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

Average Error: 11.7 → 4.6

Time: 53.5s

Precision: binary64

Cost: 19080

Math

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

↓

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_3 := c \cdot \left(z \cdot b\right)\\ t_4 := a \cdot c - y \cdot i\\ t_5 := t_2 + j \cdot t_4\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;\left(t_1 - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - t_3\right)\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_2 + \mathsf{fma}\left(j, t_4, \mathsf{fma}\left(-i, y, y \cdot i\right) \cdot \left(j + j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot \left(x \cdot y\right) + {\left(\sqrt[3]{t_1}\right)}^{3}\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - t_3\\ \end{array} \]

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 (* c (* a j)))
        (t_2 (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* t i)))))
        (t_3 (* c (* z b)))
        (t_4 (- (* a c) (* y i)))
        (t_5 (+ t_2 (* j t_4))))
   (if (<= t_5 (- INFINITY))
     (+ (- t_1 (* a (* x t))) (- (* i (* t b)) t_3))
     (if (<= t_5 2e+302)
       (+ t_2 (fma j t_4 (* (fma (- i) y (* y i)) (+ j j))))
       (-
        (+ (+ (* z (* x y)) (pow (cbrt t_1) 3.0)) (* i (- (* t b) (* y j))))
        t_3)))))

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 = c * (a * j);
	double t_2 = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	double t_3 = c * (z * b);
	double t_4 = (a * c) - (y * i);
	double t_5 = t_2 + (j * t_4);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = (t_1 - (a * (x * t))) + ((i * (t * b)) - t_3);
	} else if (t_5 <= 2e+302) {
		tmp = t_2 + fma(j, t_4, (fma(-i, y, (y * i)) * (j + j)));
	} else {
		tmp = (((z * (x * y)) + pow(cbrt(t_1), 3.0)) + (i * ((t * b) - (y * j)))) - t_3;
	}
	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(c * Float64(a * j))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))))
	t_3 = Float64(c * Float64(z * b))
	t_4 = Float64(Float64(a * c) - Float64(y * i))
	t_5 = Float64(t_2 + Float64(j * t_4))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(t_1 - Float64(a * Float64(x * t))) + Float64(Float64(i * Float64(t * b)) - t_3));
	elseif (t_5 <= 2e+302)
		tmp = Float64(t_2 + fma(j, t_4, Float64(fma(Float64(-i), y, Float64(y * i)) * Float64(j + j))));
	else
		tmp = Float64(Float64(Float64(Float64(z * Float64(x * y)) + (cbrt(t_1) ^ 3.0)) + Float64(i * Float64(Float64(t * b) - Float64(y * j)))) - t_3);
	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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$3 = N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 + N[(j * t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+302], N[(t$95$2 + N[(j * t$95$4 + N[(N[((-i) * y + N[(y * i), $MachinePrecision]), $MachinePrecision] * N[(j + j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[Power[N[Power[t$95$1, 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]]

Target

Original	11.7
Target	19.5
Herbie	4.6

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

Derivation

1. Split input into 3 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

   1. Initial program 64.0

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

   2. Simplified 64.0

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

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

   3. Taylor expanded in y around 0 40.2

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

   4. Taylor expanded in c around 0 26.1

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

   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)))) < 2.0000000000000002e302

   1. Initial program 0.8

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

   2. Simplified 0.8

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

      [Start] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      sub-neg [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)} \]
      distribute-rgt-in [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]
      associate-+r+ [=>] 0.8	\[ \color{blue}{\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) + \left(-y \cdot i\right) \cdot j} \]
      *-commutative [=>] 0.8	\[ \left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) + \color{blue}{j \cdot \left(-y \cdot i\right)} \]
      cancel-sign-sub [<=] 0.8	\[ \color{blue}{\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(c \cdot a\right) \cdot j\right) - \left(-j\right) \cdot \left(-y \cdot i\right)} \]
      associate-+r- [<=] 0.8	\[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j - \left(-j\right) \cdot \left(-y \cdot i\right)\right)} \]
      *-commutative [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j - \left(-j\right) \cdot \left(-y \cdot i\right)\right) \]
      cancel-sign-sub [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + j \cdot \left(-y \cdot i\right)\right)} \]
      *-commutative [<=] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(\left(c \cdot a\right) \cdot j + \color{blue}{\left(-y \cdot i\right) \cdot j}\right) \]
      distribute-rgt-in [<=] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j \cdot \left(c \cdot a + \left(-y \cdot i\right)\right)} \]

   3. Applied egg-rr 0.8

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

   4. Simplified 0.8

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

      [Start] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right) + j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right)\right)\right) \]
      distribute-lft-out [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \color{blue}{j \cdot \left(\mathsf{fma}\left(-i, y, y \cdot i\right) + \mathsf{fma}\left(-i, y, y \cdot i\right)\right)}\right) \]
      distribute-rgt-out [<=] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \color{blue}{\left(\mathsf{fma}\left(-i, y, y \cdot i\right) \cdot j + \mathsf{fma}\left(-i, y, y \cdot i\right) \cdot j\right)}\right) \]
      fma-def [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-i, y, y \cdot i\right) \cdot j + \mathsf{fma}\left(-i, y, y \cdot i\right) \cdot j\right)} \]
      distribute-lft-out [=>] 0.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-i, y, y \cdot i\right) \cdot \left(j + j\right)}\right) \]

   if 2.0000000000000002e302 < (+.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 59.9

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

   2. Simplified 59.9

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

      [Start] 59.9	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      +-commutative [=>] 59.9	\[ \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      fma-def [=>] 59.9	\[ \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]
      *-commutative [=>] 59.9	\[ \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]
      *-commutative [=>] 59.9	\[ \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Taylor expanded in i around -inf 26.3

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

   4. Applied egg-rr 26.4

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{{\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}}\right)\right) - c \cdot \left(b \cdot z\right) \]

   5. Taylor expanded in y around inf 19.1

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(\color{blue}{y \cdot \left(z \cdot x\right)} + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right)\right) - c \cdot \left(b \cdot z\right) \]

   6. Simplified 18.6

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(\color{blue}{z \cdot \left(y \cdot x\right)} + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right)\right) - c \cdot \left(b \cdot z\right) \]
      Proof

      [Start] 19.1	\[ \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right)\right) - c \cdot \left(b \cdot z\right) \]
      associate-*r* [=>] 27.0	\[ \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(\color{blue}{\left(y \cdot z\right) \cdot x} + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right)\right) - c \cdot \left(b \cdot z\right) \]
      *-commutative [<=] 27.0	\[ \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(\color{blue}{\left(z \cdot y\right)} \cdot x + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right)\right) - c \cdot \left(b \cdot z\right) \]
      associate-*l* [=>] 18.6	\[ \left(-1 \cdot \left(i \cdot \left(y \cdot j - t \cdot b\right)\right) + \left(\color{blue}{z \cdot \left(y \cdot x\right)} + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right)\right) - c \cdot \left(b \cdot z\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 4.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-i, y, y \cdot i\right) \cdot \left(j + j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot \left(x \cdot y\right) + {\left(\sqrt[3]{c \cdot \left(a \cdot j\right)}\right)}^{3}\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.6
Cost	18440

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_2 + t_3\\ t_5 := c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(t_1 - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - t_5\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_2 + \left(j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right) + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot \left(x \cdot y\right) + {\left(\sqrt[3]{t_1}\right)}^{3}\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - t_5\\ \end{array} \]

Alternative 2
Error	6.9
Cost	12680

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_1 + t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_1 + \left(j \cdot \mathsf{fma}\left(-i, y, y \cdot i\right) + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 3
Error	6.9
Cost	11976

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := t_1 + j \cdot t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(j, t_2, t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4
Error	6.9
Cost	5704

\[\begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5
Error	24.5
Cost	2932

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{if}\;c \leq -175000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq -3.35 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-206}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-210}:\\ \;\;\;\;t_2 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.32 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	38.7
Cost	2689

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_5 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-193}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-299}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-171}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-141}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+55}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+150} \lor \neg \left(a \leq 1.04 \cdot 10^{+157}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	38.5
Cost	2424

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_5 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_6 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-129}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-268}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-268}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-58}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	37.4
Cost	2412

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-141}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 0.007:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 9
Error	24.0
Cost	2404

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-157}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-250}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 0.0037:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+151}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_2\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+273}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	25.5
Cost	2396

\[\begin{array}{l} t_1 := \left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + \left(i \cdot \left(t \cdot b\right) - c \cdot \left(z \cdot b\right)\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-215}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \]

Alternative 11
Error	38.0
Cost	2160

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-203}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 12
Error	38.9
Cost	2160

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-298}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-140}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-11}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{+55}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	38.9
Cost	2160

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-10}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 14
Error	37.6
Cost	2028

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{-10}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-185}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-256}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	24.7
Cost	2008

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.00092:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 16
Error	11.9
Cost	1988

\[\begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(c \cdot \left(a \cdot j - z \cdot b\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 17
Error	50.7
Cost	1904

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_4 := c \cdot \left(a \cdot j\right)\\ t_5 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+252}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+157}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -4.35 \cdot 10^{+74}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -445000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.06 \cdot 10^{-144}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 18
Error	44.5
Cost	1896

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+143}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	38.4
Cost	1896

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-268}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-143}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 20
Error	36.9
Cost	1896

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-11}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-267}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	27.8
Cost	1877

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 370000000 \lor \neg \left(t \leq 1.7 \cdot 10^{+236}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Error	42.2
Cost	1632

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	38.4
Cost	1632

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.00165:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	49.7
Cost	1572

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ t_3 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 25
Error	49.9
Cost	1572

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 21500000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	50.1
Cost	1308

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+75}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	49.7
Cost	1112

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 28
Error	49.2
Cost	980

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -0.56:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 29
Error	51.5
Cost	849

\[\begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-216} \lor \neg \left(j \leq 1.35 \cdot 10^{-125}\right) \land j \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 30
Error	50.9
Cost	848

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 31
Error	53.2
Cost	320

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

Alternative 32
Error	53.5
Cost	320

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

Reproduce

herbie shell --seed 2023016 
(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)))))