Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 18.9% → 12.44%

Time: 52.5s

Precision: binary64

Cost: 18248

Math

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

↓

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - z \cdot c, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- t_1 (+ (* b (- (* z c) (* a i))) (* x (- (* t a) (* y z)))))))
   (if (<= t_2 (- INFINITY))
     (- (* i (* a b)) (* c (* z b)))
     (if (<= t_2 2e+303)
       (fma x (- (* y z) (* t a)) (fma b (- (* a i) (* z c)) t_1))
       (- (* y (- (* x z) (* i j))) (* a (* x t)))))))

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (i * (a * b)) - (c * (z * b));
	} else if (t_2 <= 2e+303) {
		tmp = fma(x, ((y * z) - (t * a)), fma(b, ((a * i) - (z * c)), t_1));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (a * (x * t));
	}
	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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

↓

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(i * Float64(a * b)) - Float64(c * Float64(z * b)));
	elseif (t_2 <= 2e+303)
		tmp = fma(x, Float64(Float64(y * z) - Float64(t * a)), fma(b, Float64(Float64(a * i) - Float64(z * c)), t_1));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(a * Float64(x * t)));
	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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+303], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	18.9%
Target	24.87%
Herbie	12.44%

\[\begin{array}{l} \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array} \]

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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -inf.0

   1. Initial program 100

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

   2. Simplified 100

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

      [Start] 100	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 100	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 100	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 100	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in b around inf 89.1

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   4. Taylor expanded in a around 0 69.72

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 2e303

   1. Initial program 1.36

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

   2. Simplified 1.36

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

      [Start] 1.36	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 1.36	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 1.36	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 1.36	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   if 2e303 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 94.1

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

   2. Simplified 94.1

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

      [Start] 94.1	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 94.1	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 94.1	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 94.1	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in b around 0 85.3

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

   4. Taylor expanded in c around 0 76

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

   5. Simplified 55

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

      [Start] 76	\[ \left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right) \]
      *-commutative [=>] 76	\[ \left(y \cdot z - \color{blue}{t \cdot a}\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right) \]
      mul-1-neg [=>] 76	\[ \left(y \cdot z - t \cdot a\right) \cdot x + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)} \]
      unsub-neg [=>] 76	\[ \color{blue}{\left(y \cdot z - t \cdot a\right) \cdot x - y \cdot \left(i \cdot j\right)} \]
      *-commutative [=>] 76	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} - y \cdot \left(i \cdot j\right) \]
      *-commutative [<=] 76	\[ x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - y \cdot \left(i \cdot j\right) \]
      cancel-sign-sub-inv [=>] 76	\[ x \cdot \color{blue}{\left(y \cdot z + \left(-a\right) \cdot t\right)} - y \cdot \left(i \cdot j\right) \]
      distribute-rgt-in [=>] 76	\[ \color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(\left(-a\right) \cdot t\right) \cdot x\right)} - y \cdot \left(i \cdot j\right) \]
      associate-*r* [<=] 65.11	\[ \left(\color{blue}{y \cdot \left(z \cdot x\right)} + \left(\left(-a\right) \cdot t\right) \cdot x\right) - y \cdot \left(i \cdot j\right) \]
      mul-1-neg [<=] 65.11	\[ \left(y \cdot \left(z \cdot x\right) + \left(\color{blue}{\left(-1 \cdot a\right)} \cdot t\right) \cdot x\right) - y \cdot \left(i \cdot j\right) \]
      associate-*r* [<=] 54.99	\[ \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)}\right) - y \cdot \left(i \cdot j\right) \]
      associate-*r* [<=] 54.99	\[ \left(y \cdot \left(z \cdot x\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)}\right) - y \cdot \left(i \cdot j\right) \]
      mul-1-neg [=>] 54.99	\[ \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - y \cdot \left(i \cdot j\right) \]
      unsub-neg [=>] 54.99	\[ \color{blue}{\left(y \cdot \left(z \cdot x\right) - a \cdot \left(t \cdot x\right)\right)} - y \cdot \left(i \cdot j\right) \]
      associate--l- [=>] 54.99	\[ \color{blue}{y \cdot \left(z \cdot x\right) - \left(a \cdot \left(t \cdot x\right) + y \cdot \left(i \cdot j\right)\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 12.44

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq -\infty:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	12.44%
Cost	5704

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 2
Error	60.57%
Cost	2556

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_5 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_6 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-35}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-153}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-191}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-259}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-150}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-141}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-65}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-15}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	56.85%
Cost	2544

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -6.7 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{-95}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-243}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -9.6 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - t_2\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.18 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - t_2\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4 + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4
Error	60.52%
Cost	2420

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j\right) - t_2\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{-49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.36 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{-242}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - t_2\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+220}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Error	59.35%
Cost	2292

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_5 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-308}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-210}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 96000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 6
Error	50.23%
Cost	2280

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := b \cdot i - x \cdot t\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+31}:\\ \;\;\;\;a \cdot t_2\\ \mathbf{elif}\;a \leq -800000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-85}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-287}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{1}{t_2}}\\ \end{array} \]

Alternative 7
Error	32.31%
Cost	2269

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;t_4 + t_2\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-165}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-65}:\\ \;\;\;\;t_4 - \left(z \cdot \left(b \cdot c\right) + t \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 8200 \lor \neg \left(x \leq 2.3 \cdot 10^{+122}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(j \cdot \left(t \cdot c\right) - j \cdot \left(y \cdot i\right)\right)\\ \end{array} \]

Alternative 8
Error	32.31%
Cost	2268

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ t_4 := a \cdot \left(x \cdot t\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;t_5 + t_2\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-165}:\\ \;\;\;\;t_5 + t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-66}:\\ \;\;\;\;t_5 - \left(z \cdot \left(b \cdot c\right) + t \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t_4\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-10}:\\ \;\;\;\;t_1 + \left(c \cdot \left(t \cdot j\right) - t_4\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+122}:\\ \;\;\;\;t_2 + \left(j \cdot \left(t \cdot c\right) - j \cdot \left(y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	28.11%
Cost	2260

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t_4 + \left(t_1 - t \cdot \left(x \cdot a\right)\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;t_4 + t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+108}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	60.18%
Cost	2160

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-295}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-234}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 7.3 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-44}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	60.15%
Cost	2156

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.12 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+220}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 12
Error	49.32%
Cost	2148

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-10}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Error	58.55%
Cost	2028

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.65 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -8.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-208}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 14
Error	59.73%
Cost	2028

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-95}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 15
Error	40.5%
Cost	2008

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - t_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	32.04%
Cost	1744

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t_3 + t_1\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{-48}:\\ \;\;\;\;t_3 + t_2\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-96}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+41}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 17
Error	71.68%
Cost	1500

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;x \leq -37000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \end{array} \]

Alternative 18
Error	33.58%
Cost	1480

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{-24}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - x \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 19
Error	58.71%
Cost	1368

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	60.69%
Cost	1368

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;c \leq -2.65 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	77.55%
Cost	1309

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.15 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+114} \lor \neg \left(c \leq 9 \cdot 10^{+273}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Error	77.08%
Cost	1308

\[\begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.3 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	78%
Cost	1176

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 24
Error	78.75%
Cost	1176

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	63.23%
Cost	1104

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	77.69%
Cost	980

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 27
Error	78.72%
Cost	848

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 1000000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	77.71%
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq -1.16 \cdot 10^{+83} \lor \neg \left(c \leq 9.2 \cdot 10^{-63}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 29
Error	84.25%
Cost	320

\[a \cdot \left(b \cdot i\right) \]

Alternative 30
Error	83.92%
Cost	320

\[b \cdot \left(a \cdot i\right) \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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