Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 19.27% → 9.37%

Time: 1.2min

Precision: binary64

Cost: 12681

Math

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

↓

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_2 + \left(t_1 + t_3\right)\\ \mathbf{if}\;t_4 \leq -2 \cdot 10^{+293} \lor \neg \left(t_4 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;\left(t_3 + \left(t_1 - b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right)\right)\right) + t_2\\ \end{array} \]

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 (* b (- (* a i) (* z c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* x (- (* y z) (* t a))))
        (t_4 (+ t_2 (+ t_1 t_3))))
   (if (or (<= t_4 -2e+293) (not (<= t_4 5e+292)))
     (+ (- (* c (- (* t j) (* z b))) (* i (- (* y j) (* a b)))) t_3)
     (+ (+ t_3 (- t_1 (* b (fma (- a) i (* a i))))) t_2))))

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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = t_2 + (t_1 + t_3);
	double tmp;
	if ((t_4 <= -2e+293) || !(t_4 <= 5e+292)) {
		tmp = ((c * ((t * j) - (z * b))) - (i * ((y * j) - (a * b)))) + t_3;
	} else {
		tmp = (t_3 + (t_1 - (b * fma(-a, i, (a * i))))) + t_2;
	}
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_4 = Float64(t_2 + Float64(t_1 + t_3))
	tmp = 0.0
	if ((t_4 <= -2e+293) || !(t_4 <= 5e+292))
		tmp = Float64(Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(i * Float64(Float64(y * j) - Float64(a * b)))) + t_3);
	else
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * fma(Float64(-a), i, Float64(a * i))))) + t_2);
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$4, -2e+293], N[Not[LessEqual[t$95$4, 5e+292]], $MachinePrecision]], N[(N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(y * j), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], N[(N[(t$95$3 + N[(t$95$1 - N[(b * N[((-a) * i + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]

Target

Original	19.27%
Target	24.96%
Herbie	9.37%

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

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)))) < -1.9999999999999998e293 or 4.9999999999999996e292 < (+.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 82.03

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

   2. Simplified 82.02

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

      [Start] 82.03	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 82.03	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 82.03	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 82.03	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 82.03	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 82.03	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 82.03	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 82.02	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in i around -inf 37.38

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

   4. Simplified 37.38

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

      [Start] 37.38	\[ -1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + \left(-1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right)\right) \]
      associate-+r+ [=>] 37.38	\[ \color{blue}{\left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right)} \]
      +-commutative [=>] 37.38	\[ \left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \color{blue}{\left(c \cdot \left(t \cdot j\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)} \]
      *-commutative [=>] 37.38	\[ \left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)}\right) \]
      *-commutative [=>] 37.38	\[ \left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right)\right) \]
      associate-+r+ [=>] 37.38	\[ \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + c \cdot \left(t \cdot j\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)} \]

   if -1.9999999999999998e293 < (+.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)))) < 4.9999999999999996e292

   1. Initial program 1.4

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

   2. Applied egg-rr 1.39

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

4. Final simplification 9.37

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \leq -2 \cdot 10^{+293} \lor \neg \left(j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) - b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.37%
Cost	5833

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_2 + \left(t_1 + t_3\right)\\ \mathbf{if}\;t_4 \leq -2 \cdot 10^{+293} \lor \neg \left(t_4 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) - x \cdot \left(t \cdot a\right)\right) + t_1\right) + t_2\\ \end{array} \]

Alternative 2
Error	9.37%
Cost	5705

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + t_1\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+293} \lor \neg \left(t_2 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	55.43%
Cost	2808

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_5 := t_4 - i \cdot \left(y \cdot j\right)\\ t_6 := j \cdot \left(t \cdot c - y \cdot i\right) + t_1\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-24}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-113}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-239}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-275}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-207}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-169}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-68}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 0.051:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{\frac{1}{x \cdot y - b \cdot c}}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+190}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	42%
Cost	2800

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + t_2\\ t_6 := t_4 + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-130}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-295}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-244}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-200}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-9}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	21.29%
Cost	2780

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right) + t_3\\ t_5 := \left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + t_3\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{-153}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-228}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-255}:\\ \;\;\;\;t_1 + \left(t_3 + i \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-221}:\\ \;\;\;\;t_4 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 6
Error	43.01%
Cost	2668

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t_3 + t_1\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_6 := t_5 + t_3\\ t_7 := t_5 + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-54}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-81}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-175}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-294}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-244}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-225}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;t_5 + t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+58}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	28.68%
Cost	2656

\[\begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := x \cdot t_1\\ t_3 := i \cdot \left(y \cdot j\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := \left(t_4 + t_2\right) - t_3\\ t_6 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_7 := t_6 + t_4\\ \mathbf{if}\;x \leq -7.1 \cdot 10^{-81}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-109}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - t_3\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-127}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq -1.96 \cdot 10^{-221}:\\ \;\;\;\;t_6 + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-114}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+49}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+101}:\\ \;\;\;\;t_6 + \frac{x}{\frac{1}{t_1}}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+182}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6 + t_2\\ \end{array} \]

Alternative 8
Error	53.56%
Cost	2544

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := i \cdot \left(a \cdot b\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + x \cdot \left(y \cdot z\right)\\ t_6 := x \cdot y - b \cdot c\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-298}:\\ \;\;\;\;t_4 + t_3\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-242}:\\ \;\;\;\;\frac{z}{\frac{1}{t_6}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;t_3 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-146}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-85}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-32}:\\ \;\;\;\;t_4 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;z \cdot t_6\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	57.12%
Cost	2424

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-309}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-252}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-177}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	49.05%
Cost	2412

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(y \cdot i\right)\\ t_3 := b \cdot i - x \cdot t\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right) - t_2\\ \mathbf{if}\;c \leq -9 \cdot 10^{-27}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-72}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-78}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-235}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-303}:\\ \;\;\;\;\frac{a}{\frac{1}{t_3}}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-266}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t_2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-248}:\\ \;\;\;\;a \cdot t_3\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-220}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	30.86%
Cost	2392

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := y \cdot z - t \cdot a\\ t_3 := x \cdot t_2\\ t_4 := i \cdot \left(a \cdot b\right)\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_6 := t_1 + t_5\\ t_7 := \left(t_5 + t_3\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;\left(t_4 + x \cdot \frac{1}{\frac{1}{t_2}}\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-129}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-221}:\\ \;\;\;\;t_1 + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-245}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-114}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+49}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(t_3 + t_4\right)\\ \end{array} \]

Alternative 12
Error	33.97%
Cost	2272

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ t_4 := t_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-242}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - x \cdot \left(t \cdot a\right)\right) + t_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-121}:\\ \;\;\;\;\left(t_1 + y \cdot \left(x \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-27}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Error	33.68%
Cost	2272

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t_1 + t_3\\ t_5 := t_3 + t_2\\ \mathbf{if}\;x \leq -9 \cdot 10^{+39}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;\left(t_1 + y \cdot \left(x \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{-81}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-110}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-126}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-222}:\\ \;\;\;\;t_1 + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-45}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+50}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \]

Alternative 14
Error	50.1%
Cost	2148

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-117}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-201}:\\ \;\;\;\;t_2 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	43.49%
Cost	2008

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	67.98%
Cost	1896

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 17
Error	59.54%
Cost	1896

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-298}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 18
Error	25.9%
Cost	1864

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := i \cdot \left(y \cdot j\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+68}:\\ \;\;\;\;\left(t_4 + t_2\right) - t_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;t_1 + \left(t_2 + i \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_4\\ \end{array} \]

Alternative 19
Error	79.17%
Cost	1837

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_3 := a \cdot \left(b \cdot i\right)\\ t_4 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-226}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 6.9 \cdot 10^{-168}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+24}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+174} \lor \neg \left(a \leq 1.9 \cdot 10^{+284}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	58.43%
Cost	1764

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-242}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-146}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	77.76%
Cost	1704

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := c \cdot \left(b \cdot \left(-z\right)\right)\\ t_3 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{-86}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-244}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+252}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	58.55%
Cost	1632

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 23
Error	58.46%
Cost	1632

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	58.43%
Cost	1632

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	62.05%
Cost	1500

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.1 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 26
Error	54.58%
Cost	1500

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-299}:\\ \;\;\;\;t_1 + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-238}:\\ \;\;\;\;\frac{z}{\frac{1}{x \cdot y - b \cdot c}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-146}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	79.54%
Cost	1441

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-225}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+91} \lor \neg \left(t \leq 10^{+280}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 28
Error	60.85%
Cost	1369

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-275}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-88} \lor \neg \left(a \leq 6.4 \cdot 10^{-46}\right) \land a \leq 1.14 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 29
Error	70.18%
Cost	1309

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{if}\;c \leq -8000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{-193}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+65} \lor \neg \left(c \leq 3.2 \cdot 10^{+196}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 30
Error	78.28%
Cost	1176

\[\begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-247}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 31
Error	77.69%
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 32
Error	78.24%
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 33
Error	80.47%
Cost	716

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-305}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 34
Error	80.09%
Cost	716

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	82.77%
Cost	452

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 36
Error	83.49%
Cost	320

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

Reproduce

herbie shell --seed 2023088 
(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)))))