Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 11.7 → 4.0

Time: 1.7min

Precision: binary64

Cost: 12680

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + \left(\left(i \cdot \left(a \cdot b\right) + y \cdot \left(x \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ t_2 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := \left(t_3 - t_2\right) + t_4\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_5 \leq 10^{+305}:\\ \;\;\;\;t_4 + \left(\left(t_3 - b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right)\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* t (- (* c j) (* x a)))
          (- (+ (* i (* a b)) (* y (* x z))) (* i (* y j)))))
        (t_2 (* x (- (* t a) (* y z))))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (* j (- (* t c) (* y i))))
        (t_5 (+ (- t_3 t_2) t_4)))
   (if (<= t_5 (- INFINITY))
     t_1
     (if (<= t_5 1e+305)
       (+ t_4 (- (- t_3 (* b (fma (- a) i (* a i)))) t_2))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (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 = (t * ((c * j) - (x * a))) + (((i * (a * b)) + (y * (x * z))) - (i * (y * j)));
	double t_2 = x * ((t * a) - (y * z));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = j * ((t * c) - (y * i));
	double t_5 = (t_3 - t_2) + t_4;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_5 <= 1e+305) {
		tmp = t_4 + ((t_3 - (b * fma(-a, i, (a * i)))) - t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(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(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(Float64(Float64(i * Float64(a * b)) + Float64(y * Float64(x * z))) - Float64(i * Float64(y * j))))
	t_2 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_5 = Float64(Float64(t_3 - t_2) + t_4)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_5 <= 1e+305)
		tmp = Float64(t_4 + Float64(Float64(t_3 - Float64(b * fma(Float64(-a), i, Float64(a * i)))) - t_2));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(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[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 - t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$1, If[LessEqual[t$95$5, 1e+305], N[(t$95$4 + N[(N[(t$95$3 - N[(b * N[((-a) * i + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Target

Original	11.7
Target	15.4
Herbie	4.0

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

Derivation

1. Split input into 2 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 or 9.9999999999999994e304 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 62.6

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

   2. Simplified 62.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)} \]
      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))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (fma.f64 i (neg.f64 y) (Rewrite<= *-commutative_binary64 (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= fma-def_binary64 (+.f64 (*.f64 i (neg.f64 y)) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i y))) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 i) y)) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 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)))))): 2 points increase in error, 0 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 t around 0 26.6

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

   4. Taylor expanded in c around 0 18.6

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

   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)))) < 9.9999999999999994e304

   1. Initial program 0.9

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

   2. Applied egg-rr 0.9

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

4. Final simplification 4.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(\left(i \cdot \left(a \cdot b\right) + y \cdot \left(x \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq 10^{+305}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(b \cdot \left(a \cdot i - z \cdot c\right) - b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right)\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(\left(i \cdot \left(a \cdot b\right) + y \cdot \left(x \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.0
Cost	5832

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + \left(\left(i \cdot \left(a \cdot b\right) + y \cdot \left(x \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := t_2 + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 10^{+305}:\\ \;\;\;\;t_2 + \left(j \cdot \left(t \cdot c\right) - j \cdot \left(y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.2
Cost	5704

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

Alternative 3
Error	4.0
Cost	5704

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + \left(\left(i \cdot \left(a \cdot b\right) + y \cdot \left(x \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ t_2 := \left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+305}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	25.0
Cost	3456

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(x \cdot t\right)\\ t_4 := t_1 + \left(t_2 - t_3\right)\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_6 := t \cdot \left(c \cdot j\right)\\ t_7 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_8 := t_1 - \left(i \cdot \left(y \cdot j\right) + t_7\right)\\ t_9 := \left(t_5 - t_7\right) + t_6\\ t_10 := t_6 + \left(y \cdot \left(x \cdot z\right) + t_5\right)\\ \mathbf{if}\;c \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;t_6 - \left(z \cdot \left(b \cdot c\right) + t_7\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq -2.3195352955740566 \cdot 10^{-85}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -8.244024762062571 \cdot 10^{-204}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq 7.129283196991016 \cdot 10^{-296}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 1.7920131662561665 \cdot 10^{-245}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 9.408043120623704 \cdot 10^{-147}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 6.148458622615977 \cdot 10^{-15}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+22}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 10^{+170}:\\ \;\;\;\;t_2 + t_5\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + \left(t_5 - t_3\right)\\ \end{array} \]

Alternative 5
Error	36.1
Cost	2808

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_4 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.4976747541765695 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.3061638971079957 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.9571441634843417 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.1955682023829298 \cdot 10^{-246}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5980391924117908 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+266}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	35.2
Cost	2804

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j\right) - \left(a \cdot \left(x \cdot t\right) + c \cdot \left(z \cdot b\right)\right)\\ t_3 := b \cdot \left(z \cdot c\right)\\ t_4 := a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.4976747541765695 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.0584395060854282 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.4695666764731467 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.655120375880322 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t_3\\ \mathbf{elif}\;c \leq -1.5950073227799923 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.5980391924117908 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right) - t_3\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+226}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	34.7
Cost	2804

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z\right) + t_1\\ t_3 := t \cdot \left(c \cdot j\right) - \left(a \cdot \left(x \cdot t\right) + c \cdot \left(z \cdot b\right)\right)\\ t_4 := a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.4976747541765695 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.0584395060854282 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.145534043333065 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.9571441634843417 \cdot 10^{-207}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -5.961071752999393 \cdot 10^{-280}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -2.356896723979423 \cdot 10^{-289}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.5980391924117908 \cdot 10^{-161}:\\ \;\;\;\;t_1 - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+226}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	32.6
Cost	2804

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ t_4 := i \cdot \left(y \cdot j\right)\\ t_5 := t_2 + \left(x \cdot \left(y \cdot z\right) - t_4\right)\\ t_6 := a \cdot \left(x \cdot t\right)\\ t_7 := t_3 + \left(b \cdot \left(a \cdot i\right) - t_6\right)\\ t_8 := t_1 - t \cdot \left(x \cdot a\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-14}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-44}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -1.3875653365669788 \cdot 10^{-164}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq -6.993967925950788 \cdot 10^{-303}:\\ \;\;\;\;t_2 - \left(t_4 + x \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 8.653096192719348 \cdot 10^{-259}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 4.452969642898109 \cdot 10^{-205}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.1665778490942654 \cdot 10^{-188}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq 1.224864353076886 \cdot 10^{-168}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 8.859978120612991 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.009265089685291 \cdot 10^{-75}:\\ \;\;\;\;t_3 - \left(t_6 + c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+200}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 9
Error	28.5
Cost	2796

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(x \cdot t\right)\\ t_3 := \left(t_1 - t_2\right) + j \cdot \left(t \cdot c\right)\\ t_4 := i \cdot \left(y \cdot j\right)\\ t_5 := t \cdot \left(c \cdot j\right)\\ t_6 := t_5 + \left(y \cdot \left(x \cdot z\right) + t_1\right)\\ t_7 := t_5 - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ t_8 := i \cdot \left(a \cdot b\right)\\ t_9 := t_8 + \left(x \cdot \left(y \cdot z\right) - t_4\right)\\ t_10 := t_8 - \left(t_4 + x \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+118}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq -1.1345922529409031 \cdot 10^{-70}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq -5.789342243138545 \cdot 10^{-96}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq -8.071474214140992 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq -1.9571441634843417 \cdot 10^{-207}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq 2.671126943967844 \cdot 10^{-274}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq 1.7696221287630645 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 10^{+55}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 10^{+225}:\\ \;\;\;\;t_5 - \left(t_2 + c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 10
Error	28.6
Cost	2796

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 - a \cdot \left(x \cdot t\right)\\ t_3 := i \cdot \left(y \cdot j\right)\\ t_4 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_5 := t_2 + j \cdot \left(t \cdot c\right)\\ t_6 := t \cdot \left(c \cdot j\right)\\ t_7 := t_6 + \left(y \cdot \left(x \cdot z\right) + t_1\right)\\ t_8 := t_6 - \left(z \cdot \left(b \cdot c\right) + t_4\right)\\ t_9 := i \cdot \left(a \cdot b\right)\\ t_10 := t_9 + \left(x \cdot \left(y \cdot z\right) - t_3\right)\\ t_11 := t_9 - \left(t_3 + x \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+118}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq -1.1345922529409031 \cdot 10^{-70}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq -5.789342243138545 \cdot 10^{-96}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;c \leq -8.071474214140992 \cdot 10^{-106}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq -6.636519994010809 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - t_4\\ \mathbf{elif}\;c \leq -1.9571441634843417 \cdot 10^{-207}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 2.671126943967844 \cdot 10^{-274}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 1.7696221287630645 \cdot 10^{-236}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;c \leq 10^{+53}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_6 + t_2\\ \end{array} \]

Alternative 11
Error	21.3
Cost	2788

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := t_1 - \left(i \cdot \left(y \cdot j\right) + t_3\right)\\ t_5 := a \cdot \left(x \cdot t\right)\\ t_6 := t_1 + \left(t_2 - t_5\right)\\ t_7 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_8 := t \cdot \left(c \cdot j\right)\\ t_9 := \left(t_7 - t_3\right) + t_8\\ \mathbf{if}\;c \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;t_8 - \left(z \cdot \left(b \cdot c\right) + t_3\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -2.3195352955740566 \cdot 10^{-85}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq -8.244024762062571 \cdot 10^{-204}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq 7.129283196991016 \cdot 10^{-296}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.7920131662561665 \cdot 10^{-245}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 10^{+170}:\\ \;\;\;\;t_2 + \left(y \cdot \left(x \cdot z\right) + t_7\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + \left(t_7 - t_5\right)\\ \end{array} \]

Alternative 12
Error	28.6
Cost	2664

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot j\right)\\ t_2 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ t_4 := t_3 + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ t_5 := i \cdot \left(a \cdot b\right)\\ t_6 := t_5 - \left(t_1 + x \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - t_2\\ \mathbf{elif}\;a \leq -3350000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.862075370183896 \cdot 10^{-64}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -2.99911053915123 \cdot 10^{-186}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 3.014319786415951 \cdot 10^{-287}:\\ \;\;\;\;t_3 - \left(z \cdot \left(b \cdot c\right) + t_2\right)\\ \mathbf{elif}\;a \leq 1.2380709247396335 \cdot 10^{-87}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.7593289721366138 \cdot 10^{-71}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-17}:\\ \;\;\;\;t_5 + \left(x \cdot \left(y \cdot z\right) - t_1\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+115}:\\ \;\;\;\;t_3 - \left(a \cdot \left(x \cdot t\right) + c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+277}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 13
Error	20.8
Cost	2656

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + t_2\\ t_4 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_5 := i \cdot \left(a \cdot b\right) - \left(i \cdot \left(y \cdot j\right) + t_4\right)\\ t_6 := \left(t_2 - t_4\right) + t_1\\ \mathbf{if}\;j \leq -1.35 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2.6691537231312254 \cdot 10^{-96}:\\ \;\;\;\;\left(t_2 - a \cdot \left(x \cdot t\right)\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -1.8418418218747257 \cdot 10^{-159}:\\ \;\;\;\;t_1 - \left(z \cdot \left(b \cdot c\right) + t_4\right)\\ \mathbf{elif}\;j \leq -4.92061731581345 \cdot 10^{-235}:\\ \;\;\;\;t_2 - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.130968205476455 \cdot 10^{-134}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 4.4138363049289196 \cdot 10^{-46}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+133}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Error	19.9
Cost	2524

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ t_3 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := t \cdot \left(c \cdot j\right)\\ t_6 := t_4 - t_3\\ t_7 := t_6 - y \cdot \left(i \cdot j\right)\\ t_8 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;c \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;t_5 - \left(z \cdot \left(b \cdot c\right) + t_3\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;t_2 - \left(i \cdot \left(y \cdot j\right) + t_3\right)\\ \mathbf{elif}\;c \leq -4.459962056747987 \cdot 10^{-67}:\\ \;\;\;\;t_6 + t_5\\ \mathbf{elif}\;c \leq 5.2594337589802685 \cdot 10^{-289}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq 1.7920131662561665 \cdot 10^{-245}:\\ \;\;\;\;t_2 + \left(t_8 - t_1\right)\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq 10^{+170}:\\ \;\;\;\;t_8 + \left(y \cdot \left(x \cdot z\right) + t_4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + \left(t_4 - t_1\right)\\ \end{array} \]

Alternative 15
Error	33.0
Cost	2408

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z\right) + t_1\\ t_3 := t \cdot \left(c \cdot j\right) - \left(a \cdot \left(x \cdot t\right) + c \cdot \left(z \cdot b\right)\right)\\ t_4 := i \cdot \left(a \cdot b\right) + \left(x \cdot \left(y \cdot z\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.4976747541765695 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.0584395060854282 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.145534043333065 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.4024577919075622 \cdot 10^{-209}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.5980391924117908 \cdot 10^{-161}:\\ \;\;\;\;t_1 - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+226}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	24.9
Cost	2400

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := i \cdot \left(a \cdot b\right) - \left(i \cdot \left(y \cdot j\right) + t_2\right)\\ t_5 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;t_3 - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq -5.126693183793623 \cdot 10^{-63}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -3.2805342918892725 \cdot 10^{-76}:\\ \;\;\;\;t_5 - \left(t_1 + c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.14105955933369 \cdot 10^{-178}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.194580467290523 \cdot 10^{-230}:\\ \;\;\;\;t_5 - \left(z \cdot \left(b \cdot c\right) + t_2\right)\\ \mathbf{elif}\;b \leq 2.357467040200958 \cdot 10^{-167}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.1889586722865872 \cdot 10^{-55}:\\ \;\;\;\;t_5 + \left(y \cdot \left(x \cdot z\right) + t_3\right)\\ \mathbf{elif}\;b \leq 100000000:\\ \;\;\;\;\left(t_3 - t_1\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 - t_2\\ \end{array} \]

Alternative 17
Error	36.8
Cost	2280

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - t_1\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -6.996742572242584 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.4695666764731467 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.9571441634843417 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.4024577919075622 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5980391924117908 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right) - t_1\\ \mathbf{elif}\;c \leq 1.5218850018999296 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	35.0
Cost	2280

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(z \cdot c\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.996742572242584 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.3061638971079957 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t_2\\ \mathbf{elif}\;c \leq -2.415473076499542 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.9571441634843417 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.1955682023829298 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3.843649138044746 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5980391924117908 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right) - t_2\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	24.8
Cost	2268

\[\begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := i \cdot \left(a \cdot b\right) - \left(i \cdot \left(y \cdot j\right) + t_1\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ t_4 := t_3 + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+118}:\\ \;\;\;\;t_3 - \left(z \cdot \left(b \cdot c\right) + t_1\right)\\ \mathbf{elif}\;c \leq -1.1345922529409031 \cdot 10^{-70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.0751554183529686 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.148458622615977 \cdot 10^{-15}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 20
Error	25.2
Cost	2144

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t_2 - \left(a \cdot \left(x \cdot t\right) + c \cdot \left(z \cdot b\right)\right)\\ t_5 := i \cdot \left(a \cdot b\right)\\ t_6 := t_5 - \left(t_1 + x \cdot \left(t \cdot a\right)\right)\\ t_7 := t_2 - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;i \leq -7.35802740254643 \cdot 10^{-42}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 3.507530665485494 \cdot 10^{-293}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 8.215005892161768 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.646012019400642 \cdot 10^{-79}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 9.247493974182052 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.45 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+52}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5 + \left(x \cdot \left(y \cdot z\right) - t_1\right)\\ \end{array} \]

Alternative 21
Error	49.5
Cost	2100

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_3 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_4 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.2628049064048355 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -7.99948771977967 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -1.7036242167626555 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4287425669466105 \cdot 10^{-304}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.715871575956753 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5404977617811568 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.0783882770484756 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+115}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 22
Error	38.1
Cost	2028

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := b \cdot \left(a \cdot i\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.1962861879619188 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.784801429446562 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7327115545772705 \cdot 10^{-233}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3667009314777457 \cdot 10^{-304}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 8.729440342849557 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.775681496959103 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.452969642898109 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.513890016644629 \cdot 10^{-196}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.224864353076886 \cdot 10^{-168}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.009265089685291 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 23
Error	22.2
Cost	2004

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right) + t_2\\ \mathbf{if}\;x \leq -2.815784963325257 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - \left(i \cdot \left(y \cdot j\right) + t_3\right)\\ \mathbf{elif}\;x \leq -1.0936806667591354 \cdot 10^{-238}:\\ \;\;\;\;t_1 + \left(t_2 - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.1850335973097382 \cdot 10^{-91}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+63}:\\ \;\;\;\;t_1 + \left(y \cdot \left(x \cdot z\right) + t_2\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1 - \left(z \cdot \left(b \cdot c\right) + t_3\right)\\ \end{array} \]

Alternative 24
Error	38.2
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.542534147571649 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.296171259647786 \cdot 10^{-93}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq -5.681949481132866 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.271542124392322 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.3681188377146244 \cdot 10^{-100}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 25
Error	49.8
Cost	1572

\[\begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -412341.8135397077:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -3.6719062169194146 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.890176068577702 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -2.2620883858768917 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 8.940810834356608 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.835527086072569 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.2948207874475228 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	39.6
Cost	1368

\[\begin{array}{l} t_1 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.0808765870352826 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -9.212442857229094 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.754589659060427 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 27
Error	38.8
Cost	1368

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.0808765870352826 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -7.045536586129594 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.111259724091772 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.754589659060427 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 28
Error	37.9
Cost	1368

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.271542124392322 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.754589659060427 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 29
Error	42.9
Cost	1236

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.296171259647786 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3094033858870097 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 2.015389564858437 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.754589659060427 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1350000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 30
Error	37.6
Cost	1236

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.0597205638237352 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.754589659060427 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 31
Error	50.3
Cost	1176

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.5995620260648244 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3094033858870097 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 6.591924659981111 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.754589659060427 \cdot 10^{-75}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 32
Error	49.6
Cost	1112

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.5995620260648244 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.3094033858870097 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.318409856856624 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 33
Error	49.7
Cost	1112

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.5995620260648244 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3094033858870097 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.60575560714395 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.6006142618386735 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{+40}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 34
Error	50.3
Cost	848

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -3.6719062169194146 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.890176068577702 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -2.2620883858768917 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	49.8
Cost	584

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.5995620260648244 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 36
Error	49.8
Cost	584

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.5995620260648244 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 37
Error	53.1
Cost	320

\[x \cdot \left(y \cdot z\right) \]

Alternative 38
Error	53.3
Cost	320

\[y \cdot \left(x \cdot z\right) \]

Reproduce

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