.35 \cdot 10^{+230}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-125}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 17
Error	24.0
Cost	2140

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;x \leq -32000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-272}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-176}:\\ \;\;\;\;t_2 + t_4\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	39.1
Cost	2028

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-245}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6200:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	23.6
Cost	2008

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;x \leq -1400000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-165}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + t_3\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	46.4
Cost	1896

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	44.3
Cost	1836

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -9.8 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+271}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	37.7
Cost	1500

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	50.1
Cost	1244

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	50.1
Cost	1244

\[\begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3800000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	50.1
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -70000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq -1.66 \cdot 10^{-271}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Error	50.1
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -48000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-271}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 27
Error	50.2
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-271}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-242}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	49.6
Cost	1112

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-269}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 29
Error	50.2
Cost	1112

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+244}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-237}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 30
Error	49.7
Cost	1112

\[\begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-271}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 31
Error	50.8
Cost	980

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{-37}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 32
Error	49.9
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;i \leq -5.4 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 33
Error	49.6
Cost	848

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+111}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 34
Error	50.2
Cost	848

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-93}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	50.1
Cost	584

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -9 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 36
Error	53.3
Cost	320

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

Reproduce

herbie shell --seed 2022330 
(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)))))