Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Average Error: 5.6 → 1.1

Time: 1.1min

Precision: binary64

Cost: 18249

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \end{array} \]

Math

\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+298}\right):\\ \;\;\;\;\mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

↓

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (+
          (+
           (+ (+ (* (* (* (* x 18.0) y) z) t) (* t (* a -4.0))) (* b c))
           (* i (* x -4.0)))
          (* k (* j -27.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+298)))
     (-
      (fma 18.0 (* x (* z (* y t))) (* b c))
      (fma x (* 4.0 i) (* 27.0 (* j k))))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))) + (k * (j * -27.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+298)) {
		tmp = fma(18.0, (x * (z * (y * t))), (b * c)) - fma(x, (4.0 * i), (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) + Float64(t * Float64(a * -4.0))) + Float64(b * c)) + Float64(i * Float64(x * -4.0))) + Float64(k * Float64(j * -27.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+298))
		tmp = Float64(fma(18.0, Float64(x * Float64(z * Float64(y * t))), Float64(b * c)) - fma(x, Float64(4.0 * i), Float64(27.0 * Float64(j * k))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+298]], $MachinePrecision]], N[(N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Target

Original	5.6
Target	1.5
Herbie	1.1

\[\begin{array}{l} \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < -inf.0 or 1.9999999999999999e298 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

   1. Initial program 53.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Simplified 35.5

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
      Proof

      [Start] 53.0	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 53.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 53.0	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 53.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 53.0	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 36.1	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 36.1	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 35.5	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in a around 0 14.6

      \[\leadsto \color{blue}{\left(c \cdot b + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

   4. Simplified 9.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(k \cdot j\right)\right)} \]
      Proof

      [Start] 14.6	\[ \left(c \cdot b + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      +-commutative [=>] 14.6	\[ \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + c \cdot b\right)} - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      fma-def [=>] 14.6	\[ \color{blue}{\mathsf{fma}\left(18, y \cdot \left(t \cdot \left(z \cdot x\right)\right), c \cdot b\right)} - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      *-commutative [=>] 14.6	\[ \mathsf{fma}\left(18, y \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      associate-*r* [=>] 38.0	\[ \mathsf{fma}\left(18, \color{blue}{\left(y \cdot \left(z \cdot x\right)\right) \cdot t}, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      associate-*r* [=>] 37.9	\[ \mathsf{fma}\left(18, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot t, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      *-commutative [<=] 37.9	\[ \mathsf{fma}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} \cdot t, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      associate-*l* [=>] 19.7	\[ \mathsf{fma}\left(18, \color{blue}{x \cdot \left(\left(y \cdot z\right) \cdot t\right)}, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      associate-*r* [<=] 8.0	\[ \mathsf{fma}\left(18, x \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      *-commutative [<=] 8.0	\[ \mathsf{fma}\left(18, x \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right), c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      associate-*r* [=>] 9.1	\[ \mathsf{fma}\left(18, x \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot z\right)}, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      *-commutative [=>] 9.1	\[ \mathsf{fma}\left(18, x \cdot \color{blue}{\left(z \cdot \left(y \cdot t\right)\right)}, c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right) \]
      associate-*r* [=>] 9.3	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(27 \cdot k\right) \cdot j}\right) \]
      *-commutative [<=] 9.3	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]
      associate-*r* [=>] 9.3	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \left(\color{blue}{\left(4 \cdot i\right) \cdot x} + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [<=] 9.3	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + j \cdot \left(27 \cdot k\right)\right) \]
      fma-udef [<=] 9.3	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)} \]
      *-commutative [=>] 9.3	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(27 \cdot k\right) \cdot j}\right) \]
      associate-*r* [<=] 9.1	\[ \mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), c \cdot b\right) - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{27 \cdot \left(k \cdot j\right)}\right) \]

   if -inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < 1.9999999999999999e298

   1. Initial program 0.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right) \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right) \leq 2 \cdot 10^{+298}\right):\\ \;\;\;\;\mathsf{fma}\left(18, x \cdot \left(z \cdot \left(y \cdot t\right)\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.8
Cost	6089

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+287}\right):\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\right) + \left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	27.2
Cost	4840

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ t_4 := k \cdot \left(j \cdot -27\right)\\ t_5 := -4 \cdot \left(t \cdot a + x \cdot i\right) + t_4\\ \mathbf{if}\;t_3 \leq -4 \cdot 10^{+82}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-64}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-312}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 40000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 3
Error	28.9
Cost	4196

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_5 := \left(j \cdot 27\right) \cdot k\\ t_6 := b \cdot c + t_2\\ \mathbf{if}\;t_5 \leq -1 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c + t_3\\ \mathbf{elif}\;t_5 \leq -1 \cdot 10^{-89}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_5 \leq -5 \cdot 10^{-223}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{-312}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{-62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 40000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+66}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \]

Alternative 4
Error	28.9
Cost	4196

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_4 := \left(j \cdot 27\right) \cdot k\\ t_5 := b \cdot c + t_1\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c + t_2\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-89}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-223}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{-312}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{-62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 40000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \]

Alternative 5
Error	10.8
Cost	3552

\[\begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + -4 \cdot \left(x \cdot i\right)\\ t_4 := b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + t_2\right)\\ t_5 := k \cdot \left(j \cdot -27\right)\\ t_6 := \left(b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\right) + t_5\\ \mathbf{if}\;j \cdot 27 \leq -2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \cdot 27 \leq -5 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \cdot 27 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-112}:\\ \;\;\;\;\left(t_2 + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_5\\ \mathbf{elif}\;j \cdot 27 \leq -5 \cdot 10^{-163}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \cdot 27 \leq -5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \cdot 27 \leq 10^{-258}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \cdot 27 \leq 2.5 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 6
Error	24.2
Cost	2281

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := \left(j \cdot k\right) \cdot -27\\ t_3 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_4 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_2\\ t_5 := b \cdot c + \left(t_2 - 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+202}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -0.0004:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-287}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-208}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-32} \lor \neg \left(y \leq 9 \cdot 10^{+19}\right):\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	24.2
Cost	2280

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := \left(j \cdot k\right) \cdot -27\\ t_3 := b \cdot c + \left(t_2 - 4 \cdot \left(x \cdot i\right)\right)\\ t_4 := x \cdot \left(i \cdot -4\right)\\ t_5 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_6 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_2\\ t_7 := \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + t_1\\ \mathbf{if}\;y \leq -2.12 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + t_4\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+202}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+46}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -0.00016:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-285}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-210}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_4\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-32}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+19}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	7.5
Cost	2249

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-52} \lor \neg \left(t_1 \leq 40000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 9
Error	2.1
Cost	2249

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+22} \lor \neg \left(t \leq 5.2 \cdot 10^{-9}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot \left(18 \cdot y\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 10
Error	31.3
Cost	2160

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + t_2\\ t_4 := -4 \cdot \left(t \cdot a\right)\\ t_5 := t_4 + t_2\\ \mathbf{if}\;t \leq -26:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-296}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-24}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-24}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+52}:\\ \;\;\;\;18 \cdot \left(\left(z \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_4\\ \end{array} \]

Alternative 11
Error	33.1
Cost	2158

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := t_1 + t_2\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ t_5 := b \cdot c + t_4\\ t_6 := t_4 + t_2\\ \mathbf{if}\;k \leq -5.8 \cdot 10^{-112}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{-210}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 8 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 8 \cdot 10^{-102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-48}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 16000 \lor \neg \left(k \leq 4.4 \cdot 10^{+25}\right) \land \left(k \leq 1.6 \cdot 10^{+54} \lor \neg \left(k \leq 3.4 \cdot 10^{+147}\right)\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \]

Alternative 12
Error	32.9
Cost	2158

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := b \cdot c + t_2\\ t_4 := t_2 + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;k \leq -7.4 \cdot 10^{-116}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 10^{-209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-143}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 16000 \lor \neg \left(k \leq 1.18 \cdot 10^{+27} \lor \neg \left(k \leq 6.5 \cdot 10^{+54}\right) \land k \leq 4 \cdot 10^{+149}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 13
Error	4.1
Cost	2121

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-82} \lor \neg \left(x \leq 1.2 \cdot 10^{-88}\right):\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + t_1\right)\right) + \left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 + \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 14
Error	1.8
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -5000000000000 \lor \neg \left(t \leq 1.5 \cdot 10^{-21}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\right) + \left(j \cdot k\right) \cdot -27\\ \end{array} \]

Alternative 15
Error	11.0
Cost	2000

\[\begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -23.5:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-299}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + \left(\left(j \cdot k\right) \cdot -27 - 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-58}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	44.8
Cost	1904

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -9 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-145}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	44.8
Cost	1904

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-144}:\\ \;\;\;\;18 \cdot \left(\left(z \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	45.5
Cost	1904

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -13500000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;18 \cdot \left(\left(z \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	45.6
Cost	1904

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-144}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.85 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	17.1
Cost	1748

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -13:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-58}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 - 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-22}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	26.6
Cost	1740

\[\begin{array}{l} t_1 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-117}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	44.2
Cost	1640

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -7.8 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 23
Error	35.0
Cost	1632

\[\begin{array}{l} t_1 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 24
Error	11.0
Cost	1612

\[\begin{array}{l} t_1 := \left(b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 25
Error	11.0
Cost	1612

\[\begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{-53}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 26
Error	19.4
Cost	1488

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right) + t_1\\ \mathbf{if}\;t \leq -17:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 - 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-29}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right) + t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 27
Error	17.2
Cost	1484

\[\begin{array}{l} t_1 := b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -32:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-59}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 - 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	37.2
Cost	1368

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -1.45 \cdot 10^{+270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{+184}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 29
Error	42.9
Cost	1245

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;k \leq -9.8 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-39}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 14000 \lor \neg \left(k \leq 6.5 \cdot 10^{+98}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 30
Error	43.5
Cost	849

\[\begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-51} \lor \neg \left(c \leq 1.65 \cdot 10^{+114}\right) \land c \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 31
Error	48.4
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023073 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))