Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.0 → 5.3

Time: 56.0s

Precision: binary64

Cost: 24008

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := \left(t_2 + t_1\right) + t_3\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_4 \leq 10^{+308}:\\ \;\;\;\;\left(t_1 - \left(b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right) - t_2\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, \mathsf{fma}\left(-b, z, t \cdot j\right), i \cdot \mathsf{fma}\left(a, b, j \cdot \left(-y\right)\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (+ (+ t_2 t_1) t_3)))
   (if (<= t_4 (- INFINITY))
     (- (+ (* c (* t j)) (* y (- (* x z) (* i j)))) (* c (* z b)))
     (if (<= t_4 1e+308)
       (+ (- t_1 (- (* b (fma (- a) i (* a i))) t_2)) t_3)
       (fma c (fma (- b) z (* t j)) (* i (fma a b (* j (- y)))))))))

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 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = (t_2 + t_1) + t_3;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((c * (t * j)) + (y * ((x * z) - (i * j)))) - (c * (z * b));
	} else if (t_4 <= 1e+308) {
		tmp = (t_1 - ((b * fma(-a, i, (a * i))) - t_2)) + t_3;
	} else {
		tmp = fma(c, fma(-b, z, (t * j)), (i * fma(a, b, (j * -y))));
	}
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(Float64(t_2 + t_1) + t_3)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(c * Float64(t * j)) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) - Float64(c * Float64(z * b)));
	elseif (t_4 <= 1e+308)
		tmp = Float64(Float64(t_1 - Float64(Float64(b * fma(Float64(-a), i, Float64(a * i))) - t_2)) + t_3);
	else
		tmp = fma(c, fma(Float64(-b), z, Float64(t * j)), Float64(i * fma(a, b, Float64(j * Float64(-y)))));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+308], N[(N[(t$95$1 - N[(N[(b * N[((-a) * i + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], N[(c * N[((-b) * z + N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b + N[(j * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	12.0
Target	15.8
Herbie	5.3

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

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 64.0

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

   2. Simplified 64.0

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

      [Start] 64.0	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 64.0	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 64.0	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 64.0	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in a around 0 43.3

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

   4. Taylor expanded in y around 0 27.2

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

   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)))) < 1e308

   1. Initial program 0.8

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

   2. Applied egg-rr 0.8

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

   if 1e308 < (+.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 63.8

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

   2. Simplified 63.8

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

      [Start] 63.8	\[ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
      associate-+l- [=>] 63.8	\[ \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]
      fma-neg [=>] 63.8	\[ \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, -\left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)\right)} \]
      neg-sub0 [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{0 - \left(b \cdot \left(c \cdot z - i \cdot a\right) - j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      associate-+l- [<=] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right) \]
      neg-sub0 [<=] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      distribute-rgt-neg-in [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\right) \]
      fma-def [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - i \cdot a\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)}\right) \]
      sub-neg [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      distribute-neg-in [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      +-commutative [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      remove-double-neg [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a} + \left(-c \cdot z\right), j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      sub-neg [<=] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{i \cdot a - c \cdot z}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, \color{blue}{a \cdot i} - c \cdot z, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]
      *-commutative [=>] 63.8	\[ \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot t - i \cdot y\right)\right)\right) \]

   3. Taylor expanded in x around 0 59.3

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

   4. Taylor expanded in b around 0 59.3

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

   5. Simplified 25.0

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

      [Start] 59.3	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \left(c \cdot t - i \cdot y\right) \cdot j \]
      *-commutative [=>] 59.3	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
      *-commutative [<=] 59.3	\[ b \cdot \left(i \cdot a - c \cdot z\right) + j \cdot \left(c \cdot t - \color{blue}{y \cdot i}\right) \]
      cancel-sign-sub-inv [=>] 59.3	\[ b \cdot \left(i \cdot a - c \cdot z\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-y\right) \cdot i\right)} \]
      distribute-rgt-in [=>] 59.3	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \color{blue}{\left(\left(c \cdot t\right) \cdot j + \left(\left(-y\right) \cdot i\right) \cdot j\right)} \]
      mul-1-neg [<=] 59.3	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \left(\left(c \cdot t\right) \cdot j + \left(\color{blue}{\left(-1 \cdot y\right)} \cdot i\right) \cdot j\right) \]
      associate-*r* [<=] 51.8	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \left(\left(c \cdot t\right) \cdot j + \color{blue}{\left(-1 \cdot y\right) \cdot \left(i \cdot j\right)}\right) \]
      associate-*r* [<=] 51.8	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \left(\left(c \cdot t\right) \cdot j + \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)}\right) \]
      associate-*r* [<=] 43.6	\[ b \cdot \left(i \cdot a - c \cdot z\right) + \left(\color{blue}{c \cdot \left(t \cdot j\right)} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]
      sub-neg [=>] 43.6	\[ b \cdot \color{blue}{\left(i \cdot a + \left(-c \cdot z\right)\right)} + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]
      distribute-rgt-neg-out [<=] 43.6	\[ b \cdot \left(i \cdot a + \color{blue}{c \cdot \left(-z\right)}\right) + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]
      distribute-rgt-out [<=] 43.6	\[ \color{blue}{\left(\left(i \cdot a\right) \cdot b + \left(c \cdot \left(-z\right)\right) \cdot b\right)} + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]
      *-commutative [<=] 43.6	\[ \left(\left(i \cdot a\right) \cdot b + \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)}\right) + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]
      associate-+l+ [=>] 43.6	\[ \color{blue}{\left(i \cdot a\right) \cdot b + \left(b \cdot \left(c \cdot \left(-z\right)\right) + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 5.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq 10^{+308}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right) - b \cdot \left(a \cdot i - z \cdot c\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, \mathsf{fma}\left(-b, z, t \cdot j\right), i \cdot \mathsf{fma}\left(a, b, j \cdot \left(-y\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.5
Cost	12680

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_1 + t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_3 \leq 10^{+308}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(-y, i, y \cdot i\right) + t_2\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 2
Error	5.5
Cost	12680

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := \left(t_2 + t_1\right) + t_3\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_4 \leq 10^{+308}:\\ \;\;\;\;\left(t_1 - \left(b \cdot \mathsf{fma}\left(-a, i, a \cdot i\right) - t_2\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 3
Error	5.5
Cost	5704

\[\begin{array}{l} t_1 := \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 10^{+308}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 4
Error	27.0
Cost	2796

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 - \left(a \cdot \left(x \cdot t\right) - a \cdot \left(b \cdot i\right)\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := t_4 + \left(c \cdot \left(t \cdot j\right) - y \cdot \left(i \cdot j\right)\right)\\ t_6 := t_4 + t_1\\ \mathbf{if}\;c \leq -2.15 \cdot 10^{+110}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -1250000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-98}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-184}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 7.9 \cdot 10^{-174}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-52}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 8:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 10^{+168}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - i \cdot \left(y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5
Error	24.3
Cost	2796

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 - \left(a \cdot \left(x \cdot t\right) - a \cdot \left(b \cdot i\right)\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := c \cdot \left(t \cdot j\right)\\ t_6 := t_1 + \left(t_5 - y \cdot \left(i \cdot j\right)\right)\\ t_7 := \left(t_5 + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ t_8 := t_1 + t_4\\ \mathbf{if}\;c \leq -2.15 \cdot 10^{+110}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq -125000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-97}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq -4.3 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{-286}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{-230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-183}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-174}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 10.6:\\ \;\;\;\;t_4 + t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 6
Error	37.3
Cost	2688

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_5 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+213}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -0.001:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-281}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 10^{-62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-14}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+58}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+122}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Error	37.2
Cost	2688

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_5 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+211}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -0.0034:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-281}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-120}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-62}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+58}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+126}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	24.0
Cost	2664

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(i \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_1 + t_3\\ t_5 := c \cdot \left(t \cdot j\right)\\ t_6 := \left(t_5 + y \cdot \left(x \cdot z - i \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ t_7 := a \cdot \left(b \cdot i\right)\\ t_8 := \left(t_7 - t_2\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ t_9 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_10 := t_9 - \left(a \cdot \left(x \cdot t\right) - t_7\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-104}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -4.3 \cdot 10^{-282}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{-286}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 7.1 \cdot 10^{-183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 7.9 \cdot 10^{-174}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;t_1 + \left(t_5 - t_2\right)\\ \mathbf{elif}\;c \leq 0.8:\\ \;\;\;\;t_3 + t_9\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 9
Error	26.4
Cost	2536

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := t_2 + t_4\\ t_6 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_7 := t_4 + t_6\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-118}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-282}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-274}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - y \cdot \left(i \cdot j\right)\right) - t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-264}:\\ \;\;\;\;t_6 - t_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-161}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - i \cdot \left(y \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-121}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-93}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 650000000000:\\ \;\;\;\;t_2 + t_6\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	35.1
Cost	2408

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i\right) + t_1\\ t_3 := c \cdot \left(z \cdot b\right)\\ t_4 := \left(y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\right) - t_3\\ \mathbf{if}\;c \leq -2.15 \cdot 10^{+110}:\\ \;\;\;\;t_1 - t_3\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-104}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{+227}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+291}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 11
Error	27.7
Cost	2404

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t_3 + t_1\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := t_3 + t_5\\ \mathbf{if}\;t \leq -8 \cdot 10^{+217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-112}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-176}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-200}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-221}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-256}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-118}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+46}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	34.4
Cost	2016

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Error	34.7
Cost	2016

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-224}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-106}:\\ \;\;\;\;\frac{a}{\frac{1}{b \cdot i - x \cdot t}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+48}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	34.8
Cost	2016

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-200}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{a}{\frac{1}{b \cdot i - x \cdot t}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+50}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	22.4
Cost	1876

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_1 + t_2\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{-12}:\\ \;\;\;\;\left(t_4 + y \cdot \left(x \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;t_1 + t_4\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_4\\ \end{array} \]

Alternative 16
Error	42.8
Cost	1765

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+82} \lor \neg \left(t \leq 1.26 \cdot 10^{+184}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 17
Error	26.9
Cost	1744

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-221}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	21.2
Cost	1744

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_1 + t_3\\ t_5 := t_3 + t_2\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{-75}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-36}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+106}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 19
Error	49.4
Cost	1640

\[\begin{array}{l} t_1 := i \cdot \left(j \cdot \left(-y\right)\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-286}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	49.5
Cost	1572

\[\begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ t_3 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;a \leq -0.0105:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-279}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	37.7
Cost	1369

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-31} \lor \neg \left(t \leq 6.5 \cdot 10^{+23}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 22
Error	39.8
Cost	1368

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-156}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-281}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 55000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	37.2
Cost	1368

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	49.6
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	41.8
Cost	1104

\[\begin{array}{l} t_1 := \left(-i\right) \cdot \left(y \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	36.8
Cost	1104

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 125000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 27
Error	49.4
Cost	848

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -0.0003:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	49.2
Cost	716

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 29
Error	50.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-93} \lor \neg \left(a \leq 2.5 \cdot 10^{-149}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 30
Error	50.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{-75} \lor \neg \left(j \leq 5.5 \cdot 10^{+106}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 31
Error	50.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-152}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 32
Error	49.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-108}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 33
Error	53.4
Cost	320

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

Reproduce

herbie shell --seed 2023018 
(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)))))