Linear.Matrix:det33 from linear-1.19.1.3

Average Error: 12.3 → 5.4

Time: 58.1s

Precision: binary64

Cost: 12680

Math

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

↓

\[\begin{array}{l} t_1 := i \cdot \left(y \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right) + t_3\\ t_5 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5 - \left(t_1 + \left(b \cdot \left(z \cdot c - a \cdot i\right) - t_2\right)\right)\\ \mathbf{elif}\;t_4 \leq 10^{+294}:\\ \;\;\;\;t_3 - \left(j \cdot \left(y \cdot i - t \cdot c\right) - j \cdot \mathsf{fma}\left(-y, i, y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5 - \left(t_1 - \left(t_2 + i \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

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 (* i (* y j)))
        (t_2 (* y (* x z)))
        (t_3 (+ (* b (- (* a i) (* z c))) (* x (- (* y z) (* t a)))))
        (t_4 (+ (* j (- (* t c) (* y i))) t_3))
        (t_5 (* t (- (* c j) (* x a)))))
   (if (<= t_4 (- INFINITY))
     (- t_5 (+ t_1 (- (* b (- (* z c) (* a i))) t_2)))
     (if (<= t_4 1e+294)
       (- t_3 (- (* j (- (* y i) (* t c))) (* j (fma (- y) i (* y i)))))
       (- t_5 (- t_1 (+ t_2 (* 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 = i * (y * j);
	double t_2 = y * (x * z);
	double t_3 = (b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)));
	double t_4 = (j * ((t * c) - (y * i))) + t_3;
	double t_5 = t * ((c * j) - (x * a));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5 - (t_1 + ((b * ((z * c) - (a * i))) - t_2));
	} else if (t_4 <= 1e+294) {
		tmp = t_3 - ((j * ((y * i) - (t * c))) - (j * fma(-y, i, (y * i))));
	} else {
		tmp = t_5 - (t_1 - (t_2 + (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(i * Float64(y * j))
	t_2 = Float64(y * Float64(x * z))
	t_3 = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_4 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_3)
	t_5 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(t_5 - Float64(t_1 + Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - t_2)));
	elseif (t_4 <= 1e+294)
		tmp = Float64(t_3 - Float64(Float64(j * Float64(Float64(y * i) - Float64(t * c))) - Float64(j * fma(Float64(-y), i, Float64(y * i)))));
	else
		tmp = Float64(t_5 - Float64(t_1 - Float64(t_2 + 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[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(t$95$5 - N[(t$95$1 + N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+294], N[(t$95$3 - N[(N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[((-y) * i + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$5 - N[(t$95$1 - N[(t$95$2 + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	12.3
Target	16.0
Herbie	5.4

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

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))))): 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 (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)))))): 1 points increase in error, 1 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 25.1

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

   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)))) < 1.00000000000000007e294

   1. Initial program 1.0

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

   2. Applied egg-rr 1.0

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

   if 1.00000000000000007e294 < (+.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 53.0

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

   2. Simplified 53.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(z, -c, a \cdot i\right), \mathsf{fma}\left(x, \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right), j \cdot \mathsf{fma}\left(i, -y, t \cdot c\right)\right)\right)} \]
      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))))): 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 (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)))))): 1 points increase in error, 1 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 26.7

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

   4. Taylor expanded in c around 0 21.5

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

4. Final simplification 5.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - \left(i \cdot \left(y \cdot j\right) + \left(b \cdot \left(z \cdot c - a \cdot i\right) - y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \leq 10^{+294}:\\ \;\;\;\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - \left(j \cdot \left(y \cdot i - t \cdot c\right) - j \cdot \mathsf{fma}\left(-y, i, y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - \left(i \cdot \left(y \cdot j\right) - \left(y \cdot \left(x \cdot z\right) + i \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.3
Cost	5704

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

Alternative 2
Error	4.9
Cost	5704

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) - \left(i \cdot \left(y \cdot j\right) - \left(y \cdot \left(x \cdot z\right) + i \cdot \left(a \cdot b\right)\right)\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+294}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	5.4
Cost	5704

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

Alternative 4
Error	38.7
Cost	3212

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := t_1 + t_2\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_6 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_7 := t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;x \leq -4.95 \cdot 10^{+92}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+47}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -700000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.133142570133263 \cdot 10^{-93}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.6847759629773935 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3.6571942063118067 \cdot 10^{-230}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -7.405420720614418 \cdot 10^{-245}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.2401666178420885 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq -5.589576586253599 \cdot 10^{-265}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 5.015706683388574 \cdot 10^{-305}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.518332506225063 \cdot 10^{-261}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.0188105496816084 \cdot 10^{-143}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq 1.022242529569321 \cdot 10^{-85}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.2662959189046723 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 10^{-21}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+47}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+73}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+197}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+216}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 5
Error	34.4
Cost	2676

\[\begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i\right)\\ t_3 := t \cdot \left(c \cdot j\right) - t \cdot \left(x \cdot a\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -12780.385283574584:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1401838506492962 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.746785771105459 \cdot 10^{-62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5.657211233827793 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.935010260026927 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4.773934904557806 \cdot 10^{-136}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -9.520428691653669 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4735510429791714 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -9.552753579802045 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.373631826195737 \cdot 10^{-149}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.331782395858947 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+27}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	18.0
Cost	2656

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := \left(t_3 - z \cdot \left(b \cdot c\right)\right) + t_2\\ t_5 := t \cdot \left(c \cdot j\right)\\ t_6 := t_1 + t_3\\ t_7 := t_5 + t_6\\ t_8 := t_6 - y \cdot \left(i \cdot j\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -1.508675203735072 \cdot 10^{-60}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.935010260026927 \cdot 10^{-126}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 4.2673549607759274 \cdot 10^{-131}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq 4.2768675991052237 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;t \leq 10^{+138}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5 - t \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 7
Error	35.8
Cost	2412

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ t_3 := t_2 - t \cdot \left(x \cdot a\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ t_5 := t_2 + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8.935010260026927 \cdot 10^{-126}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.301544279164943 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4735510429791714 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -9.552753579802045 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.373631826195737 \cdot 10^{-149}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.3705533121975317 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.107460183914467 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 150000000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+75}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{+114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+144}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	26.0
Cost	2272

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8.8 \cdot 10^{+195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -920:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.802645815902666 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.606808498294765 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 14000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	27.6
Cost	2272

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.643791842069366 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.840833490584342 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.015331005832762 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.0880246795116037 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.6567638203221172 \cdot 10^{-182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	38.2
Cost	2156

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z\right) - c \cdot \left(z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := t \cdot \left(c \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{if}\;t \leq -5.807609208067992 \cdot 10^{-46}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.935010260026927 \cdot 10^{-126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.236822950870398 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.552753579802045 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.373631826195737 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3705533121975317 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.107460183914467 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+73}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 9.1 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	20.5
Cost	2128

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t_1 - z \cdot \left(b \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t \cdot \left(c \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.90445554218412 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.75621958881196 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + t_1\\ \mathbf{elif}\;t \leq 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	15.0
Cost	1864

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t \cdot \left(c \cdot j\right) + \left(b \cdot \left(a \cdot i - z \cdot c\right) + t_1\right)\\ \mathbf{if}\;b \leq -1.496266909562325 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.10435826932629 \cdot 10^{-118}:\\ \;\;\;\;\left(t_1 - z \cdot \left(b \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	42.3
Cost	1632

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+199}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.856649154496723 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.14329159901062 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.3621047469871 \cdot 10^{-288}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.2128199814400032 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.687644464505037 \cdot 10^{-178}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	37.8
Cost	1632

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.856649154496723 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -4.14329159901062 \cdot 10^{-214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.15987989173795 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.3881048070435066 \cdot 10^{-257}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.2128199814400032 \cdot 10^{-214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.287537362019025 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	37.6
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.856649154496723 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -4.14329159901062 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 4.15987989173795 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 5.36 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	37.8
Cost	1500

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5.856649154496723 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -4.14329159901062 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3621047469871 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2128199814400032 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.687644464505037 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	49.9
Cost	1440

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_3 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_4 := t \cdot \left(-x \cdot a\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5.375993206837307 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.784248732093181 \cdot 10^{-81}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.301544279164943 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6556757081788068 \cdot 10^{-264}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.75621958881196 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3705533121975317 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.673204205955838 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 18
Error	42.3
Cost	1368

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;x \leq -5.7 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.681550328397542 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 5.971110234241862 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.80745973052261 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.904561814306014 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.1821073524128777 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	53.6
Cost	1308

\[\begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;j \leq -3.3041988675355596 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.0514783722215553 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.2479687234804942 \cdot 10^{-263}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.0011989124346627 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9.541697587183573 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.926792781933771 \cdot 10^{-88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	49.9
Cost	1308

\[\begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := t \cdot \left(-x \cdot a\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.375993206837307 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.784248732093181 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.301544279164943 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -1.6556757081788068 \cdot 10^{-264}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 3.75621958881196 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.864757815832802 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	50.2
Cost	1044

\[\begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -9.371297165650891 \cdot 10^{-164}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.5408701604159702 \cdot 10^{-194}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	49.5
Cost	912

\[\begin{array}{l} t_1 := t \cdot \left(-x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;b \leq -0.12619818852606196:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.641550599250613 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3178907025153255 \cdot 10^{-137}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	36.5
Cost	840

\[\begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	49.4
Cost	648

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;b \leq -0.12619818852606196:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	53.4
Cost	320

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

Alternative 26
Error	53.4
Cost	320

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

Reproduce

herbie shell --seed 2022297 
(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)))))