Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.1 → 4.9

Time: 1.5min

Precision: binary64

Cost: 37256

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := i \cdot \left(y \cdot j\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(t_2 - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ t_5 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_1 + \left(\left(t_5 + t_2\right) - t_3\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - \left(t_3 - \left(t_5 + i \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

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 (* t (- (* c j) (* x a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* i (* y j)))
        (t_4 (+ (* j (- (* t c) (* y i))) (- t_2 (* x (- (* t a) (* y z))))))
        (t_5 (* y (* x z))))
   (if (<= t_4 (- INFINITY))
     (+ t_1 (- (+ t_5 t_2) t_3))
     (if (<= t_4 2e+300)
       (fma
        b
        (fma z (- c) (* a i))
        (fma x (fma y z (* t (- a))) (* j (fma i (- y) (* t c)))))
       (- t_1 (- t_3 (+ t_5 (* i (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = i * (y * j);
	double t_4 = (j * ((t * c) - (y * i))) + (t_2 - (x * ((t * a) - (y * z))));
	double t_5 = y * (x * z);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_1 + ((t_5 + t_2) - t_3);
	} else if (t_4 <= 2e+300) {
		tmp = fma(b, fma(z, -c, (a * i)), fma(x, fma(y, z, (t * -a)), (j * fma(i, -y, (t * c)))));
	} else {
		tmp = t_1 - (t_3 - (t_5 + (i * (a * b))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(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(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(i * Float64(y * j))
	t_4 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	t_5 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(t_1 + Float64(Float64(t_5 + t_2) - t_3));
	elseif (t_4 <= 2e+300)
		tmp = fma(b, fma(z, Float64(-c), Float64(a * i)), fma(x, fma(y, z, Float64(t * Float64(-a))), Float64(j * fma(i, Float64(-y), Float64(t * c)))));
	else
		tmp = Float64(t_1 - Float64(t_3 - Float64(t_5 + Float64(i * Float64(a * b)))));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * 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[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(t$95$1 + N[(N[(t$95$5 + t$95$2), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+300], N[(b * N[(z * (-c) + N[(a * i), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision] + N[(j * N[(i * (-y) + N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t$95$3 - N[(t$95$5 + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	12.1
Target	15.9
Herbie	4.9

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

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

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)} \]
      Proof
      (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (fma.f64 z (neg.f64 c) (Rewrite<= *-commutative_binary64 (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 z (neg.f64 c)) (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z c))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a t)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 t a)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (fma.f64 i (neg.f64 y) (Rewrite<= *-commutative_binary64 (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= fma-def_binary64 (+.f64 (*.f64 i (neg.f64 y)) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i y))) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 i) y)) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 2 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.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)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around 0 25.6

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

   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)))) < 2.0000000000000001e300

   1. Initial program 0.9

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

   2. Simplified 0.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)} \]
      Proof
      (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (fma.f64 z (neg.f64 c) (Rewrite<= *-commutative_binary64 (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 z (neg.f64 c)) (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z c))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a t)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 t a)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (fma.f64 i (neg.f64 y) (Rewrite<= *-commutative_binary64 (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= fma-def_binary64 (+.f64 (*.f64 i (neg.f64 y)) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i y))) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 i) y)) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 2 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.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)))): 0 points increase in error, 0 points decrease in error

   if 2.0000000000000001e300 < (+.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 57.1

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

   2. Simplified 57.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)} \]
      Proof
      (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (fma.f64 z (neg.f64 c) (Rewrite<= *-commutative_binary64 (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 z (neg.f64 c)) (*.f64 i a))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z c))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (fma.f64 x (fma.f64 y z (*.f64 a (neg.f64 t))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a t)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (fma.f64 y z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 t a)))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (fma.f64 i (neg.f64 y) (Rewrite<= *-commutative_binary64 (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= fma-def_binary64 (+.f64 (*.f64 i (neg.f64 y)) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i y))) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 i) y)) (*.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))): 2 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a)))) (+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 (neg.f64 b) (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.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)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around 0 28.9

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

   4. Taylor expanded in c around 0 19.7

      \[\leadsto \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t + \left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(\color{blue}{i \cdot \left(a \cdot b\right)} + y \cdot \left(z \cdot x\right)\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 4.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(\left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - \left(i \cdot \left(y \cdot j\right) - \left(y \cdot \left(x \cdot z\right) + i \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.4
Cost	5704

\[\begin{array}{l} t_1 := \left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	4.8
Cost	5704

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - \left(i \cdot \left(y \cdot j\right) - \left(y \cdot \left(x \cdot z\right) + i \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	4.9
Cost	5704

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := i \cdot \left(y \cdot j\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(t_2 - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ t_5 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_1 + \left(\left(t_5 + t_2\right) - t_3\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1 - \left(t_3 - \left(t_5 + i \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 4
Error	23.7
Cost	2532

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot c\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - t_1\right) - y \cdot \left(i \cdot j\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := \left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t \cdot \left(c \cdot j\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - t_1\right)\\ \mathbf{if}\;t \leq -0.0032:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.4589754878515604 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.0591478433896123 \cdot 10^{-267}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.2953351391677608 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.921884381135078 \cdot 10^{-232}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.024930669486598 \cdot 10^{-87}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.3022742433363814 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+199}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Error	22.8
Cost	2400

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(b \cdot c\right)\\ t_3 := t_1 + \left(y \cdot \left(x \cdot z\right) - t_2\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) - t_2\\ t_5 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_6 := t_1 + t_5\\ t_7 := t_5 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t_4\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq -7.026753497827033 \cdot 10^{-125}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -1.4211261907490828 \cdot 10^{-169}:\\ \;\;\;\;t_4 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq -2.4047269265112507 \cdot 10^{-216}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7.3832744679522245 \cdot 10^{-289}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 95000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 6
Error	40.0
Cost	2292

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.45 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -9.637621070901288 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.368947984559198 \cdot 10^{-103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.4351507489000179 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq -1.1862323151451443 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.0126098906828472 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	26.7
Cost	2268

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ t_4 := \left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t_1\\ \mathbf{if}\;x \leq -1 \cdot 10^{+120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.390856672189101 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.7370950157021607 \cdot 10^{-148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.4047269265112507 \cdot 10^{-216}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 8.262336952132111 \cdot 10^{-201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{+190}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	19.1
Cost	2260

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot c\right)\\ t_2 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := \left(t_3 - t_2\right) - y \cdot \left(i \cdot j\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+178}:\\ \;\;\;\;t_5 + t_3\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{+30}:\\ \;\;\;\;t_5 - \left(t_1 + t_2\right)\\ \mathbf{elif}\;j \leq 1.0126098906828472 \cdot 10^{-294}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 7.41678833235763 \cdot 10^{-125}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+212}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5 + \left(y \cdot \left(x \cdot z\right) - t_1\right)\\ \end{array} \]

Alternative 9
Error	33.0
Cost	2148

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right) + t_2\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.390856672189101 \cdot 10^{-123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -3.94541976471646 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8640413978692037 \cdot 10^{-258}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq -6.976614961546994 \cdot 10^{-265}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + t_2\\ \mathbf{elif}\;x \leq 3.6422399528893995 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.3832744679522245 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-30}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	25.5
Cost	2136

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := \left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t_2\\ t_4 := t_2 + \left(x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{if}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.390856672189101 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7370950157021607 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.4047269265112507 \cdot 10^{-216}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 8.262336952132111 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	16.7
Cost	2124

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(b \cdot c\right)\\ t_3 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.4211261907490828 \cdot 10^{-169}:\\ \;\;\;\;t_4 - \left(t_2 + t_3\right)\\ \mathbf{elif}\;x \leq 7.3832744679522245 \cdot 10^{-289}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;x \leq 10^{-56}:\\ \;\;\;\;t_4 - \left(t_2 - \left(y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 - t_3\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \]

Alternative 12
Error	50.9
Cost	2100

\[\begin{array}{l} t_1 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := c \cdot \left(b \cdot \left(-z\right)\right)\\ t_4 := c \cdot \left(t \cdot j\right)\\ t_5 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -4.207448334431398 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.547585916611995 \cdot 10^{-135}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -5.2821584145020475 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.5531188899189576 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.259666346622799 \cdot 10^{-245}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.2034861482100224 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+174}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	34.4
Cost	2016

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right) + t_2\\ t_4 := t_2 - t \cdot \left(x \cdot a\right)\\ \mathbf{if}\;z \leq -2.870238422480665 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.554055239134922 \cdot 10^{-163}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.535111180108959 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.939216521640729 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + t_2\\ \mathbf{elif}\;z \leq 7.278897641068905 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.033142547375608 \cdot 10^{-99}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Error	24.6
Cost	2004

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) - t_1\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+175}:\\ \;\;\;\;t_3 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -7.552239715743819 \cdot 10^{-181}:\\ \;\;\;\;t_4 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq -1.0666610708693906 \cdot 10^{-287}:\\ \;\;\;\;t_2 + t_4\\ \mathbf{elif}\;j \leq 1.0126098906828472 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6094360879261254 \cdot 10^{-73}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - t \cdot \left(x \cdot a\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(y \cdot \left(x \cdot z\right) - t_1\right)\\ \end{array} \]

Alternative 15
Error	50.2
Cost	1968

\[\begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ t_4 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+121}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.642055659049239 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -4.207448334431398 \cdot 10^{-83}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -9.547585916611995 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -5.2821584145020475 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5531188899189576 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.259666346622799 \cdot 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.2034861482100224 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 16
Error	50.4
Cost	1968

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ t_3 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.4094591822090489 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.5491584506338164 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.0937871444432606 \cdot 10^{-197}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.429646131976616 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 5.161061891524277 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.110200384458933 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.0506242923043584 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 1.602228155701941 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.537320693536754 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+104}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	44.8
Cost	1896

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.017:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.7370950157021607 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.244751741816136 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.431109442934064 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	51.0
Cost	1836

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := c \cdot \left(b \cdot \left(-z\right)\right)\\ t_4 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.026187872313927 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.177059832835734 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -5.2821584145020475 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.5531188899189576 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.259666346622799 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2034861482100224 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+174}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \end{array} \]

Alternative 19
Error	36.8
Cost	1760

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;z \leq -8.245795009978895 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -8.937196931815207 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.535111180108959 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.939216521640729 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3535370516242243 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.033142547375608 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 20
Error	37.0
Cost	1760

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := t_2 - t \cdot \left(x \cdot a\right)\\ \mathbf{if}\;z \leq -1.3818958715271592 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.554055239134922 \cdot 10^{-163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.535111180108959 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.939216521640729 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + t_2\\ \mathbf{elif}\;z \leq 7.278897641068905 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.033142547375608 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 21
Error	30.1
Cost	1752

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -7.026753497827033 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.4047269265112507 \cdot 10^{-216}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 22
Error	19.7
Cost	1740

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(b \cdot c\right)\\ t_3 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.4211261907490828 \cdot 10^{-169}:\\ \;\;\;\;t_4 - \left(t_2 + t_3\right)\\ \mathbf{elif}\;x \leq 7.3832744679522245 \cdot 10^{-289}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;x \leq 95000:\\ \;\;\;\;t_4 + \left(y \cdot \left(x \cdot z\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_3\\ \end{array} \]

Alternative 23
Error	37.6
Cost	1632

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.500242956413021 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 8.626675083141574 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 9.663054486945432 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.4842550662084083 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.491130569785552 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.7578934600068293 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	36.8
Cost	1632

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right) + t \cdot \left(c \cdot j\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -8.245795009978895 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.937196931815207 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.535111180108959 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.939216521640729 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1167011741382796 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3535370516242243 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.033142547375608 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 25
Error	22.9
Cost	1608

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - t_1\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	41.7
Cost	1368

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -9.431846494867821 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.407587274707096 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.9659845285937427 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.7578934600068293 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 27
Error	49.7
Cost	1308

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2581714260277057 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.2642923579347585 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1014094161888052 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2927196968252786 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 28
Error	51.0
Cost	1244

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -8.026187872313927 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.414732088232102 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.337663832850257 \cdot 10^{-256}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+215}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 29
Error	37.9
Cost	1236

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.500242956413021 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 8.626675083141574 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.7578934600068293 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 30
Error	36.5
Cost	1236

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -8.245795009978895 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.937196931815207 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 7.278897641068905 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0619468743201336 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 31
Error	49.5
Cost	848

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;i \leq -1.3354224078394405 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 32
Error	49.2
Cost	848

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;i \leq -1.3354224078394405 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.828512635855373 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 33
Error	49.3
Cost	848

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -1.462958932707002 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.638438615464912 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5061191809416788 \cdot 10^{-306}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 4.4908993838459305 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 34
Error	53.1
Cost	320

\[z \cdot \left(x \cdot y\right) \]

Reproduce

herbie shell --seed 2022300 
(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)))))