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

Average Error: 8.93% → 5.1%

Time: 41.9s

Precision: binary64

Cost: 5321

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

↓

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (* (* (* (* x 18.0) y) z) t) (* t (* a -4.0))) (* b c))
          (* i (* x -4.0))))
        (t_2 (* k (* j -27.0))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306)))
     (+ (* 18.0 (* (* y t) (* x z))) t_2)
     (+ 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 * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double t_2 = k * (j * -27.0);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+306)) {
		tmp = (18.0 * ((y * t) * (x * z))) + t_2;
	} else {
		tmp = 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 * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double t_2 = k * (j * -27.0);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+306)) {
		tmp = (18.0 * ((y * t) * (x * z))) + t_2;
	} else {
		tmp = 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 * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))
	t_2 = k * (j * -27.0)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = (18.0 * ((y * t) * (x * z))) + t_2
	else:
		tmp = 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(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)))
	t_2 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+306))
		tmp = Float64(Float64(18.0 * Float64(Float64(y * t) * Float64(x * z))) + t_2);
	else
		tmp = Float64(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 * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	t_2 = k * (j * -27.0);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+306)))
		tmp = (18.0 * ((y * t) * (x * z))) + t_2;
	else
		tmp = 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[(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]}, Block[{t$95$2 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(N[(18.0 * N[(N[(y * t), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]

Target

Original	8.93%
Target	2.45%
Herbie	5.1%

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

Derivation

1. Split input into 2 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 or 4.99999999999999993e306 < (-.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 97.71

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

   2. Simplified 67.47

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

      [Start] 97.71	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      cancel-sign-sub-inv [=>] 97.71	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-j \cdot 27\right) \cdot k} \]
      associate--l+ [=>] 97.71	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} + \left(-j \cdot 27\right) \cdot k \]

   3. Taylor expanded in y around inf 51.57

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

   4. Simplified 53.71

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

      [Start] 51.57	\[ 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]
      associate-*r* [=>] 53.71	\[ 18 \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot x\right)\right)} + k \cdot \left(j \cdot -27\right) \]

   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)) < 4.99999999999999993e306

   1. Initial program 0.47

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 5.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	51.55%
Cost	2816

\[\begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := t_3 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;k \leq -6.2 \cdot 10^{-210}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \leq -1.3 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-81}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 350000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right) + t_3\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{+152}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3 + b \cdot c\\ \end{array} \]

Alternative 2
Error	51.62%
Cost	2816

\[\begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := t_3 + t \cdot \left(a \cdot -4\right)\\ t_5 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;k \leq -4.6 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \leq -1.7 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(18 \cdot t_5 + a \cdot -4\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-81}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1300000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{+84}:\\ \;\;\;\;t_3 + t_5 \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{+113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{+147}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3 + b \cdot c\\ \end{array} \]

Alternative 3
Error	70.36%
Cost	2696

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := x \cdot \left(i \cdot -4\right)\\ t_4 := 18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1420000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -95000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-142}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-305}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 4
Error	70.38%
Cost	2696

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := x \cdot \left(i \cdot -4\right)\\ t_4 := 18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -182000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3900:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-239}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-307}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 5
Error	70.45%
Cost	2696

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := x \cdot \left(i \cdot -4\right)\\ t_4 := 18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+83}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -135000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(\left(18 \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.36 \cdot 10^{-241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-307}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 6
Error	50.99%
Cost	2548

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := t_2 + t \cdot \left(a \cdot -4\right)\\ t_4 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_5 := t_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+131}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+102}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{+84}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -0.00155:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-125}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-130}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-286}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-212}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1040000:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 + b \cdot c\\ \end{array} \]

Alternative 7
Error	35.82%
Cost	2412

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right) + t_1\\ t_3 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + -27 \cdot \left(k \cdot j\right)\\ t_4 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) - 27 \cdot \left(k \cdot j\right)\right)\\ t_5 := \left(b \cdot c + t_1\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+243}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+173}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.95 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-146}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-172}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-308}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	35.85%
Cost	2412

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot -27\right) + t_1\\ t_4 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + -27 \cdot \left(k \cdot j\right)\\ t_5 := b \cdot c + \left(t_2 - 27 \cdot \left(k \cdot j\right)\right)\\ t_6 := \left(b \cdot c + t_1\right) + x \cdot \left(i \cdot -4\right)\\ t_7 := \left(b \cdot c + t_2\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+242}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-147}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-172}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-220}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-308}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 9
Error	8.84%
Cost	2121

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+27} \lor \neg \left(t \leq 2.7 \cdot 10^{-115}\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \end{array} \]

Alternative 10
Error	28.65%
Cost	2016

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) - 27 \cdot \left(k \cdot j\right)\right)\\ t_3 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) + -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	15.05%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{-218} \lor \neg \left(k \leq 1.3 \cdot 10^{-72}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 12
Error	69.93%
Cost	1640

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;c \leq -8 \cdot 10^{-149}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-306}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.32 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-33}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 13
Error	48.98%
Cost	1633

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot -27\right) + b \cdot c\\ \mathbf{if}\;k \leq -6.4 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 8.8 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1300:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+77} \lor \neg \left(k \leq 2.4 \cdot 10^{+84}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(t \cdot \left(18 \cdot y\right)\right)\\ \end{array} \]

Alternative 14
Error	48.82%
Cost	1632

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot -27\right) + b \cdot c\\ t_4 := b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;k \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1300:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+84}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(t \cdot \left(18 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	35.63%
Cost	1621

\[\begin{array}{l} t_1 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+37} \lor \neg \left(a \leq 7.8 \cdot 10^{+149}\right) \land a \leq 1.4 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 16
Error	56.12%
Cost	1500

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right) + b \cdot c\\ \mathbf{if}\;x \leq -16000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	49.8%
Cost	1500

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+217}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot c\\ \end{array} \]

Alternative 18
Error	48.98%
Cost	1368

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-33}:\\ \;\;\;\;t_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+217}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot c\\ \end{array} \]

Alternative 19
Error	15.83%
Cost	1344

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

Alternative 20
Error	68.24%
Cost	980

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;j \leq -4.7 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2800000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-136}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	68.35%
Cost	980

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -22000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{-139}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-83}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 22
Error	68.31%
Cost	850

\[\begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{+101} \lor \neg \left(j \leq -2.8 \cdot 10^{+15} \lor \neg \left(j \leq -8.5 \cdot 10^{-75}\right) \land j \leq 1.35 \cdot 10^{-83}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 23
Error	75.09%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023089 
(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)))