Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.3 → 3.7

Time: 53.4s

Precision: binary64

Cost: 11977

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := j \cdot t_2 + t_1\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;\left(t \cdot \left(b \cdot i - x \cdot a\right) + c \cdot \left(a \cdot j\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, t_2, t_1\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* t i)))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (+ (* j t_2) t_1)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 4e+307)))
     (+ (+ (* t (- (* b i) (* x a))) (* c (* a j))) (* z (- (* x y) (* b c))))
     (fma j t_2 t_1))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	double t_2 = (a * c) - (y * i);
	double t_3 = (j * t_2) + t_1;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 4e+307)) {
		tmp = ((t * ((b * i) - (x * a))) + (c * (a * j))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = fma(j, t_2, t_1);
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(Float64(j * t_2) + t_1)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 4e+307))
		tmp = Float64(Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + Float64(c * Float64(a * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = fma(j, t_2, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 4e+307]], $MachinePrecision]], N[(N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * t$95$2 + t$95$1), $MachinePrecision]]]]]

Target

Original	12.3
Target	20.1
Herbie	3.7

\[\begin{array}{l} \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < -inf.0 or 3.99999999999999994e307 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 63.8

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

   2. Simplified 63.8

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

      [Start] 63.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      associate-+l- [=>] 63.8	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]
      fma-neg [=>] 63.8	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
      neg-sub0 [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)}\right) \]
      associate-+l- [<=] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)}\right) \]
      neg-sub0 [<=] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]
      distribute-rgt-neg-in [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]
      fma-def [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right)\right)}\right) \]
      sub-neg [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      distribute-neg-in [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      +-commutative [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      remove-double-neg [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{t \cdot i} + \left(-c \cdot z\right), j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      sub-neg [<=] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{t \cdot i - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      *-commutative [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      *-commutative [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, t \cdot i - z \cdot c, j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right)\right) \]

   3. Taylor expanded in z around -inf 29.3

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

   4. Simplified 25.5

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

      [Start] 29.3	\[ i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(\left(c \cdot b + -1 \cdot \left(y \cdot x\right)\right) \cdot z\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]
      +-commutative [=>] 29.3	\[ i \cdot \left(t \cdot b\right) + \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(\left(c \cdot b + -1 \cdot \left(y \cdot x\right)\right) \cdot z\right)\right)} \]
      mul-1-neg [=>] 29.3	\[ i \cdot \left(t \cdot b\right) + \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + \color{blue}{\left(-\left(c \cdot b + -1 \cdot \left(y \cdot x\right)\right) \cdot z\right)}\right) \]
      unsub-neg [=>] 29.3	\[ i \cdot \left(t \cdot b\right) + \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) - \left(c \cdot b + -1 \cdot \left(y \cdot x\right)\right) \cdot z\right)} \]
      associate-+r- [=>] 29.3	\[ \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) - \left(c \cdot b + -1 \cdot \left(y \cdot x\right)\right) \cdot z} \]

   5. Taylor expanded in c around inf 16.5

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 3.99999999999999994e307

   1. Initial program 0.9

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

   2. Simplified 0.9

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

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

3. Recombined 2 regimes into one program.

4. Final simplification 3.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) \leq -\infty \lor \neg \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;\left(t \cdot \left(b \cdot i - x \cdot a\right) + c \cdot \left(a \cdot j\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	3.7
Cost	5705

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;\left(t \cdot \left(b \cdot i - x \cdot a\right) + c \cdot \left(a \cdot j\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	21.2
Cost	3052

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := \left(t \cdot \left(b \cdot i - x \cdot a\right) + t_1\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := \left(y \cdot \left(x \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_5 := \left(t_1 - a \cdot \left(x \cdot t\right)\right) + t_4\\ t_6 := y \cdot \left(x \cdot z - i \cdot j\right) + t_4\\ t_7 := \left(j \cdot \left(a \cdot c\right) - x \cdot \left(t \cdot a\right)\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-108}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-155}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-225}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-90}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 16200:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+23}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+59}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	22.4
Cost	2800

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := \left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_2\\ t_4 := \left(j \cdot \left(a \cdot c\right) - x \cdot \left(t \cdot a\right)\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_6 := i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_7 := y \cdot \left(x \cdot z - i \cdot j\right) + t_2\\ \mathbf{if}\;i \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.26 \cdot 10^{-173}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-235}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{-237}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-181}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-39}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 0.0037:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 4
Error	23.6
Cost	2669

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + t_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-190}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-75} \lor \neg \left(x \leq 1.3 \cdot 10^{+99}\right) \land x \leq 1.75 \cdot 10^{+140}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	23.8
Cost	2668

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_1 + t_2\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_6 := \left(t_1 + j \cdot \left(a \cdot c\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;i \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-120}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{-235}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-237}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-194}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t_2\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-122}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-39}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Error	38.3
Cost	2556

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_6 := z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+142}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -7 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-12}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-175}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-220}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-264}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \leq -2.15 \cdot 10^{-295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 7
Error	36.4
Cost	2544

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-309}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	35.0
Cost	2544

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := c \cdot j - x \cdot t\\ t_3 := c \cdot \left(a \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{+113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -0.0065:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-153}:\\ \;\;\;\;\frac{a}{\frac{1}{t_2}}\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-250}:\\ \;\;\;\;a \cdot t_2\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-237}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 9
Error	26.6
Cost	2538

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-212} \lor \neg \left(t \leq 4 \cdot 10^{-104}\right) \land \left(t \leq 3.2 \cdot 10^{-53} \lor \neg \left(t \leq 2.95 \cdot 10^{-31}\right) \land t \leq 2.7 \cdot 10^{+42}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	26.7
Cost	2536

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.16 \cdot 10^{-124}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-39}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	24.5
Cost	2532

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c\right)\\ t_3 := \left(t_2 - x \cdot \left(t \cdot a\right)\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_5 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_6 := \left(t_5 + t_2\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+131}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-35}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t_4\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 11000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+60}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5 + t_4\\ \end{array} \]

Alternative 12
Error	31.1
Cost	2404

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(a \cdot j\right) + t_2\\ t_4 := z \cdot \left(x \cdot y\right) + t_2\\ \mathbf{if}\;y \leq -6 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-115}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+68}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+218}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+249}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+290}:\\ \;\;\;\;\frac{a}{\frac{1}{c \cdot j - x \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 13
Error	39.1
Cost	2028

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+151}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-308}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 14
Error	38.1
Cost	1897

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+67}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-7} \lor \neg \left(t \leq 4.8 \cdot 10^{+23}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	50.4
Cost	1836

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_3 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 16
Error	38.5
Cost	1764

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	50.1
Cost	1704

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-245}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 18
Error	49.5
Cost	1704

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-261}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 19
Error	49.5
Cost	1704

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-203}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 20
Error	49.5
Cost	1704

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-245}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 21
Error	43.5
Cost	1632

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;i \leq -1.8 \cdot 10^{+175}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -0.07:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -9.4 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-235}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.05 \cdot 10^{-212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 17:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	39.2
Cost	1632

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{+65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-237}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 23
Error	38.2
Cost	1501

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-202}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 35000000000 \lor \neg \left(a \leq 4.6 \cdot 10^{+92}\right) \land a \leq 10^{+147}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	43.7
Cost	1500

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -9 \cdot 10^{+174}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -7.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.12 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-235}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-177}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	51.1
Cost	1376

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 26
Error	38.0
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	49.5
Cost	1308

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-148}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 75000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	50.4
Cost	1244

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-152}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 29
Error	37.6
Cost	1237

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 8200000000 \lor \neg \left(a \leq 2.9 \cdot 10^{+96}\right) \land a \leq 9.6 \cdot 10^{+144}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 30
Error	51.1
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -1.09 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 31
Error	50.9
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 32
Error	49.7
Cost	585

\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-86} \lor \neg \left(a \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 33
Error	50.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 34
Error	53.0
Cost	320

\[a \cdot \left(c \cdot j\right) \]

Reproduce

herbie shell --seed 2023018 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))