Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.2 → 5.9

Time: 53.0s

Precision: binary64

Cost: 17672

Math

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

↓

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

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

↓

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(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(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) - Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a * Float64(b * i)) - Float64(y * Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = fma(t, fma(j, c, Float64(x * Float64(-a))), Float64(i * Float64(Float64(a * b) - Float64(y * j))));
	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[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+301], t$95$1, N[(t * N[(j * c + N[(x * (-a)), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	12.2
Target	16.2
Herbie	5.9

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

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

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right)} \]
      Proof
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 a i) (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 i a)) (*.f64 c z)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 i a) (neg.f64 (*.f64 c z)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (*.f64 c z)) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c t)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 c t) (Rewrite<= *-commutative_binary64 (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (neg.f64 i) y) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i 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 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i 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 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (*.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.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
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 1 points increase in error, 1 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 z around 0 39.9

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

   4. Taylor expanded in t around 0 27.1

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

   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)))) < 1.00000000000000005e301

   1. Initial program 0.8

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

   if 1.00000000000000005e301 < (+.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 58.5

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

   2. Simplified 58.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(b, a \cdot i - z \cdot c, j \cdot \left(t \cdot c - y \cdot i\right)\right)\right)} \]
      Proof
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (*.f64 a i) (Rewrite<= *-commutative_binary64 (*.f64 c z))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 i a)) (*.f64 c z)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 i a) (neg.f64 (*.f64 c z)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (*.f64 c z)) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 c z))) (*.f64 i a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 c t)) (*.f64 y i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 c t) (Rewrite<= *-commutative_binary64 (*.f64 i y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (*.f64 c t) (*.f64 (neg.f64 i) y)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (neg.f64 i) y) (*.f64 c t)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i 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 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i 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 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b (neg.f64 (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (*.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
      (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.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
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (-.f64 (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))))): 1 points increase in error, 1 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 z around 0 41.8

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

   4. Taylor expanded in c around 0 31.6

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

   5. Simplified 28.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(j, c, a \cdot \left(-x\right)\right), i \cdot \left(a \cdot b - y \cdot j\right)\right)} \]
      Proof
      (fma.f64 t (fma.f64 j c (*.f64 a (neg.f64 x))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 y j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (fma.f64 j c (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a x)))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 y j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (fma.f64 j c (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 a x)))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 y j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j c) (*.f64 -1 (*.f64 a x)))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 y j)))): 0 points increase in error, 1 points decrease in error
      (fma.f64 t (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 c j)) (*.f64 -1 (*.f64 a x))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 y j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 a b) i) (*.f64 (*.f64 y j) i)))): 1 points increase in error, 0 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (-.f64 (Rewrite=> associate-*l*_binary64 (*.f64 a (*.f64 b i))) (*.f64 (*.f64 y j) i))): 5 points increase in error, 24 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (-.f64 (*.f64 a (Rewrite<= *-commutative_binary64 (*.f64 i b))) (*.f64 (*.f64 y j) i))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (-.f64 (*.f64 a (*.f64 i b)) (Rewrite=> associate-*l*_binary64 (*.f64 y (*.f64 j i))))): 13 points increase in error, 15 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (-.f64 (*.f64 a (*.f64 i b)) (*.f64 y (Rewrite<= *-commutative_binary64 (*.f64 i j))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 a (*.f64 i b)) (neg.f64 (*.f64 y (*.f64 i j)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (+.f64 (*.f64 a (*.f64 i b)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 y (*.f64 i j)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (+.f64 (*.f64 c j) (*.f64 -1 (*.f64 a x)))) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b))))): 3 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 (*.f64 c j) t) (*.f64 (*.f64 -1 (*.f64 a x)) t))) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 0 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 c (*.f64 j t))) (*.f64 (*.f64 -1 (*.f64 a x)) t)) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 15 points increase in error, 21 points decrease in error
      (+.f64 (+.f64 (*.f64 c (Rewrite<= *-commutative_binary64 (*.f64 t j))) (*.f64 (*.f64 -1 (*.f64 a x)) t)) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 c (*.f64 t j)) (*.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 a) x)) t)) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 c (*.f64 t j)) (Rewrite<= associate-*r*_binary64 (*.f64 (*.f64 -1 a) (*.f64 x t)))) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 15 points increase in error, 16 points decrease in error
      (+.f64 (+.f64 (*.f64 c (*.f64 t j)) (*.f64 (*.f64 -1 a) (Rewrite<= *-commutative_binary64 (*.f64 t x)))) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 c (*.f64 t j)) (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 a (*.f64 t x))))) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 c (*.f64 t j)) (+.f64 (*.f64 -1 (*.f64 a (*.f64 t x))) (+.f64 (*.f64 -1 (*.f64 y (*.f64 i j))) (*.f64 a (*.f64 i b)))))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 5.9

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

Alternatives

Alternative 1
Error	6.0
Cost	5704

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

Alternative 2
Error	23.9
Cost	2664

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_3 + c \cdot \left(t \cdot j - z \cdot b\right)\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_6 := t_5 + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ t_7 := t_5 + t_1\\ \mathbf{if}\;a \leq -3 \cdot 10^{-14}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-275}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-297}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-102}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 65000000:\\ \;\;\;\;t_3 + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+42}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 3
Error	29.6
Cost	2536

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right) - j \cdot \left(y \cdot i\right)\\ t_4 := c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_5 := c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - t_5\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-193}:\\ \;\;\;\;t_1 - t_5\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-82}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - i \cdot \left(y \cdot j\right)\\ \end{array} \]

Alternative 4
Error	32.9
Cost	2412

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	32.3
Cost	2412

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - t_2\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-55}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-103}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-201}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+79}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	32.8
Cost	2412

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := t_1 - t_2\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-9}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - t_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-104}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+75}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1 - i \cdot \left(y \cdot j\right)\\ \end{array} \]

Alternative 7
Error	26.7
Cost	2404

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + t_2\\ t_4 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_5 := t_2 - t_4\\ t_6 := c \cdot \left(t \cdot j\right) - t_4\\ \mathbf{if}\;i \leq -3.7 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.85 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-157}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-189}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-285}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-184}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+65}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	38.5
Cost	2292

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -6500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	33.0
Cost	2280

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - i \cdot \left(y \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ t_4 := t_3 - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_5 := c \cdot \left(t \cdot j - z \cdot b\right) - j \cdot \left(y \cdot i\right)\\ t_6 := b \cdot \left(a \cdot i - z \cdot c\right) + t_3\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-103}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-192}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-199}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+75}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	46.2
Cost	2232

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c\right)\\ t_4 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 1.76 \cdot 10^{-228}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-176}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{-170}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 11
Error	37.8
Cost	2156

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := a \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-198}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-225}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-174}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-55}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 0.0098:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	33.3
Cost	2148

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+75}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	41.7
Cost	2028

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.18 \cdot 10^{+145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Error	37.8
Cost	2028

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -40000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-268}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	42.7
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-186}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-174}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	22.7
Cost	1744

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8.1 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	48.1
Cost	1632

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;i \leq -5.6 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-285}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-118}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	20.7
Cost	1612

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.05 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-106}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-53}:\\ \;\;\;\;t_1 + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	49.3
Cost	1572

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.72 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	49.2
Cost	1572

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{-27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-261}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	49.4
Cost	1508

\[\begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 22
Error	49.9
Cost	1440

\[\begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-261}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2800000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	50.2
Cost	1112

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 24
Error	50.8
Cost	1112

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 25
Error	49.6
Cost	980

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 26
Error	49.4
Cost	980

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 27
Error	51.3
Cost	584

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	50.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;i \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 29
Error	53.8
Cost	320

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

Reproduce

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