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

Average Error: 5.6 → 0.8

Time: 46.3s

Precision: binary64

Cost: 5320

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

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t_1\right) + b \cdot c\right) + t_2\\ t_4 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(\left(\left(\left(z \cdot \left(x \cdot t\right)\right) \cdot \left(18 \cdot y\right) + t_1\right) + b \cdot c\right) + t_2\right) + t_4\\ \mathbf{elif}\;t_3 \leq 10^{+308}:\\ \;\;\;\;t_3 + t_4\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

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 (* t (* a -4.0)))
        (t_2 (* i (* x -4.0)))
        (t_3 (+ (+ (+ (* (* (* (* x 18.0) y) z) t) t_1) (* b c)) t_2))
        (t_4 (* k (* j -27.0))))
   (if (<= t_3 (- INFINITY))
     (+ (+ (+ (+ (* (* z (* x t)) (* 18.0 y)) t_1) (* b c)) t_2) t_4)
     (if (<= t_3 1e+308)
       (+ t_3 t_4)
       (+
        (+ (* x (* (* y t) (* 18.0 z))) (* b c))
        (+ (* x (* i -4.0)) (* j (* k -27.0))))))))

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 = t * (a * -4.0);
	double t_2 = i * (x * -4.0);
	double t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	double t_4 = k * (j * -27.0);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (((((z * (x * t)) * (18.0 * y)) + t_1) + (b * c)) + t_2) + t_4;
	} else if (t_3 <= 1e+308) {
		tmp = t_3 + t_4;
	} else {
		tmp = ((x * ((y * t) * (18.0 * z))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	}
	return tmp;
}

Java

public static 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);
}

↓

public static 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 = t * (a * -4.0);
	double t_2 = i * (x * -4.0);
	double t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	double t_4 = k * (j * -27.0);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (((((z * (x * t)) * (18.0 * y)) + t_1) + (b * c)) + t_2) + t_4;
	} else if (t_3 <= 1e+308) {
		tmp = t_3 + t_4;
	} else {
		tmp = ((x * ((y * t) * (18.0 * z))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = i * (x * -4.0)
	t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2
	t_4 = k * (j * -27.0)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (((((z * (x * t)) * (18.0 * y)) + t_1) + (b * c)) + t_2) + t_4
	elif t_3 <= 1e+308:
		tmp = t_3 + t_4
	else:
		tmp = ((x * ((y * t) * (18.0 * z))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)))
	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(t * Float64(a * -4.0))
	t_2 = Float64(i * Float64(x * -4.0))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) + t_1) + Float64(b * c)) + t_2)
	t_4 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(z * Float64(x * t)) * Float64(18.0 * y)) + t_1) + Float64(b * c)) + t_2) + t_4);
	elseif (t_3 <= 1e+308)
		tmp = Float64(t_3 + t_4);
	else
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))) + Float64(b * c)) + Float64(Float64(x * Float64(i * -4.0)) + Float64(j * Float64(k * -27.0))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = i * (x * -4.0);
	t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	t_4 = k * (j * -27.0);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (((((z * (x * t)) * (18.0 * y)) + t_1) + (b * c)) + t_2) + t_4;
	elseif (t_3 <= 1e+308)
		tmp = t_3 + t_4;
	else
		tmp = ((x * ((y * t) * (18.0 * z))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	end
	tmp_2 = 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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(N[(N[(N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision] * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[t$95$3, 1e+308], N[(t$95$3 + t$95$4), $MachinePrecision], N[(N[(N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	5.6
Target	1.5
Herbie	0.8

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

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. Taylor expanded in x around 0 11.7

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

   3. Simplified 4.6

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

      [Start] 11.7	\[ \left(\left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*r* [=>] 11.8	\[ \left(\left(\left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 11.8	\[ \left(\left(\left(\color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 11.8	\[ \left(\left(\left(\left(t \cdot \color{blue}{\left(x \cdot z\right)}\right) \cdot \left(18 \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*r* [=>] 4.6	\[ \left(\left(\left(\color{blue}{\left(\left(t \cdot x\right) \cdot z\right)} \cdot \left(18 \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 4.6	\[ \left(\left(\left(\color{blue}{\left(z \cdot \left(t \cdot x\right)\right)} \cdot \left(18 \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if -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)) < 1e308

   1. Initial program 0.3

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

   if 1e308 < (-.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 63.8

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

   2. Simplified 38.5

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

      [Start] 63.8	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 63.8	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 63.8	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 63.8	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 63.8	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 38.5	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 38.5	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 38.5	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 12.5

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

   4. Simplified 7.0

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

      [Start] 12.5	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 12.7	\[ \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 5.0	\[ \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 5.9	\[ \left(\color{blue}{\left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right)\right) \cdot x} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [<=] 5.7	\[ \left(\color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 5.7	\[ \left(\color{blue}{\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot 18\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 6.8	\[ \left(\left(\color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot 18\right) \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*l* [=>] 7.0	\[ \left(\color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot 18\right)\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty:\\ \;\;\;\;\left(\left(\left(\left(z \cdot \left(x \cdot t\right)\right) \cdot \left(18 \cdot y\right) + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 10^{+308}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	32.7
Cost	2816

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + t_2\\ t_4 := t_1 + t_2\\ t_5 := -4 \cdot \left(x \cdot i\right)\\ t_6 := b \cdot c + t_5\\ \mathbf{if}\;i \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;t_2 - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-23}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-216}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-89}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_2\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{-41}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 5400000000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+204}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + t_5\\ \end{array} \]

Alternative 2
Error	32.6
Cost	2816

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + t_2\\ t_4 := t_1 + t_2\\ t_5 := -4 \cdot \left(x \cdot i\right)\\ t_6 := b \cdot c + t_5\\ \mathbf{if}\;i \leq -8.8 \cdot 10^{+72}:\\ \;\;\;\;t_2 - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-23}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.08 \cdot 10^{-218}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.9 \cdot 10^{-89}:\\ \;\;\;\;t_2 + x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-37}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+128}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{+144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+203}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + t_5\\ \end{array} \]

Alternative 3
Error	7.2
Cost	2376

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \cdot 4 \leq -1 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;a \cdot 4 \leq 5 \cdot 10^{-287}:\\ \;\;\;\;\left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + b \cdot c\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + t_1\\ \end{array} \]

Alternative 4
Error	38.9
Cost	2160

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-269}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{+173}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{+216}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{+240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+268}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	32.4
Cost	2160

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_3 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;t \leq -175:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-105}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+222}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 6
Error	2.3
Cost	2120

\[\begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+26}:\\ \;\;\;\;\left(\left(\left(\left(z \cdot \left(x \cdot t\right)\right) \cdot \left(18 \cdot y\right) + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+87}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	32.2
Cost	2025

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 - \left(x \cdot 4\right) \cdot i\\ t_3 := b \cdot c + t_1\\ t_4 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+101}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-116}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+106} \lor \neg \left(a \leq 1.25 \cdot 10^{+170}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	32.2
Cost	2025

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot k\right) \cdot -27 + t_1\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := b \cdot c + t_3\\ t_5 := b \cdot c + t_1\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+101}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-256}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-301}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-115}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+104} \lor \neg \left(a \leq 2.3 \cdot 10^{+161}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 9
Error	8.3
Cost	1865

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-87} \lor \neg \left(a \leq 8 \cdot 10^{-129}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + b \cdot c\right) + t_1\\ \end{array} \]

Alternative 10
Error	34.2
Cost	1764

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_4 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{-111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+91}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	19.7
Cost	1744

\[\begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := b \cdot c + \left(t_1 + -4 \cdot \left(x \cdot i\right)\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;j \leq -9.8 \cdot 10^{+92}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-238}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	17.0
Cost	1620

\[\begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_1\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 750000:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+239}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	17.6
Cost	1620

\[\begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_1\\ \mathbf{if}\;t \leq -26.5:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1350000:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	30.8
Cost	1501

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-193}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 0.12:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+40} \lor \neg \left(c \leq 2 \cdot 10^{+175}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	9.5
Cost	1476

\[\begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+87}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	43.9
Cost	1376

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+89}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -7500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-66}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-103}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-156}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]

Alternative 17
Error	36.0
Cost	1369

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;j \leq -9 \cdot 10^{+200}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{+136}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;j \leq -40000 \lor \neg \left(j \leq -5.9 \cdot 10^{-155}\right) \land j \leq -5.5 \cdot 10^{-278}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	22.0
Cost	1357

\[\begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+157}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;a \leq 0.00078 \lor \neg \left(a \leq 8.5 \cdot 10^{+69}\right):\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 19
Error	44.7
Cost	1112

\[\begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20
Error	44.6
Cost	1112

\[\begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-157}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21
Error	43.4
Cost	850

\[\begin{array}{l} \mathbf{if}\;k \leq -1.06 \cdot 10^{-144} \lor \neg \left(k \leq 2.5 \cdot 10^{-18} \lor \neg \left(k \leq 1.5 \cdot 10^{+156}\right) \land k \leq 4.6 \cdot 10^{+198}\right):\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Error	48.4
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023041 
(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)))