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

Percentage Accurate: 74.0% → 82.8%

Time: 25.7s

Precision: binary64

Cost: 3780

• 57.7% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

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
         (-
          (* j (- (* a c) (* y i)))
          (+ (* b (- (* z c) (* t i))) (* x (- (* t a) (* y z)))))))
   (if (<= t_1 INFINITY)
     t_1
     (+ (* y (- (* x z) (* i j))) (* c (- (* a j) (* z b)))))))

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 = (j * ((a * c) - (y * i))) - ((b * ((z * c) - (t * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	}
	return tmp;
}

Java

public static 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)));
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - ((b * ((z * c) - (t * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

↓

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - ((b * ((z * c) - (t * i))) + (x * ((t * a) - (y * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)))
	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(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(t * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(a * j) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

↓

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) - ((b * ((z * c) - (t * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	end
	tmp_2 = 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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	74.0%
Target	60.3%
Herbie	82.8%

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

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

   1. Initial program 88.0%

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

   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))))

   1. Initial program 0.0%

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

   2. Simplified 0.0%

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

      [Start] 0.0%	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      cancel-sign-sub [<=] 0.0%	\[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]
      cancel-sign-sub-inv [=>] 0.0%	\[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]
      *-commutative [=>] 0.0%	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]
      remove-double-neg [=>] 0.0%	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]
      *-commutative [=>] 0.0%	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Taylor expanded in a around 0 29.3%

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

   4. Taylor expanded in t around 0 48.6%

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

   5. Simplified 63.9%

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

      [Start] 48.6%	\[ \left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(y \cdot \left(z \cdot x\right) + c \cdot \left(a \cdot j\right)\right)\right) - c \cdot \left(b \cdot z\right) \]
      associate-+r+ [=>] 48.6%	\[ \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right)} - c \cdot \left(b \cdot z\right) \]
      associate--l+ [=>] 48.6%	\[ \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right)} \]
      associate-*r* [=>] 43.3%	\[ \left(-1 \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot j\right)} + y \cdot \left(z \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      *-commutative [<=] 43.3%	\[ \left(-1 \cdot \left(\color{blue}{\left(y \cdot i\right)} \cdot j\right) + y \cdot \left(z \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      associate-*r* [<=] 50.2%	\[ \left(-1 \cdot \color{blue}{\left(y \cdot \left(i \cdot j\right)\right)} + y \cdot \left(z \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      *-commutative [=>] 50.2%	\[ \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + y \cdot \left(z \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      associate-*r* [=>] 50.2%	\[ \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + y \cdot \left(z \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      *-commutative [=>] 50.2%	\[ \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(z \cdot x\right) \cdot y}\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      distribute-rgt-in [<=] 55.3%	\[ \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      +-commutative [=>] 55.3%	\[ y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      neg-mul-1 [<=] 55.3%	\[ y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      sub-neg [<=] 55.3%	\[ y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\right) \]
      sub-neg [=>] 55.3%	\[ y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(-c \cdot \left(b \cdot z\right)\right)\right)} \]
      distribute-rgt-neg-in [=>] 55.3%	\[ y \cdot \left(z \cdot x - i \cdot j\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{c \cdot \left(-b \cdot z\right)}\right) \]
      *-commutative [=>] 55.3%	\[ y \cdot \left(z \cdot x - i \cdot j\right) + \left(c \cdot \left(a \cdot j\right) + c \cdot \left(-\color{blue}{z \cdot b}\right)\right) \]
      distribute-lft-neg-in [=>] 55.3%	\[ y \cdot \left(z \cdot x - i \cdot j\right) + \left(c \cdot \left(a \cdot j\right) + c \cdot \color{blue}{\left(\left(-z\right) \cdot b\right)}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 82.5%

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

Alternatives

Alternative 1
Accuracy	82.8%
Cost	3780

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

Alternative 2
Accuracy	63.9%
Cost	2008

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.035:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 3
Accuracy	58.1%
Cost	1490

\[\begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+209} \lor \neg \left(t \leq -1.15 \cdot 10^{+146}\right) \land \left(t \leq -4.8 \cdot 10^{+27} \lor \neg \left(t \leq 5 \cdot 10^{+89}\right)\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 4
Accuracy	59.7%
Cost	1489

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+166} \lor \neg \left(t \leq -1.22 \cdot 10^{+28}\right) \land t \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 5
Accuracy	65.3%
Cost	1480

\[\begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6
Accuracy	50.8%
Cost	1236

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-201}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-166}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 0.0118:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	51.9%
Cost	1104

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	44.1%
Cost	973

\[\begin{array}{l} \mathbf{if}\;z \leq -1.34 \cdot 10^{+250}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+82} \lor \neg \left(z \leq 8.2 \cdot 10^{+150}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 9
Accuracy	41.8%
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+241}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+144}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10
Accuracy	29.7%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-239}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-215}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq 0.00027:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 11
Accuracy	30.1%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-203}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-215}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 0.00025:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12
Accuracy	29.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{+26} \lor \neg \left(j \leq 6.9 \cdot 10^{-85}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 13
Accuracy	28.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-19} \lor \neg \left(y \leq 3.1 \cdot 10^{+149}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 14
Accuracy	29.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-20} \lor \neg \left(y \leq 2.4 \cdot 10^{+150}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 15
Accuracy	29.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 16
Accuracy	23.0%
Cost	320

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

Reproduce

herbie shell --seed 2023272 
(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)))))