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

Average Error: 5.5 → 1.8

Time: 1.0min

Precision: binary64

Cost: 9540

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

Math

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

↓

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(c, b, t_1\right) + t_2\\ \mathbf{elif}\;t_3 \leq 10^{+301}:\\ \;\;\;\;t_3 + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t_1\right) + t_2\\ \end{array} \]

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 (* 18.0 (* y (* t (* x z)))))
        (t_2 (+ (* j (* k -27.0)) (* x (* i -4.0))))
        (t_3
         (+
          (+ (+ (* (* (* (* x 18.0) y) z) t) (* t (* a -4.0))) (* b c))
          (* i (* x -4.0)))))
   (if (<= t_3 (- INFINITY))
     (+ (fma c b t_1) t_2)
     (if (<= t_3 1e+301) (+ t_3 (* k (* j -27.0))) (+ (+ (* b c) t_1) t_2)))))

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 = 18.0 * (y * (t * (x * z)));
	double t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	double t_3 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = fma(c, b, t_1) + t_2;
	} else if (t_3 <= 1e+301) {
		tmp = t_3 + (k * (j * -27.0));
	} else {
		tmp = ((b * c) + t_1) + t_2;
	}
	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(18.0 * Float64(y * Float64(t * Float64(x * z))))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(i * -4.0)))
	t_3 = 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)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(fma(c, b, t_1) + t_2);
	elseif (t_3 <= 1e+301)
		tmp = Float64(t_3 + Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + t_1) + t_2);
	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[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(c * b + t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 1e+301], N[(t$95$3 + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]

Target

Original	5.5
Target	1.5
Herbie	1.8

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

Derivation

1. Split input into 3 regimes

2. if (-.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)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 40.5

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

      [Start] 64.0	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 64.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 64.0	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 64.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 64.0	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 40.5	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 40.5	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 40.5	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in a around 0 12.4

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

   4. Simplified 12.4

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

      [Start] 12.4	\[ \left(c \cdot b + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      fma-def [=>] 12.4	\[ \color{blue}{\mathsf{fma}\left(c, b, 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 12.4	\[ \mathsf{fma}\left(c, b, 18 \cdot \left(y \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if -inf.0 < (-.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)) < 1.00000000000000005e301

   1. Initial program 0.4

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

   if 1.00000000000000005e301 < (-.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))

   1. Initial program 51.5

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

   2. Simplified 36.1

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

      [Start] 51.5	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 51.5	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 51.5	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 51.5	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 51.5	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      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* [=>] 36.1	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in a around 0 18.9

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

4. Final simplification 1.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(c, b, 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 10^{+301}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.8
Cost	5321

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+301}\right):\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 2
Error	15.3
Cost	2901

\[\begin{array}{l} t_1 := b \cdot c + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{-21}:\\ \;\;\;\;b \cdot c + \left(t_2 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+108} \lor \neg \left(t_3 \leq 5 \cdot 10^{+135}\right):\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + \left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \end{array} \]

Alternative 3
Error	26.3
Cost	2808

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ t_4 := k \cdot \left(j \cdot -27\right)\\ t_5 := b \cdot c + \left(t_1 + t_3\right)\\ t_6 := -27 \cdot \left(j \cdot k\right) + t_2\\ t_7 := t_4 + \left(b \cdot c + t_1\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+242}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{+178}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+125}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq -20500000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-45}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-61}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-162}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-188}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-205}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-263}:\\ \;\;\;\;t_4 + t_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-305}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-253}:\\ \;\;\;\;t_3 + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-98}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Error	46.6
Cost	2557

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-237}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-7}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 16000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+69} \lor \neg \left(t \leq 5.5 \cdot 10^{+101}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	46.5
Cost	2557

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-160}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-239}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-142}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-112}:\\ \;\;\;\;\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(18 \cdot y\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-5}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3400000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+41}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+69} \lor \neg \left(t \leq 1.4 \cdot 10^{+101}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	46.6
Cost	2557

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-160}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-235}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-142}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-112}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 4.15 \cdot 10^{-7}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 9200000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+42}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+69} \lor \neg \left(t \leq 1.38 \cdot 10^{+101}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	34.6
Cost	2548

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ t_4 := x \cdot \left(i \cdot -4\right) - t_3\\ t_5 := b \cdot c - t_3\\ t_6 := t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+132}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-42}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-46}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-269}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-173}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{-122}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+193}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 8
Error	34.6
Cost	2548

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := x \cdot \left(i \cdot -4\right) - t_2\\ t_4 := b \cdot c - t_2\\ t_5 := t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+132}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-54}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-187}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-269}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{-122}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 9
Error	37.2
Cost	2544

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_2 := -4 \cdot \left(x \cdot i\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ t_4 := k \cdot \left(j \cdot 27\right)\\ t_5 := x \cdot \left(i \cdot -4\right) - t_4\\ t_6 := b \cdot c - t_4\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-233}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-228}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-54}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+140}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + \left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \end{array} \]

Alternative 10
Error	37.1
Cost	2544

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_3 := -4 \cdot \left(x \cdot i\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_4 := t \cdot \left(a \cdot -4\right) + t_1\\ t_5 := k \cdot \left(j \cdot 27\right)\\ t_6 := x \cdot \left(i \cdot -4\right) - t_5\\ t_7 := b \cdot c - t_5\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-255}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-233}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-227}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-55}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-13}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+21}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+96}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+139}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+238}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \end{array} \]

Alternative 11
Error	34.7
Cost	2421

\[\begin{array}{l} t_1 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2200000 \lor \neg \left(x \leq 3.9 \cdot 10^{+58}\right) \land x \leq 1.6 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	37.7
Cost	2417

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_2 := t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ t_4 := x \cdot \left(i \cdot -4\right) - t_3\\ t_5 := b \cdot c - t_3\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+14}:\\ \;\;\;\;\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(18 \cdot y\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-233}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-228}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+96} \lor \neg \left(z \leq 2.2 \cdot 10^{+105}\right) \land z \leq 2.25 \cdot 10^{+135}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	11.3
Cost	2385

\[\begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ t_2 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq 4 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-11}:\\ \;\;\;\;t_2 + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+56} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+123}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + y \cdot \left(z \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	46.1
Cost	2300

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+94}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-128}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-169}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -6.1 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-291}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-128}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+14}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 15
Error	22.7
Cost	2273

\[\begin{array}{l} t_1 := \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := \left(t \cdot \left(a \cdot -4\right) + i \cdot \left(x \cdot -4\right)\right) + t_3\\ \mathbf{if}\;k \leq -2.45 \cdot 10^{-57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -1.1 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-279}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c + \left(t_2 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+144}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+182} \lor \neg \left(k \leq 1.7 \cdot 10^{+233}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(b \cdot c + t_2\right)\\ \end{array} \]

Alternative 16
Error	22.8
Cost	2273

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := t_1 + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_5 := \left(t \cdot \left(a \cdot -4\right) + i \cdot \left(x \cdot -4\right)\right) + t_3\\ \mathbf{if}\;k \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq -6.4 \cdot 10^{-206}:\\ \;\;\;\;t_1 + y \cdot \left(z \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-279}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c + \left(t_2 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 3.15 \cdot 10^{+143}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{+182} \lor \neg \left(k \leq 1.35 \cdot 10^{+233}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(b \cdot c + t_2\right)\\ \end{array} \]

Alternative 17
Error	22.3
Cost	2273

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ t_5 := t_1 + t_2\\ t_6 := \left(t \cdot \left(a \cdot -4\right) + i \cdot \left(x \cdot -4\right)\right) + t_3\\ t_7 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;k \leq -6.6 \cdot 10^{-57}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-203}:\\ \;\;\;\;t_1 + y \cdot \left(z \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.2 \cdot 10^{-239}:\\ \;\;\;\;\left(t_4 + t_2\right) + t_3\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c + \left(t_7 + t_4\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{+143}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+182} \lor \neg \left(k \leq 8.5 \cdot 10^{+232}\right):\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(b \cdot c + t_7\right)\\ \end{array} \]

Alternative 18
Error	10.2
Cost	2265

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := t_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{if}\;k \leq -1.7 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -7.6 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+40} \lor \neg \left(k \leq 2.05 \cdot 10^{+108}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 19
Error	4.8
Cost	2248

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+158}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot y\right) \cdot \left(18 \cdot \left(z \cdot t\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 20
Error	33.5
Cost	2156

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := x \cdot \left(i \cdot -4\right) - t_2\\ t_4 := b \cdot c - t_2\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+53}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -230000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-271}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	11.5
Cost	2128

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ t_2 := \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_1\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 22
Error	6.9
Cost	2120

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ t_2 := \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_1\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+175}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+294}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 23
Error	9.6
Cost	2000

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right) + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ t_2 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{if}\;i \leq -105000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-167}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 24
Error	19.2
Cost	1884

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := t_1 + \left(b \cdot c + t_2\right)\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ t_5 := b \cdot c + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right) + i \cdot \left(x \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-65}:\\ \;\;\;\;t_4 + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-65}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 21500:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+224}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_2 + t_4\right)\\ \end{array} \]

Alternative 25
Error	45.4
Cost	1640

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1020000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 26
Error	45.4
Cost	1640

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -700000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-82}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 27
Error	45.3
Cost	1640

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -35000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-280}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-83}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 28
Error	21.8
Cost	1488

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-65}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1150000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 29
Error	34.7
Cost	1369

\[\begin{array}{l} t_1 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-39} \lor \neg \left(x \leq 3800000\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 30
Error	44.6
Cost	1244

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;c \leq -2.45 \cdot 10^{-163}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 31
Error	43.9
Cost	849

\[\begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+242}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+173} \lor \neg \left(b \leq -1.6 \cdot 10^{+32}\right) \land b \leq 3 \cdot 10^{-84}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 32
Error	48.3
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023057 
(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)))