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

Average Error: 5.3 → 1.0

Time: 48.9s

Precision: binary64

Cost: 6088

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right) - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t_1 \leq 7 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

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) (* (* a 4.0) t)) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 (- INFINITY))
     (- (- (* (* x (* t z)) (* 18.0 y)) (* 4.0 (* i x))) (* j (* k 27.0)))
     (if (<= t_1 7e+305)
       t_1
       (-
        (- (+ (* y (* z (* 18.0 (* x t)))) (* b c)) (* x (* 4.0 i)))
        (* j (* 27.0 k)))))))

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) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((x * (t * z)) * (18.0 * y)) - (4.0 * (i * x))) - (j * (k * 27.0));
	} else if (t_1 <= 7e+305) {
		tmp = t_1;
	} else {
		tmp = (((y * (z * (18.0 * (x * t)))) + (b * c)) - (x * (4.0 * i))) - (j * (27.0 * k));
	}
	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) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((x * (t * z)) * (18.0 * y)) - (4.0 * (i * x))) - (j * (k * 27.0));
	} else if (t_1 <= 7e+305) {
		tmp = t_1;
	} else {
		tmp = (((y * (z * (18.0 * (x * t)))) + (b * c)) - (x * (4.0 * i))) - (j * (27.0 * k));
	}
	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) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((x * (t * z)) * (18.0 * y)) - (4.0 * (i * x))) - (j * (k * 27.0))
	elif t_1 <= 7e+305:
		tmp = t_1
	else:
		tmp = (((y * (z * (18.0 * (x * t)))) + (b * c)) - (x * (4.0 * i))) - (j * (27.0 * k))
	return tmp

Julia

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

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(x * Float64(t * z)) * Float64(18.0 * y)) - Float64(4.0 * Float64(i * x))) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 7e+305)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(y * Float64(z * Float64(18.0 * Float64(x * t)))) + Float64(b * c)) - Float64(x * Float64(4.0 * i))) - Float64(j * Float64(27.0 * k)));
	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) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((x * (t * z)) * (18.0 * y)) - (4.0 * (i * x))) - (j * (k * 27.0));
	elseif (t_1 <= 7e+305)
		tmp = t_1;
	else
		tmp = (((y * (z * (18.0 * (x * t)))) + (b * c)) - (x * (4.0 * i))) - (j * (27.0 * k));
	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[(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]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision] * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 7e+305], t$95$1, N[(N[(N[(N[(y * N[(z * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	5.3
Target	1.7
Herbie	1.0

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

Derivation

1. Split input into 3 regimes

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

   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 41.2

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

      [Start] 64.0	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 64.0	\[ \left(\left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-48 [=>] 64.0	\[ \left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 64.0	\[ \left(\left(t \cdot \left(\color{blue}{z \cdot \left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-44 [=>] 42.1	\[ \left(\left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(z \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 42.1	\[ \left(\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{i \cdot \left(x \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-44 [=>] 42.1	\[ \left(\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{x \cdot \left(i \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 42.1	\[ \left(\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(i \cdot 4\right)\right) - \color{blue}{k \cdot \left(j \cdot 27\right)} \]
      rational_best-simplify-44 [=>] 41.2	\[ \left(\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(i \cdot 4\right)\right) - \color{blue}{j \cdot \left(k \cdot 27\right)} \]

   3. Taylor expanded in x around 0 41.2

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

   4. Taylor expanded in x around inf 19.3

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

   5. Simplified 10.8

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

      [Start] 19.3	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right) \]
      rational_best-simplify-2 [=>] 19.3	\[ \left(18 \cdot \color{blue}{\left(\left(t \cdot \left(z \cdot x\right)\right) \cdot y\right)} - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right) \]
      rational_best-simplify-44 [=>] 19.5	\[ \left(\color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right) \]
      rational_best-simplify-2 [=>] 19.5	\[ \left(\left(t \cdot \color{blue}{\left(x \cdot z\right)}\right) \cdot \left(18 \cdot y\right) - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right) \]
      rational_best-simplify-44 [=>] 10.8	\[ \left(\color{blue}{\left(x \cdot \left(t \cdot z\right)\right)} \cdot \left(18 \cdot y\right) - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right) \]

   if -inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < 7e305

   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 7e305 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

   1. Initial program 57.7

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

   2. Simplified 37.5

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

      [Start] 57.7	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 57.7	\[ \left(\left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-48 [=>] 57.7	\[ \left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 57.7	\[ \left(\left(t \cdot \left(\color{blue}{z \cdot \left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 57.7	\[ \left(\left(t \cdot \left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-44 [=>] 38.2	\[ \left(\left(t \cdot \left(\color{blue}{y \cdot \left(z \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 38.2	\[ \left(\left(t \cdot \left(y \cdot \left(z \cdot \color{blue}{\left(18 \cdot x\right)}\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-44 [=>] 38.2	\[ \left(\left(t \cdot \left(y \cdot \color{blue}{\left(18 \cdot \left(z \cdot x\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 38.2	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \color{blue}{\left(x \cdot z\right)}\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 38.2	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{i \cdot \left(x \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-44 [=>] 38.1	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{x \cdot \left(i \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 38.1	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \color{blue}{\left(4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      rational_best-simplify-2 [=>] 38.1	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \color{blue}{k \cdot \left(j \cdot 27\right)} \]
      rational_best-simplify-44 [=>] 37.5	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \color{blue}{j \cdot \left(k \cdot 27\right)} \]
      rational_best-simplify-2 [=>] 37.5	\[ \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \color{blue}{\left(27 \cdot k\right)} \]

   3. Taylor expanded in y around inf 14.5

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

   4. Simplified 8.1

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

      [Start] 14.5	\[ \left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right) \]
      rational_best-simplify-44 [=>] 14.5	\[ \left(\left(\color{blue}{y \cdot \left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right) \]
      rational_best-simplify-44 [=>] 8.1	\[ \left(\left(y \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot x\right)\right)}\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right) \]
      rational_best-simplify-44 [=>] 8.1	\[ \left(\left(y \cdot \color{blue}{\left(z \cdot \left(18 \cdot \left(t \cdot x\right)\right)\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right) \]
      rational_best-simplify-2 [=>] 8.1	\[ \left(\left(y \cdot \left(z \cdot \left(18 \cdot \color{blue}{\left(x \cdot t\right)}\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;\left(\left(x \cdot \left(t \cdot z\right)\right) \cdot \left(18 \cdot y\right) - 4 \cdot \left(i \cdot x\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 7 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.4
Cost	2516

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ t_3 := \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(y \cdot \left(t \cdot \left(z \cdot \left(18 \cdot x\right)\right)\right) + b \cdot c\right) - x \cdot \left(i \cdot 4\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - t_1\right) - t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+222}:\\ \;\;\;\;\left(c \cdot b + -4 \cdot \left(a \cdot t + i \cdot x\right)\right) - t_2\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+227}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - t_1\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	19.2
Cost	2408

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) - i \cdot 4\right) - 27 \cdot \left(k \cdot j\right)\\ t_3 := j \cdot \left(k \cdot 27\right)\\ t_4 := \left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_3\\ t_5 := \left(c \cdot b - t_1\right) - t_3\\ t_6 := \left(t \cdot \left(a \cdot -4\right) - t_1\right) - t_3\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{+158}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{+52}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{+32}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1080000000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+150}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 3
Error	19.7
Cost	2408

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ t_3 := x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right) - i \cdot 4\right) - t_2\\ t_4 := \left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_2\\ t_5 := \left(c \cdot b - t_1\right) - t_2\\ t_6 := \left(t \cdot \left(a \cdot -4\right) - t_1\right) - t_2\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.02 \cdot 10^{-44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-85}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+148}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Error	18.5
Cost	2144

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ t_3 := \left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_2\\ t_4 := \left(c \cdot b - t_1\right) - t_2\\ t_5 := \left(t \cdot \left(a \cdot -4\right) - t_1\right) - t_2\\ \mathbf{if}\;i \leq -1.46 \cdot 10^{+159}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{+52}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+32}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-91}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-133}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 215000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+152}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Error	9.8
Cost	2128

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - x \cdot \left(i \cdot 4\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 95000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+95}:\\ \;\;\;\;\left(c \cdot b + -4 \cdot \left(a \cdot t + i \cdot x\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	10.5
Cost	2128

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ t_3 := \left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right) - t_2\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-5}:\\ \;\;\;\;\left(\left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - t_1\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 10^{+44}:\\ \;\;\;\;\left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - t_1\right) - t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+95}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	10.5
Cost	2128

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot 4\right)\\ t_2 := 27 \cdot \left(k \cdot j\right)\\ t_3 := j \cdot \left(k \cdot 27\right)\\ t_4 := \left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right) - t_3\\ \mathbf{if}\;t \leq -2.02 \cdot 10^{-60}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-6}:\\ \;\;\;\;\left(\left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - t_1\right) - t_2\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+44}:\\ \;\;\;\;\left(\left(y \cdot \left(t \cdot \left(z \cdot \left(18 \cdot x\right)\right)\right) + b \cdot c\right) - t_1\right) - t_2\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+95}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	10.5
Cost	2128

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ t_3 := \left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right) - t_2\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 0.00375:\\ \;\;\;\;\left(\left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - t_1\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+46}:\\ \;\;\;\;\left(\left(y \cdot \left(t \cdot \left(z \cdot \left(18 \cdot x\right)\right)\right) + b \cdot c\right) - t_1\right) - t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+96}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	10.5
Cost	2128

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{if}\;t \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;\left(\left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - x \cdot \left(i \cdot 4\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+95}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	10.5
Cost	2128

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ t_3 := \left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right) - t_1\right) - t_2\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 0.005:\\ \;\;\;\;\left(\left(c \cdot b + \left(a \cdot \left(-4 \cdot t\right) + t_1\right)\right) + \left(-i \cdot \left(x \cdot 8\right)\right)\right) - t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+43}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot \left(18 \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+95}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	4.7
Cost	2120

\[\begin{array}{l} t_1 := \left(\left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-124}:\\ \;\;\;\;\left(\left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - x \cdot \left(i \cdot 4\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	31.6
Cost	1760

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := c \cdot b - t_1\\ t_3 := -4 \cdot \left(i \cdot x\right) - t_1\\ t_4 := t \cdot \left(-4 \cdot a\right) - t_1\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.14 \cdot 10^{-29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 13
Error	10.7
Cost	1736

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(c \cdot b + -4 \cdot \left(a \cdot t + i \cdot x\right)\right) - t_1\\ \mathbf{if}\;j \cdot 27 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \cdot 27 \leq 5 \cdot 10^{-105}:\\ \;\;\;\;\left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) \cdot x - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	12.1
Cost	1608

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(c \cdot b + -4 \cdot \left(a \cdot t + i \cdot x\right)\right) - t_1\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+149}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right)\right) - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	12.1
Cost	1608

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(c \cdot b + -4 \cdot \left(a \cdot t + i \cdot x\right)\right) - t_1\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+149}:\\ \;\;\;\;\left(t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	11.0
Cost	1608

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(c \cdot b + -4 \cdot \left(a \cdot t + i \cdot x\right)\right) - t_1\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+261}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+149}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right) - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	31.0
Cost	1496

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := -4 \cdot \left(i \cdot x\right) - t_1\\ t_3 := c \cdot b - t_1\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+176}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	21.1
Cost	1224

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) - t_1\\ \end{array} \]

Alternative 19
Error	17.5
Cost	1224

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := \left(t \cdot \left(-4 \cdot a\right) + c \cdot b\right) - t_1\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-12}:\\ \;\;\;\;\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	35.2
Cost	1104

\[\begin{array}{l} t_1 := c \cdot b - j \cdot \left(k \cdot 27\right)\\ t_2 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;t \leq -6.3 \cdot 10^{+235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-29}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	44.5
Cost	716

\[\begin{array}{l} t_1 := i \cdot \left(-4 \cdot x\right)\\ \mathbf{if}\;i \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+49}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	44.0
Cost	584

\[\begin{array}{l} t_1 := i \cdot \left(-4 \cdot x\right)\\ \mathbf{if}\;i \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{+49}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	48.2
Cost	320

\[-27 \cdot \left(k \cdot j\right) \]

Reproduce

herbie shell --seed 2023092 
(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)))