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

Average Error: 5.7 → 1.5

Time: 1.2min

Precision: binary64

Cost: 5320

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

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := j \cdot \left(27 \cdot k\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right) + \left(\left(b \cdot c - t_2\right) - t_1\right)\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+291}:\\ \;\;\;\;t_3 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) - t_1\right) - t_2\right)\\ \end{array} \]

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 (* 4.0 i)))
        (t_2 (* j (* 27.0 k)))
        (t_3
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_3 (- INFINITY))
     (+ (* y (* x (* t (* 18.0 z)))) (- (- (* b c) t_2) t_1))
     (if (<= t_3 4e+291)
       (- t_3 (* (* j 27.0) k))
       (+ (* b c) (- (- (* y (* 18.0 (* z (* t x)))) t_1) t_2))))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (4.0 * i);
	double t_2 = j * (27.0 * k);
	double t_3 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (y * (x * (t * (18.0 * z)))) + (((b * c) - t_2) - t_1);
	} else if (t_3 <= 4e+291) {
		tmp = t_3 - ((j * 27.0) * k);
	} else {
		tmp = (b * c) + (((y * (18.0 * (z * (t * x)))) - t_1) - t_2);
	}
	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 * (4.0 * i);
	double t_2 = j * (27.0 * k);
	double t_3 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * (x * (t * (18.0 * z)))) + (((b * c) - t_2) - t_1);
	} else if (t_3 <= 4e+291) {
		tmp = t_3 - ((j * 27.0) * k);
	} else {
		tmp = (b * c) + (((y * (18.0 * (z * (t * x)))) - t_1) - t_2);
	}
	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 * (4.0 * i)
	t_2 = j * (27.0 * k)
	t_3 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (y * (x * (t * (18.0 * z)))) + (((b * c) - t_2) - t_1)
	elif t_3 <= 4e+291:
		tmp = t_3 - ((j * 27.0) * k)
	else:
		tmp = (b * c) + (((y * (18.0 * (z * (t * x)))) - t_1) - t_2)
	return tmp

Julia

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

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(4.0 * i))
	t_2 = Float64(j * Float64(27.0 * k))
	t_3 = 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))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(x * Float64(t * Float64(18.0 * z)))) + Float64(Float64(Float64(b * c) - t_2) - t_1));
	elseif (t_3 <= 4e+291)
		tmp = Float64(t_3 - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(b * c) + Float64(Float64(Float64(y * Float64(18.0 * Float64(z * Float64(t * x)))) - t_1) - t_2));
	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 * (4.0 * i);
	t_2 = j * (27.0 * k);
	t_3 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (y * (x * (t * (18.0 * z)))) + (((b * c) - t_2) - t_1);
	elseif (t_3 <= 4e+291)
		tmp = t_3 - ((j * 27.0) * k);
	else
		tmp = (b * c) + (((y * (18.0 * (z * (t * x)))) - t_1) - t_2);
	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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(y * N[(x * N[(t * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+291], N[(t$95$3 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(N[(N[(y * N[(18.0 * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	5.7
Target	1.7
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 38.3

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

      [Start] 64.0	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-1 [=>] 64.0	\[ \left(\color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-48 [=>] 64.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-1 [=>] 64.0	\[ \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-48 [=>] 64.0	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

   3. Taylor expanded in x around inf 14.9

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

   4. Simplified 40.1

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

      [Start] 14.9	\[ 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [=>] 39.5	\[ 18 \cdot \color{blue}{\left(t \cdot \left(\left(z \cdot x\right) \cdot y\right)\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [<=] 39.5	\[ 18 \cdot \left(t \cdot \color{blue}{\left(y \cdot \left(z \cdot x\right)\right)}\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [=>] 39.9	\[ \color{blue}{t \cdot \left(\left(y \cdot \left(z \cdot x\right)\right) \cdot 18\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [<=] 39.9	\[ t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [=>] 39.9	\[ t \cdot \color{blue}{\left(y \cdot \left(\left(z \cdot x\right) \cdot 18\right)\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [=>] 39.9	\[ t \cdot \left(y \cdot \color{blue}{\left(18 \cdot \left(z \cdot x\right)\right)}\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [=>] 40.1	\[ t \cdot \left(y \cdot \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right)}\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [<=] 40.1	\[ t \cdot \left(y \cdot \left(z \cdot \color{blue}{\left(18 \cdot x\right)}\right)\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]

   5. Taylor expanded in t around 0 14.9

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

   6. Simplified 6.0

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

      [Start] 14.9	\[ 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [=>] 14.9	\[ 18 \cdot \color{blue}{\left(\left(t \cdot \left(z \cdot x\right)\right) \cdot y\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [<=] 14.9	\[ \color{blue}{y \cdot \left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [=>] 14.9	\[ y \cdot \color{blue}{\left(t \cdot \left(\left(z \cdot x\right) \cdot 18\right)\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [<=] 14.9	\[ y \cdot \left(t \cdot \color{blue}{\left(18 \cdot \left(z \cdot x\right)\right)}\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [<=] 14.9	\[ y \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot z\right)\right)}\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-43 [=>] 6.0	\[ y \cdot \color{blue}{\left(x \cdot \left(\left(18 \cdot z\right) \cdot t\right)\right)} + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]
      rational.json-simplify-2 [=>] 6.0	\[ y \cdot \left(x \cdot \color{blue}{\left(t \cdot \left(18 \cdot z\right)\right)}\right) + \left(\left(b \cdot c - j \cdot \left(27 \cdot k\right)\right) - x \cdot \left(4 \cdot i\right)\right) \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < 3.9999999999999998e291

   1. Initial program 0.4

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

   if 3.9999999999999998e291 < (-.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 43.1

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

   2. Simplified 29.8

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

      [Start] 43.1	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-48 [=>] 43.1	\[ \color{blue}{\left(b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-1 [=>] 43.1	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) + b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-48 [=>] 43.1	\[ \color{blue}{b \cdot c + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      rational.json-simplify-2 [=>] 43.1	\[ b \cdot c + \left(\left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-52 [=>] 43.1	\[ b \cdot c + \left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 43.1	\[ b \cdot c + \left(\left(t \cdot \left(\color{blue}{z \cdot \left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 43.1	\[ b \cdot c + \left(\left(t \cdot \left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 29.8	\[ b \cdot c + \left(\left(t \cdot \left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot z\right)} - a \cdot 4\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 29.8	\[ b \cdot c + \left(\left(t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right) - a \cdot 4\right) - \color{blue}{i \cdot \left(x \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 29.8	\[ b \cdot c + \left(\left(t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right) - a \cdot 4\right) - \color{blue}{x \cdot \left(4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 29.8	\[ b \cdot c + \left(\left(t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right) - a \cdot 4\right) - x \cdot \left(4 \cdot i\right)\right) - \color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]

   3. Taylor expanded in y around inf 21.2

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

   4. Applied egg-rr 49.2

      \[\leadsto b \cdot c + \left(\left(\color{blue}{\left(t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right) + 0\right)} - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]

   5. Simplified 31.8

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

      [Start] 49.2	\[ b \cdot c + \left(\left(\left(t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right) + 0\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-4 [=>] 49.2	\[ b \cdot c + \left(\left(\color{blue}{t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)} - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [=>] 49.2	\[ b \cdot c + \left(\left(t \cdot \color{blue}{\left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z\right)} - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [<=] 31.8	\[ b \cdot c + \left(\left(\color{blue}{z \cdot \left(t \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)} - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [=>] 31.8	\[ b \cdot c + \left(\left(z \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot 18\right)}\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in z around 0 21.2

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

   7. Simplified 14.7

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

      [Start] 21.2	\[ b \cdot c + \left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 21.2	\[ b \cdot c + \left(\left(\color{blue}{y \cdot \left(\left(t \cdot \left(z \cdot x\right)\right) \cdot 18\right)} - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [=>] 21.2	\[ b \cdot c + \left(\left(y \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 14.7	\[ b \cdot c + \left(\left(y \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(x \cdot t\right)\right)}\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [<=] 14.7	\[ b \cdot c + \left(\left(y \cdot \left(18 \cdot \left(z \cdot \color{blue}{\left(t \cdot x\right)}\right)\right) - x \cdot \left(4 \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.5

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

Alternatives

Alternative 1
Error	29.9
Cost	2916

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(a \cdot t\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_3 := t \cdot \left(-4 \cdot a\right)\\ t_4 := t_3 - 4 \cdot \left(i \cdot x\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-297}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-138}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq 500000000000:\\ \;\;\;\;t_3 - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 10^{+35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 10^{+138}:\\ \;\;\;\;b \cdot c + \left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	32.0
Cost	2420

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(a \cdot t\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_3 := t \cdot \left(-4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\\ t_4 := b \cdot c + -27 \cdot \left(k \cdot j\right)\\ t_5 := c \cdot b - j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;k \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -7.2 \cdot 10^{-190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -2.75 \cdot 10^{-239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.22 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-126}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 3.95 \cdot 10^{-109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-92}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6500000000000:\\ \;\;\;\;b \cdot c + \left(i \cdot x\right) \cdot -4\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{+79}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	24.7
Cost	2392

\[\begin{array}{l} t_1 := c \cdot b + -4 \cdot \left(i \cdot x + a \cdot t\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 500000000000:\\ \;\;\;\;-\left(4 \cdot \left(i \cdot x\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	4.0
Cost	2384

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+203}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right) + \left(\left(b \cdot c - t_2\right) - t_1\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c + \left(\left(t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right) - a \cdot 4\right) - t_1\right) - t_2\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(x \cdot \left(\left(z \cdot t\right) \cdot y\right)\right) - t_1\right) - t_2\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) - a \cdot 4\right) + \left(\left(b \cdot c - 27 \cdot \left(k \cdot j\right)\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(z \cdot \left(18 \cdot \left(t \cdot \left(y \cdot x\right)\right)\right) - t_1\right) - t_2\right)\\ \end{array} \]

Alternative 5
Error	4.4
Cost	2120

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := b \cdot c + \left(\left(18 \cdot \left(x \cdot \left(\left(z \cdot t\right) \cdot y\right)\right) - t_1\right) - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c + \left(\left(t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right) - a \cdot 4\right) - t_1\right) - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	4.9
Cost	2120

\[\begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ t_3 := t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) + \left(\left(b \cdot c - t_1\right) - t_2\right)\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-145}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(x \cdot \left(\left(z \cdot t\right) \cdot y\right)\right) - t_2\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	14.7
Cost	2000

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ t_3 := c \cdot b + \left(t_2 - j \cdot \left(27 \cdot k\right)\right)\\ t_4 := 27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+33}:\\ \;\;\;\;t_2 - \left(t_1 + t_4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+138}:\\ \;\;\;\;c \cdot b - \left(t_4 + t_1\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(i \cdot x + a \cdot t\right)\\ \end{array} \]

Alternative 8
Error	38.4
Cost	1876

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(k \cdot j\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-224}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	27.9
Cost	1876

\[\begin{array}{l} t_1 := 27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - t_1\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-99}:\\ \;\;\;\;-\left(4 \cdot \left(i \cdot x\right) + t_1\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+138}:\\ \;\;\;\;b \cdot c + \left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(a \cdot t\right)\\ \end{array} \]

Alternative 10
Error	27.9
Cost	1876

\[\begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-99}:\\ \;\;\;\;-\left(4 \cdot \left(i \cdot x\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+138}:\\ \;\;\;\;b \cdot c + \left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(a \cdot t\right)\\ \end{array} \]

Alternative 11
Error	9.7
Cost	1864

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := j \cdot \left(27 \cdot k\right)\\ t_3 := b \cdot c + \left(\left(a \cdot \left(t \cdot -4\right) - t_1\right) - t_2\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-145}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(x \cdot \left(\left(z \cdot t\right) \cdot y\right)\right) - t_1\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	8.1
Cost	1864

\[\begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+167}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - t_2\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + \left(\left(a \cdot \left(t \cdot -4\right) - t_2\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(x \cdot \left(\left(z \cdot t\right) \cdot y\right)\right) - t_2\right) - t_1\right)\\ \end{array} \]

Alternative 13
Error	7.7
Cost	1864

\[\begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+163}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - t_2\right) - t_1\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;b \cdot c + \left(\left(a \cdot \left(t \cdot -4\right) - t_2\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) - t_2\right) - t_1\right)\\ \end{array} \]

Alternative 14
Error	7.7
Cost	1864

\[\begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+163}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - t_2\right) - t_1\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-61}:\\ \;\;\;\;b \cdot c + \left(\left(a \cdot \left(t \cdot -4\right) - t_2\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) - t_2\right) - t_1\right)\\ \end{array} \]

Alternative 15
Error	8.0
Cost	1864

\[\begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{-131}:\\ \;\;\;\;b \cdot c + \left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - t_2\right) - t_1\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c + \left(\left(a \cdot \left(t \cdot -4\right) - t_2\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(z \cdot \left(18 \cdot \left(t \cdot \left(y \cdot x\right)\right)\right) - t_2\right) - 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 16
Error	8.0
Cost	1864

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right) + \left(\left(b \cdot c - t_2\right) - t_1\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c + \left(\left(a \cdot \left(t \cdot -4\right) - t_1\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(z \cdot \left(18 \cdot \left(t \cdot \left(y \cdot x\right)\right)\right) - t_1\right) - 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 17
Error	43.9
Cost	1772

\[\begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;k \leq -7.4 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -7.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.1 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.9 \cdot 10^{-239}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq -1.04 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+27}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.85 \cdot 10^{+79}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq 1.06 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	43.8
Cost	1772

\[\begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;k \leq -2.85 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -7.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.36 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-237}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq -1.05 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.15 \cdot 10^{-134}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-94}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;k \leq 10^{+25}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq 8.8 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \leq 1.06 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	31.1
Cost	1632

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(a \cdot t\right)\\ t_2 := b \cdot c + \left(i \cdot x\right) \cdot -4\\ t_3 := b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;k \leq -2.8 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 31000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.06 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 20
Error	31.2
Cost	1632

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(a \cdot t\right)\\ t_2 := b \cdot c + \left(i \cdot x\right) \cdot -4\\ t_3 := c \cdot b - j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;k \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-291}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-93}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \leq 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 44000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 21
Error	19.1
Cost	1620

\[\begin{array}{l} t_1 := c \cdot b + -4 \cdot \left(i \cdot x + a \cdot t\right)\\ t_2 := c \cdot b + \left(-4 \cdot \left(a \cdot t\right) - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.04 \cdot 10^{+23}:\\ \;\;\;\;-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Error	37.3
Cost	1616

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(a \cdot t\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	37.3
Cost	1616

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(a \cdot t\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	17.9
Cost	1488

\[\begin{array}{l} t_1 := c \cdot b - \left(27 \cdot \left(k \cdot j\right) + 4 \cdot \left(i \cdot x\right)\right)\\ t_2 := c \cdot b + \left(-4 \cdot \left(a \cdot t\right) - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{if}\;i \leq -1.55 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -400:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	9.8
Cost	1344

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

Alternative 26
Error	45.5
Cost	1244

\[\begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;c \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-204}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7200000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]

Alternative 27
Error	45.3
Cost	848

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-151}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+57}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 28
Error	48.6
Cost	192

\[c \cdot b \]

Reproduce

herbie shell --seed 2023064 
(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)))