Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.4 → 5.6

Time: 1.6min

Precision: binary64

Cost: 25224

Math

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

↓

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ t_3 := y \cdot z - t \cdot a\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + x \cdot t_3\\ \mathbf{elif}\;t_2 \leq 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, t_3 + 2 \cdot \mathsf{fma}\left(-a, t, t \cdot a\right), \mathsf{fma}\left(b, a \cdot i - z \cdot c, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, c \cdot j - x \cdot a, y \cdot \left(x \cdot z - i \cdot j\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- t_1 (+ (* b (- (* z c) (* a i))) (* x (- (* t a) (* y z))))))
        (t_3 (- (* y z) (* t a))))
   (if (<= t_2 (- INFINITY))
     (+ (- (* c (- (* t j) (* z b))) (* i (- (* y j) (* a b)))) (* x t_3))
     (if (<= t_2 1e+305)
       (fma
        x
        (+ t_3 (* 2.0 (fma (- a) t (* t a))))
        (fma b (- (* a i) (* z c)) t_1))
       (fma t (- (* c j) (* x a)) (* y (- (* x z) (* i j))))))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	double t_3 = (y * z) - (t * a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((c * ((t * j) - (z * b))) - (i * ((y * j) - (a * b)))) + (x * t_3);
	} else if (t_2 <= 1e+305) {
		tmp = fma(x, (t_3 + (2.0 * fma(-a, t, (t * a)))), fma(b, ((a * i) - (z * c)), t_1));
	} else {
		tmp = fma(t, ((c * j) - (x * a)), (y * ((x * z) - (i * j))));
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	t_3 = Float64(Float64(y * z) - Float64(t * a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(i * Float64(Float64(y * j) - Float64(a * b)))) + Float64(x * t_3));
	elseif (t_2 <= 1e+305)
		tmp = fma(x, Float64(t_3 + Float64(2.0 * fma(Float64(-a), t, Float64(t * a)))), fma(b, Float64(Float64(a * i) - Float64(z * c)), t_1));
	else
		tmp = fma(t, Float64(Float64(c * j) - Float64(x * a)), Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], 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] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], N[(x * N[(t$95$3 + N[(2.0 * N[((-a) * t + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	12.4
Target	16.2
Herbie	5.6

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 64.0

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

      [Start] 64.0	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 64.0	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 64.0	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in i around -inf 24.0

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

   4. Simplified 24.0

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

      [Start] 24.0	\[ -1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + \left(-1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right)\right) \]
      +-commutative [<=] 24.0	\[ -1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + \left(-1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right) + \color{blue}{\left(c \cdot \left(t \cdot j\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)}\right) \]
      associate-+r+ [=>] 24.0	\[ \color{blue}{\left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)} \]
      *-commutative [=>] 24.0	\[ \left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)}\right) \]
      *-commutative [<=] 24.0	\[ \left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right)\right) \]
      associate-+r+ [=>] 24.0	\[ \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)\right) + c \cdot \left(t \cdot j\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)} \]

   if -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 0.8

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

   2. Simplified 0.8

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

      [Start] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 0.8	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 0.8	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 0.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Applied egg-rr 0.9

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

   4. Simplified 0.9

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

      [Start] 0.9	\[ \mathsf{fma}\left(x, \left(y \cdot z - t \cdot a\right) + \left(\mathsf{fma}\left(-a, t, t \cdot a\right) + \mathsf{fma}\left(-a, t, t \cdot a\right)\right), \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right) \]
      *-commutative [=>] 0.9	\[ \mathsf{fma}\left(x, \left(\color{blue}{z \cdot y} - t \cdot a\right) + \left(\mathsf{fma}\left(-a, t, t \cdot a\right) + \mathsf{fma}\left(-a, t, t \cdot a\right)\right), \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right) \]
      *-commutative [=>] 0.9	\[ \mathsf{fma}\left(x, \left(z \cdot y - \color{blue}{a \cdot t}\right) + \left(\mathsf{fma}\left(-a, t, t \cdot a\right) + \mathsf{fma}\left(-a, t, t \cdot a\right)\right), \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right) \]
      count-2 [=>] 0.9	\[ \mathsf{fma}\left(x, \left(z \cdot y - a \cdot t\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-a, t, t \cdot a\right)}, \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right) \]
      *-commutative [=>] 0.9	\[ \mathsf{fma}\left(x, \left(z \cdot y - a \cdot t\right) + 2 \cdot \mathsf{fma}\left(-a, t, \color{blue}{a \cdot t}\right), \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right) \]

   if 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 60.7

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

   2. Simplified 60.7

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

      [Start] 60.7	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 60.7	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 60.7	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 60.7	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in b around 0 55.6

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

   4. Simplified 27.3

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

      [Start] 55.6	\[ \left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x \]
      *-commutative [=>] 55.6	\[ \color{blue}{j \cdot \left(c \cdot t - y \cdot i\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
      *-commutative [<=] 55.6	\[ j \cdot \left(\color{blue}{t \cdot c} - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      cancel-sign-sub-inv [=>] 55.6	\[ j \cdot \color{blue}{\left(t \cdot c + \left(-y\right) \cdot i\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
      distribute-lft-in [=>] 55.6	\[ \color{blue}{\left(j \cdot \left(t \cdot c\right) + j \cdot \left(\left(-y\right) \cdot i\right)\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
      distribute-lft-neg-in [<=] 55.6	\[ \left(j \cdot \left(t \cdot c\right) + j \cdot \color{blue}{\left(-y \cdot i\right)}\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      distribute-rgt-neg-out [<=] 55.6	\[ \left(j \cdot \left(t \cdot c\right) + j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)}\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      associate-*r* [=>] 49.1	\[ \left(\color{blue}{\left(j \cdot t\right) \cdot c} + j \cdot \left(y \cdot \left(-i\right)\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      *-commutative [<=] 49.1	\[ \left(\color{blue}{\left(t \cdot j\right)} \cdot c + j \cdot \left(y \cdot \left(-i\right)\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      *-commutative [<=] 49.1	\[ \left(\color{blue}{c \cdot \left(t \cdot j\right)} + j \cdot \left(y \cdot \left(-i\right)\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      distribute-rgt-neg-out [=>] 49.1	\[ \left(c \cdot \left(t \cdot j\right) + j \cdot \color{blue}{\left(-y \cdot i\right)}\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      distribute-rgt-neg-out [=>] 49.1	\[ \left(c \cdot \left(t \cdot j\right) + \color{blue}{\left(-j \cdot \left(y \cdot i\right)\right)}\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      *-commutative [<=] 49.1	\[ \left(c \cdot \left(t \cdot j\right) + \left(-\color{blue}{\left(y \cdot i\right) \cdot j}\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      associate-*r* [<=] 43.9	\[ \left(c \cdot \left(t \cdot j\right) + \left(-\color{blue}{y \cdot \left(i \cdot j\right)}\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      mul-1-neg [<=] 43.9	\[ \left(c \cdot \left(t \cdot j\right) + \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)}\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]
      *-commutative [=>] 43.9	\[ \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
      *-commutative [<=] 43.9	\[ \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 5.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot z - t \cdot a\right) + 2 \cdot \mathsf{fma}\left(-a, t, t \cdot a\right), \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, c \cdot j - x \cdot a, y \cdot \left(x \cdot z - i \cdot j\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.5
Cost	18248

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

Alternative 2
Error	5.5
Cost	12680

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

Alternative 3
Error	5.5
Cost	11336

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

Alternative 4
Error	5.4
Cost	5704

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

Alternative 5
Error	34.7
Cost	3205

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 + a \cdot \left(b \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_6 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_7 := t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+144}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.05:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-189}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-169}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-151}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.36 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-36}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{+56}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+114} \lor \neg \left(i \leq 7 \cdot 10^{+157}\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Error	35.1
Cost	3072

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + a \cdot \left(b \cdot i\right)\\ t_6 := x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ t_7 := t_4 - t_2\\ \mathbf{if}\;b \leq -0.0024:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-240}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-286}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-176}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-156}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 2.02 \cdot 10^{-137}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-92}:\\ \;\;\;\;t_4 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+110}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 7
Error	35.2
Cost	2940

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t_3 + a \cdot \left(b \cdot i\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := t_5 + t \cdot \left(c \cdot j\right)\\ t_7 := t_3 - t_2\\ t_8 := y \cdot \left(i \cdot j\right)\\ t_9 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;b \leq -12800:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-240}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-286}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - t_8\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-175}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-156}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 1.34 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - t_2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-62}:\\ \;\;\;\;t_5 - t_8\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+29}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+39}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+110}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+138}:\\ \;\;\;\;t_9\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 8
Error	23.4
Cost	2928

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t_3 + t_1\\ t_5 := t_3 + t_2\\ t_6 := t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_7 := y \cdot \left(i \cdot j\right)\\ t_8 := t_2 + \left(a \cdot \left(b \cdot i\right) - t_7\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+211}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-104}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{-162}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-291}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-307}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-224}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-174}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-132}:\\ \;\;\;\;t_1 + \left(y \cdot \left(x \cdot z\right) - t_7\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-69}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;t_3 + \left(i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 9
Error	29.8
Cost	2801

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 + a \cdot \left(b \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_3 + t \cdot \left(c \cdot j\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_6 := t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_7 := y \cdot \left(i \cdot j\right)\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{-5}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-240}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-306}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - t_7\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-229}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-156}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-114}:\\ \;\;\;\;t_3 - t_7\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+116} \lor \neg \left(b \leq 1.35 \cdot 10^{+245}\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 10
Error	29.2
Cost	2668

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - y \cdot \left(i \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right) + t_1\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_6 := t_5 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{-17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-94}:\\ \;\;\;\;t_1 + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-205}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-74}:\\ \;\;\;\;t_5 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-20}:\\ \;\;\;\;t_5 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+120}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	25.4
Cost	2668

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := t_1 + t_4\\ t_6 := t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -2.7 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-211}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-151}:\\ \;\;\;\;t_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) + t_4\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+90}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+151}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	37.7
Cost	2552

\[\begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := y \cdot z - t \cdot a\\ t_5 := t \cdot \left(c \cdot j\right) - t_1\\ t_6 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-18}:\\ \;\;\;\;x \cdot t_4\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-254}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-304}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-276}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-270}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-236}:\\ \;\;\;\;\frac{z}{\frac{1}{x \cdot y - b \cdot c}}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-181}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right) - t_1\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{1}{t_4}}\\ \end{array} \]

Alternative 13
Error	33.7
Cost	2545

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.76 \cdot 10^{-174}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-83}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+56}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+114} \lor \neg \left(i \leq 1.85 \cdot 10^{+158}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	25.3
Cost	2532

\[\begin{array}{l} t_1 := y \cdot \left(i \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t_3 + \left(y \cdot \left(x \cdot z\right) - t_1\right)\\ t_5 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_6 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_7 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{+112}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -7.6:\\ \;\;\;\;t_5 - t_1\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-107}:\\ \;\;\;\;t_5 + t_2\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-150}:\\ \;\;\;\;t_6 + t_3\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-210}:\\ \;\;\;\;t_6 + t_2\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-151}:\\ \;\;\;\;t_6 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+178}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+290}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_6 + b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 15
Error	23.6
Cost	2532

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(i \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + \left(a \cdot \left(b \cdot i\right) - t_3\right)\\ t_5 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_6 := t_5 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -23500:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-52}:\\ \;\;\;\;t_5 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-178}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-294}:\\ \;\;\;\;t_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-167}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-106}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - t_3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;t_2 + \left(y \cdot \left(x \cdot z\right) - t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 16
Error	15.2
Cost	2516

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := \left(c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j - a \cdot b\right)\right) + t_2\\ \mathbf{if}\;i \leq -1.55 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.2 \cdot 10^{-210}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-151}:\\ \;\;\;\;t_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.85 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + \left(y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	33.6
Cost	2413

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{+112}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-138}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.75 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+114} \lor \neg \left(i \leq 7 \cdot 10^{+157}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	25.7
Cost	2272

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right) + t_1\\ t_5 := t_2 + t_1\\ \mathbf{if}\;i \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-139}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-220}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.32 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-218}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-151}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+89}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+153}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	40.3
Cost	2160

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	40.2
Cost	2160

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -750000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.9 \cdot 10^{-155}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{+151}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	50.3
Cost	2100

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 22
Error	50.2
Cost	2100

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 23
Error	50.3
Cost	2100

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+32}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	32.1
Cost	2016

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-293}:\\ \;\;\;\;t_2 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-89}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 25
Error	50.2
Cost	1968

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-257}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 70000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 26
Error	40.1
Cost	1896

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;a \leq -5.7 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 27
Error	37.0
Cost	1892

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+20}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 28
Error	37.1
Cost	1892

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-294}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 29
Error	37.9
Cost	1764

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -96000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -7.4 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-242}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.25 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 30
Error	37.2
Cost	1764

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 18000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 31
Error	37.1
Cost	1764

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+15}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-294}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 64000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 32
Error	41.4
Cost	1632

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 33
Error	50.4
Cost	1572

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ t_3 := b \cdot \left(c \cdot \left(-z\right)\right)\\ t_4 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+248}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{-100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.012:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+120}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 34
Error	44.3
Cost	1500

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := y \cdot \left(-i \cdot j\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -270000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 35
Error	32.6
Cost	1488

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 36
Error	50.2
Cost	1308

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := b \cdot \left(c \cdot \left(-z\right)\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 37
Error	51.7
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 38
Error	49.8
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 39
Error	49.8
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 40
Error	51.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{+108} \lor \neg \left(i \leq 3.6 \cdot 10^{-44}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 41
Error	50.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;i \leq -2.15 \cdot 10^{+107} \lor \neg \left(i \leq 9 \cdot 10^{-43}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 42
Error	53.6
Cost	320

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

Reproduce

herbie shell --seed 2023031 
(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)))))