Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.1 → 7.7

Time: 1.1min

Precision: binary64

Cost: 12680

Math

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

↓

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

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)))))))
   (if (<= t_2 (- INFINITY))
     (* i (- (* a b) (* y j)))
     (if (<= t_2 2e+305)
       (+
        t_1
        (+
         (+ (* x (- (* y z) (* t a))) (* x (fma (- a) t (* t a))))
         (* b (- (* a i) (* z c)))))
       (+ t_1 (- (* z (- (* x y) (* b c))) (* t (* x a))))))))

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

Target

Original	12.1
Target	15.7
Herbie	7.7

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 64.0

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

      [Start] 64.0	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      +-commutative [=>] 64.0	\[ \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]
      fma-def [=>] 64.0	\[ \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Taylor expanded in i around inf 43.3

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

   4. Simplified 43.3

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

      [Start] 43.3	\[ \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i \]
      *-commutative [=>] 43.3	\[ \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
      associate-*r* [=>] 43.3	\[ i \cdot \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} - -1 \cdot \left(a \cdot b\right)\right) \]
      fma-neg [=>] 43.3	\[ i \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, --1 \cdot \left(a \cdot b\right)\right)} \]
      mul-1-neg [=>] 43.3	\[ i \cdot \mathsf{fma}\left(-1 \cdot y, j, -\color{blue}{\left(-a \cdot b\right)}\right) \]
      remove-double-neg [=>] 43.3	\[ i \cdot \mathsf{fma}\left(-1 \cdot y, j, \color{blue}{a \cdot b}\right) \]
      mul-1-neg [=>] 43.3	\[ i \cdot \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \]
      *-commutative [=>] 43.3	\[ i \cdot \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \]

   5. Applied egg-rr 43.3

      \[\leadsto i \cdot \color{blue}{\left(b \cdot a - y \cdot j\right)} \]

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 1.9999999999999999e305

   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. Applied egg-rr 0.8

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

   if 1.9999999999999999e305 < (+.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 61.8

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

   2. Taylor expanded in i around 0 50.2

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

   3. Simplified 35.3

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

      [Start] 50.2	\[ \left(\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      sub-neg [=>] 50.2	\[ \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + \left(-c \cdot \left(z \cdot b\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
      mul-1-neg [<=] 50.2	\[ \left(\left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      +-commutative [=>] 50.2	\[ \color{blue}{\left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
      *-commutative [=>] 50.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      cancel-sign-sub-inv [=>] 50.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + x \cdot \color{blue}{\left(y \cdot z + \left(-a\right) \cdot t\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      *-commutative [<=] 50.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + x \cdot \left(y \cdot z + \color{blue}{t \cdot \left(-a\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      distribute-lft-out [<=] 50.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) + x \cdot \left(t \cdot \left(-a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-*r* [=>] 44.8	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(x \cdot \left(y \cdot z\right) + \color{blue}{\left(x \cdot t\right) \cdot \left(-a\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      *-commutative [<=] 44.8	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(x \cdot \left(y \cdot z\right) + \color{blue}{\left(t \cdot x\right)} \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      *-commutative [=>] 44.8	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(x \cdot \left(y \cdot z\right) + \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      neg-mul-1 [=>] 44.8	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(x \cdot \left(y \cdot z\right) + \color{blue}{\left(-1 \cdot a\right)} \cdot \left(t \cdot x\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-*r* [<=] 44.8	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(x \cdot \left(y \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      *-commutative [<=] 44.8	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(\color{blue}{\left(y \cdot z\right) \cdot x} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-*r* [<=] 37.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(\color{blue}{y \cdot \left(z \cdot x\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      mul-1-neg [=>] 37.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      unsub-neg [=>] 37.2	\[ \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) - a \cdot \left(t \cdot x\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 7.7

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

Alternatives

Alternative 1
Error	7.7
Cost	11976

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

Alternative 2
Error	7.7
Cost	5704

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

Alternative 3
Error	29.3
Cost	3196

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_3 + t_2\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_6 := t_3 + t_5\\ t_7 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_8 := t_2 - x \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+173}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+73}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -20500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-45}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-112}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-271}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-229}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-180}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-155}:\\ \;\;\;\;t_5 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+67}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+92}:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 4
Error	37.7
Cost	2941

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-145}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-172}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \frac{-1}{\frac{1}{x \cdot t - b \cdot i}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+161} \lor \neg \left(z \leq 1.05 \cdot 10^{+227}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	20.2
Cost	2788

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := \left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_1\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + t_3\\ t_5 := t_3 + \left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-95}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-280}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-268}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-248}:\\ \;\;\;\;t_3 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-180}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-130}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 6
Error	36.7
Cost	2676

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;c \leq -6 \cdot 10^{+27}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \frac{-1}{\frac{1}{x \cdot t - b \cdot i}}\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7
Error	43.2
Cost	2557

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-116}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-206}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+113} \lor \neg \left(z \leq 3 \cdot 10^{+187}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	43.1
Cost	2557

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-193}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-206}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+112} \lor \neg \left(z \leq 8.5 \cdot 10^{+186}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	38.6
Cost	2544

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-159}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-172}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \frac{-1}{\frac{1}{x \cdot t - b \cdot i}}\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 10^{+228}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	28.0
Cost	2536

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-266}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \frac{-1}{\frac{1}{x \cdot t - b \cdot i}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	26.1
Cost	2401

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := \left(c \cdot \left(t \cdot j\right) - t_1\right) + t_2\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t_5 + t_2\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-253}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-279}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-258}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-196}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{-152} \lor \neg \left(x \leq 1.9 \cdot 10^{-93}\right) \land x \leq 1.9 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5 + t_4\\ \end{array} \]

Alternative 12
Error	33.2
Cost	2148

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + t_4\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-271}:\\ \;\;\;\;t_1 + t_4\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-227}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-198}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 0.16:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	33.4
Cost	2148

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-270}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-227}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 0.0066:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Error	33.1
Cost	2148

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+75}:\\ \;\;\;\;t_4 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-271}:\\ \;\;\;\;t_1 + t_5\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-227}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-43}:\\ \;\;\;\;t_5 - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	32.2
Cost	1884

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -31000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	50.1
Cost	1837

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+142} \lor \neg \left(c \leq 3.65 \cdot 10^{+289}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 17
Error	41.4
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-99}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	37.6
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6500:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.00035:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	36.9
Cost	1632

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-197}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	50.9
Cost	1572

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	51.0
Cost	1572

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-197}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	49.8
Cost	1572

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-197}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	48.0
Cost	1440

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;x \leq -14500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 24
Error	50.1
Cost	1309

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+142} \lor \neg \left(c \leq 3.65 \cdot 10^{+289}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 25
Error	36.8
Cost	1236

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 26
Error	49.7
Cost	980

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 27
Error	49.4
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	37.1
Cost	841

\[\begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+23} \lor \neg \left(c \leq 1.4 \cdot 10^{-61}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 29
Error	49.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{-30} \lor \neg \left(c \leq 8.5 \cdot 10^{-15}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 30
Error	49.6
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq -5.9 \cdot 10^{-30} \lor \neg \left(c \leq 8 \cdot 10^{-15}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 31
Error	53.5
Cost	320

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

Alternative 32
Error	53.4
Cost	320

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

Reproduce

herbie shell --seed 2023039 
(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)))))