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

Average Error: 9.2% → 2.37%

Time: 53.8s

Precision: binary64

Cost: 5320

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right) + \left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t_1 + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \end{array} \]

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
         (+
          (+ (+ (* (* (* (* x 18.0) y) z) t) (* t (* a -4.0))) (* b c))
          (* i (* x -4.0)))))
   (if (<= t_1 (- INFINITY))
     (+
      (+ (* b c) (* x (+ (* 18.0 (* y (* z t))) (* i -4.0))))
      (* (* k j) -27.0))
     (if (<= t_1 5e+291)
       (+ t_1 (* k (* j -27.0)))
       (+
        (+ (* b c) (* x (* (* y t) (* 18.0 z))))
        (+ (* j (* k -27.0)) (* x (* i -4.0))))))))

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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)))) + ((k * j) * -27.0);
	} else if (t_1 <= 5e+291) {
		tmp = t_1 + (k * (j * -27.0));
	} else {
		tmp = ((b * c) + (x * ((y * t) * (18.0 * z)))) + ((j * (k * -27.0)) + (x * (i * -4.0)));
	}
	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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)))) + ((k * j) * -27.0);
	} else if (t_1 <= 5e+291) {
		tmp = t_1 + (k * (j * -27.0));
	} else {
		tmp = ((b * c) + (x * ((y * t) * (18.0 * z)))) + ((j * (k * -27.0)) + (x * (i * -4.0)));
	}
	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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)))) + ((k * j) * -27.0)
	elif t_1 <= 5e+291:
		tmp = t_1 + (k * (j * -27.0))
	else:
		tmp = ((b * c) + (x * ((y * t) * (18.0 * z)))) + ((j * (k * -27.0)) + (x * (i * -4.0)))
	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(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_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0)))) + Float64(Float64(k * j) * -27.0));
	elseif (t_1 <= 5e+291)
		tmp = Float64(t_1 + Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(y * t) * Float64(18.0 * z)))) + Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(i * -4.0))));
	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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)))) + ((k * j) * -27.0);
	elseif (t_1 <= 5e+291)
		tmp = t_1 + (k * (j * -27.0));
	else
		tmp = ((b * c) + (x * ((y * t) * (18.0 * z)))) + ((j * (k * -27.0)) + (x * (i * -4.0)));
	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[(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$1, (-Infinity)], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+291], N[(t$95$1 + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	9.2%
Target	2.85%
Herbie	2.37%

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

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 100

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

   2. Simplified 65.14

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

      [Start] 100	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 100	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 100	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 100	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 100	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 65.14	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 65.14	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 65.14	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 24.42

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

   4. Simplified 10.36

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

      [Start] 24.42	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 25.62	\[ \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 9.68	\[ \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 10.26	\[ \left(\color{blue}{\left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right)\right) \cdot x} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [<=] 9.35	\[ \left(\color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 9.35	\[ \left(\color{blue}{\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot 18\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 10.4	\[ \left(\left(\color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot 18\right) \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*l* [=>] 10.36	\[ \left(\color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot 18\right)\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Taylor expanded in x around 0 9.34

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

   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)) < 5.0000000000000001e291

   1. Initial program 0.56

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

   if 5.0000000000000001e291 < (-.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 67.86

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

   2. Simplified 47.74

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

      [Start] 67.86	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 67.86	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 67.86	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 67.86	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 67.86	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 47.57	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 47.57	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 47.74	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 29.63

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

   4. Simplified 21.72

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

      [Start] 29.63	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 30.18	\[ \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 20.24	\[ \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 21.57	\[ \left(\color{blue}{\left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right)\right) \cdot x} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [<=] 21	\[ \left(\color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 21	\[ \left(\color{blue}{\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot 18\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 21.73	\[ \left(\left(\color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot 18\right) \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*l* [=>] 21.72	\[ \left(\color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot 18\right)\right)} \cdot x + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 2.37

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right) + \left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	59.72%
Cost	2552

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_4 := -4 \cdot \left(t \cdot a\right)\\ t_5 := t_4 + \left(k \cdot j\right) \cdot -27\\ t_6 := b \cdot c + t_1\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;t_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-59}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+201}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+230}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+288}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	59.53%
Cost	2548

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_4 := -4 \cdot \left(t \cdot a\right)\\ t_5 := \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-139}:\\ \;\;\;\;t_4 + t_5\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-169}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-108}:\\ \;\;\;\;t_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+202}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+215}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_5\\ \end{array} \]

Alternative 3
Error	57.7%
Cost	2420

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + t_2\\ t_4 := t_2 + t \cdot \left(a \cdot -4\right)\\ t_5 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-133}:\\ \;\;\;\;t_2 + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-276}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-260}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-169}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-109}:\\ \;\;\;\;t_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-42}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+288}:\\ \;\;\;\;t_1 + \left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Error	35.86%
Cost	2272

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ t_3 := \left(k \cdot j\right) \cdot -27\\ t_4 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_3\\ t_5 := \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_3\\ \mathbf{if}\;y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+50}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-120}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-156}:\\ \;\;\;\;b \cdot c + \left(t_1 + t_3\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-135}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Error	22.59%
Cost	2264

\[\begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ t_2 := \left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right) + t_1\\ t_3 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + t_1\\ t_4 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-9}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+249}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Error	22.37%
Cost	2264

\[\begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ t_2 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ t_3 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + t_1\\ t_4 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_2\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-8}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+154}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\right) + t_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+197}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+249}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Error	31.38%
Cost	2140

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(k \cdot j\right) \cdot -27\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ t_4 := b \cdot c + \left(t_1 + t_2\right)\\ t_5 := \left(b \cdot c + y \cdot \left(x \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\right) + t_2\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-59}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-196}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_2\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-67}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_2\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+224}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	22.28%
Cost	2132

\[\begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + \left(k \cdot j\right) \cdot -27\\ t_2 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	7.41%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-117} \lor \neg \left(t \leq 2.15 \cdot 10^{-56}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right) + \left(k \cdot j\right) \cdot -27\\ \end{array} \]

Alternative 10
Error	59.12%
Cost	2029

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-256}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-169}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+202} \lor \neg \left(z \leq 6 \cdot 10^{+215}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 11
Error	59.01%
Cost	2028

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ t_3 := b \cdot c + \left(k \cdot j\right) \cdot -27\\ t_4 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-257}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-161}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+202}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+215}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	59.66%
Cost	2028

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := t_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-111}:\\ \;\;\;\;t_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-55}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+201}:\\ \;\;\;\;b \cdot c + t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+216}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(k \cdot j\right) \cdot -27\\ \end{array} \]

Alternative 13
Error	59.67%
Cost	2028

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_4 := -4 \cdot \left(t \cdot a\right)\\ t_5 := \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-144}:\\ \;\;\;\;t_4 + t_5\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-274}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-109}:\\ \;\;\;\;t_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 10^{-57}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+201}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+216}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_5\\ \end{array} \]

Alternative 14
Error	22.81%
Cost	2004

\[\begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + t_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+191}:\\ \;\;\;\;\left(b \cdot c + t_2\right) + t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+200}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	59.35%
Cost	1764

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_4 := b \cdot c + \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+46}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-274}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+202}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 16
Error	36.94%
Cost	1753

\[\begin{array}{l} t_1 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{if}\;k \leq -8.2 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{-244} \lor \neg \left(k \leq 4 \cdot 10^{-33}\right) \land k \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	70.08%
Cost	1641

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;k \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 8 \cdot 10^{-162}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.9 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+106} \lor \neg \left(k \leq 1.8 \cdot 10^{+190}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18
Error	70.12%
Cost	1641

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -4.4 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{-167}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.55 \cdot 10^{-33}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 0.48:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+106} \lor \neg \left(k \leq 1.8 \cdot 10^{+190}\right):\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 19
Error	70.22%
Cost	1641

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -4.1 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-167}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8.4 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 0.52:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 7.1 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{+106} \lor \neg \left(k \leq 2.3 \cdot 10^{+190}\right):\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20
Error	61.02%
Cost	1632

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-39}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq 480000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21
Error	61.07%
Cost	1632

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq 36000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Error	53.35%
Cost	1500

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq 6900000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 23
Error	28.61%
Cost	1489

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(k \cdot j\right) \cdot -27\\ t_3 := b \cdot c + \left(t_1 + t_2\right)\\ \mathbf{if}\;j \leq -1.05 \cdot 10^{+231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+103}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_2\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-60} \lor \neg \left(j \leq 3.1 \cdot 10^{-174}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \end{array} \]

Alternative 24
Error	28%
Cost	1357

\[\begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-28} \lor \neg \left(t \leq 7 \cdot 10^{-69}\right) \land t \leq 8.8 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ \end{array} \]

Alternative 25
Error	69.66%
Cost	1245

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;k \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 0.48:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.76 \cdot 10^{+99} \lor \neg \left(k \leq 1.8 \cdot 10^{+190}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 26
Error	58.98%
Cost	1236

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -750000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-130}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 27
Error	51.7%
Cost	1236

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-78}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.35 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	68.91%
Cost	584

\[\begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-143}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 29
Error	76.33%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023088 
(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)))