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

Average Error: 12.5 → 8.3

Time: 42.2s

Precision: binary64

Cost: 12680

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t_2 \leq 10^{+301}:\\ \;\;\;\;t_1 - \left(\left(b \cdot \mathsf{fma}\left(-i, t, t \cdot i\right) + b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(y \cdot i - a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z - i \cdot j, \left(x \cdot t\right) \cdot \left(-a\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* 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))))
        (t_2 (+ (* j (- (* a c) (* y i))) (+ t_1 (* b (- (* t i) (* z c)))))))
   (if (<= t_2 (- INFINITY))
     (* a (- (* c j) (* x t)))
     (if (<= t_2 1e+301)
       (-
        t_1
        (+
         (+ (* b (fma (- i) t (* t i))) (* b (- (* z c) (* t i))))
         (* j (- (* y i) (* a c)))))
       (fma y (- (* x z) (* i j)) (* (* x t) (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (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));
	double t_2 = (j * ((a * c) - (y * i))) + (t_1 + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = a * ((c * j) - (x * t));
	} else if (t_2 <= 1e+301) {
		tmp = t_1 - (((b * fma(-i, t, (t * i))) + (b * ((z * c) - (t * i)))) + (j * ((y * i) - (a * c))));
	} else {
		tmp = fma(y, ((x * z) - (i * j)), ((x * t) * -a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (t_2 <= 1e+301)
		tmp = Float64(t_1 - Float64(Float64(Float64(b * fma(Float64(-i), t, Float64(t * i))) + Float64(b * Float64(Float64(z * c) - Float64(t * i)))) + Float64(j * Float64(Float64(y * i) - Float64(a * c)))));
	else
		tmp = fma(y, Float64(Float64(x * z) - Float64(i * j)), Float64(Float64(x * t) * Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+301], N[(t$95$1 - N[(N[(N[(b * N[((-i) * t + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	12.5
Target	19.9
Herbie	8.3

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

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

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, t \cdot i - z \cdot c, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]
      Proof
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 t i) (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 t i) (neg.f64 (*.f64 c z)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (*.f64 c z)) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 t i)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c a)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (neg.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 1 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.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))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in a around inf 45.1

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

   4. Simplified 45.1

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
      Proof
      (*.f64 a (-.f64 (*.f64 c j) (*.f64 t x))): 0 points increase in error, 0 points decrease in error
      (*.f64 a (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 c j) (neg.f64 (*.f64 t x))))): 0 points increase in error, 0 points decrease in error
      (*.f64 a (+.f64 (*.f64 c j) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 t x))))): 0 points increase in error, 0 points decrease in error
      (*.f64 a (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 t x)) (*.f64 c j)))): 0 points increase in error, 0 points decrease in error

   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)))) < 1.00000000000000005e301

   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

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
      Proof
      (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 z c) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z)) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 j))) (-.f64 (*.f64 a c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 (neg.f64 (neg.f64 j)) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c a)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (Rewrite=> cancel-sign-sub_binary64 (+.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 (neg.f64 j) (-.f64 (*.f64 c a) (*.f64 y i)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.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))))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 0.8

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

   4. Taylor expanded in b around 0 0.8

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

   if 1.00000000000000005e301 < (+.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 59.4

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

   2. Simplified 59.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
      Proof
      (fma.f64 j (-.f64 (*.f64 a c) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 t i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c a)) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 z c) (*.f64 t i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (-.f64 (*.f64 c a) (*.f64 y i)) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z)) (*.f64 t i))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))) (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))))): 1 points increase in error, 1 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.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))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in b around 0 54.7

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

   4. Taylor expanded in c around 0 48.6

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

   5. Simplified 36.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x \cdot z - j \cdot i, \left(t \cdot x\right) \cdot \left(-a\right)\right)} \]
      Proof
      (fma.f64 y (-.f64 (*.f64 x z) (*.f64 j i)) (*.f64 (*.f64 t x) (neg.f64 a))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 z x)) (*.f64 j i)) (*.f64 (*.f64 t x) (neg.f64 a))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (-.f64 (*.f64 z x) (Rewrite<= *-commutative_binary64 (*.f64 i j))) (*.f64 (*.f64 t x) (neg.f64 a))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 z x) (neg.f64 (*.f64 i j)))) (*.f64 (*.f64 t x) (neg.f64 a))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (+.f64 (*.f64 z x) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 i j)))) (*.f64 (*.f64 t x) (neg.f64 a))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (+.f64 (*.f64 z x) (*.f64 -1 (*.f64 i j))) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 t x) a)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (+.f64 (*.f64 z x) (*.f64 -1 (*.f64 i j))) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 a (*.f64 t x))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (+.f64 (*.f64 z x) (*.f64 -1 (*.f64 i j))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 a (*.f64 t x))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 (*.f64 z x) (*.f64 -1 (*.f64 i j)))) (*.f64 -1 (*.f64 a (*.f64 t x))))): 2 points increase in error, 1 points decrease in error
      (+.f64 (*.f64 y (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 i j)) (*.f64 z x)))) (*.f64 -1 (*.f64 a (*.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 (*.f64 -1 (*.f64 i j)) y) (*.f64 (*.f64 z x) y))) (*.f64 -1 (*.f64 a (*.f64 t x)))): 2 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (*.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 i) j)) y) (*.f64 (*.f64 z x) y)) (*.f64 -1 (*.f64 a (*.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (*.f64 -1 i) (*.f64 j y))) (*.f64 (*.f64 z x) y)) (*.f64 -1 (*.f64 a (*.f64 t x)))): 19 points increase in error, 22 points decrease in error
      (+.f64 (+.f64 (*.f64 (*.f64 -1 i) (Rewrite<= *-commutative_binary64 (*.f64 y j))) (*.f64 (*.f64 z x) y)) (*.f64 -1 (*.f64 a (*.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 i (*.f64 y j)))) (*.f64 (*.f64 z x) y)) (*.f64 -1 (*.f64 a (*.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (Rewrite<= *-commutative_binary64 (*.f64 y (*.f64 z x)))) (*.f64 -1 (*.f64 a (*.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (+.f64 (*.f64 y (*.f64 z x)) (*.f64 -1 (*.f64 a (*.f64 t x)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (*.f64 y (*.f64 z x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 y (*.f64 z x)) (*.f64 -1 (*.f64 a (*.f64 t x)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (+.f64 (*.f64 y (*.f64 z x)) (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 a (*.f64 t x)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (Rewrite=> unsub-neg_binary64 (-.f64 (*.f64 y (*.f64 z x)) (*.f64 a (*.f64 t x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (-.f64 (*.f64 y (*.f64 z x)) (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 a t) x)))): 30 points increase in error, 18 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y z) x)) (*.f64 (*.f64 a t) x))): 11 points increase in error, 24 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (Rewrite=> distribute-rgt-out--_binary64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 a t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (*.f64 i (*.f64 y j))) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (*.f64 y z) (*.f64 a t)) x))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (-.f64 (*.f64 y z) (*.f64 a t)) x) (*.f64 -1 (*.f64 i (*.f64 y j))))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 8.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) \leq 10^{+301}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot \mathsf{fma}\left(-i, t, t \cdot i\right) + b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(y \cdot i - a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z - i \cdot j, \left(x \cdot t\right) \cdot \left(-a\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	8.4
Cost	11144

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t_1 \leq 10^{+301}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z - i \cdot j, \left(x \cdot t\right) \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 2
Error	9.2
Cost	5704

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]

Alternative 3
Error	41.7
Cost	2952

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_6 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.62 \cdot 10^{+148}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.75 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-12}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.75 \cdot 10^{-36}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-142}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.32 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-235}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-260}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	41.9
Cost	2820

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-121}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-198}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+58}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	37.5
Cost	2676

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z\right) - i \cdot \left(y \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+24}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-77}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-222}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	40.1
Cost	2556

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_5 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.62 \cdot 10^{+148}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -3.3 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -9.4 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -2.75 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-220}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+101}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 2.75 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	37.8
Cost	2556

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	41.9
Cost	2424

\[\begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.12:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{+124}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	38.1
Cost	2420

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z\right) - i \cdot \left(y \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-172}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	23.2
Cost	2268

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := i \cdot \left(t \cdot b\right) + \left(t_3 - a \cdot \left(x \cdot t\right)\right)\\ t_5 := t_1 + t_3\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-99}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-188}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-254}:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{-70}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	19.3
Cost	2260

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + \left(b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + \left(t_3 - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+36}:\\ \;\;\;\;t_1 + t_3\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+231}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	41.0
Cost	2160

\[\begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;i \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -5.9 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-141}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.05 \cdot 10^{-233}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{-261}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 13
Error	43.7
Cost	2028

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-180}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	27.8
Cost	1884

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	26.2
Cost	1876

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-210}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+140}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	51.0
Cost	1772

\[\begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 17
Error	44.9
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -460:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-47}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 360000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 18
Error	20.4
Cost	1744

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.22 \cdot 10^{-76}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	51.1
Cost	1704

\[\begin{array}{l} t_1 := \left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{if}\;t \leq -1.62 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 20
Error	51.1
Cost	1704

\[\begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-259}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 21
Error	50.9
Cost	1704

\[\begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-260}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-94}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 22
Error	49.8
Cost	1112

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -66000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	49.9
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-47}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	50.3
Cost	980

\[\begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.48 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	49.6
Cost	980

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-265}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Error	49.3
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -210000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-47}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	49.6
Cost	716

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-265}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	49.6
Cost	584

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -9.4 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-30}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 29
Error	53.5
Cost	320

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

Reproduce

herbie shell --seed 2022329 
(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)))))