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

Percentage Accurate: 73.2% → 82.4%

Time: 42.4s

Precision: binary64

Cost: 3780

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	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 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	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 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	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 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * ((x * z) - (i * j));
	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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	73.2%
Target	59.2%
Herbie	82.4%

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

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 91.0%

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

   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 18.0%

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

      [Start] 0.0%	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
      sub-neg [=>] 0.0%	\[ \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
      +-commutative [=>] 0.0%	\[ \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
      associate-+l+ [=>] 0.0%	\[ \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]
      distribute-rgt-neg-in [=>] 0.0%	\[ \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]
      +-commutative [<=] 0.0%	\[ b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]
      fma-def [=>] 6.0%	\[ \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]
      sub-neg [=>] 6.0%	\[ \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]
      +-commutative [=>] 6.0%	\[ \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]
      distribute-neg-in [=>] 6.0%	\[ \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]
      unsub-neg [=>] 6.0%	\[ \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]
      remove-double-neg [=>] 6.0%	\[ \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]
      *-commutative [=>] 6.0%	\[ \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Taylor expanded in y around inf 52.3%

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

   4. Simplified 52.3%

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

      [Start] 52.3%	\[ \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y \]
      *-commutative [=>] 52.3%	\[ \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]
      mul-1-neg [=>] 52.3%	\[ y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]
      unsub-neg [=>] 52.3%	\[ y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

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

Alternatives

Alternative 1
Accuracy	82.4%
Cost	3780

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

Alternative 2
Accuracy	55.2%
Cost	1752

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	63.3%
Cost	1744

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-246}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - i \cdot \left(y \cdot j\right)\\ \end{array} \]

Alternative 4
Accuracy	50.8%
Cost	1620

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-189}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 5
Accuracy	60.2%
Cost	1620

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - t_1\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;t_3 - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	67.9%
Cost	1612

\[\begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	52.2%
Cost	1369

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+102} \lor \neg \left(y \leq 2.3 \cdot 10^{+172}\right) \land y \leq 5.2 \cdot 10^{+186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	56.4%
Cost	1356

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.42 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	29.8%
Cost	1308

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -3.75 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.05 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	30.4%
Cost	1308

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	30.4%
Cost	1308

\[\begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-264}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	50.1%
Cost	1236

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	30.5%
Cost	1176

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-180}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-200}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	52.2%
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	48.6%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-188}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 16
Accuracy	29.5%
Cost	1044

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -6.7 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	40.9%
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-186}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 18
Accuracy	37.1%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 19
Accuracy	30.3%
Cost	716

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Accuracy	30.5%
Cost	716

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Accuracy	30.8%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 22
Accuracy	28.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+84} \lor \neg \left(b \leq 1.12 \cdot 10^{-90}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 23
Accuracy	29.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+83} \lor \neg \left(b \leq 2.7 \cdot 10^{-90}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 24
Accuracy	22.0%
Cost	320

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

Reproduce

herbie shell --seed 2023263 
(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)))))