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

Average Error: 9.06% → 1.42%

Time: 33.3s

Precision: binary64

Cost: 6089

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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)))
          (* k (* j -27.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+306)))
     (+
      (+ (* 18.0 (* y (* z (* x t)))) (* b c))
      (- (* x (* i -4.0)) (* j (* 27.0 k))))
     t_1)))

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

Target

Original	9.06%
Target	2.47%
Herbie	1.42%

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.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 or 2.00000000000000003e306 < (-.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 96.93

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

   2. Simplified 61.72

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

      [Start] 96.93	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 96.93	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 96.93	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 96.93	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 96.93	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 63.24	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 63.24	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 61.72	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 23.29

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

   4. Simplified 11.58

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

      [Start] 23.29	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 23.29	\[ \left(18 \cdot \left(y \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*l* [=>] 11.58	\[ \left(18 \cdot \left(y \cdot \color{blue}{\left(z \cdot \left(x \cdot t\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   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)) < 2.00000000000000003e306

   1. Initial program 0.42

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

4. Final simplification 1.42

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right) \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right) \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.28%
Cost	2121

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-39} \lor \neg \left(z \leq 3.1 \cdot 10^{+145}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + t_1\\ \end{array} \]

Alternative 2
Error	52.13%
Cost	2028

\[\begin{array}{l} t_1 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ t_2 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.12 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	51.45%
Cost	2028

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ t_3 := \left(j \cdot 27\right) \cdot k\\ t_4 := -4 \cdot \left(t \cdot a\right) - t_3\\ \mathbf{if}\;c \leq -5.8 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-301}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-202}:\\ \;\;\;\;t_1 - t_3\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-164}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-101}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-64}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{+70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+182}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_3\\ \end{array} \]

Alternative 4
Error	29.96%
Cost	1876

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;k \leq -3.6 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{+134}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	12.87%
Cost	1865

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+63} \lor \neg \left(y \leq 4.05 \cdot 10^{-19}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \end{array} \]

Alternative 6
Error	60.78%
Cost	1632

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -7.4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.04 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 7
Error	32.34%
Cost	1621

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+158} \lor \neg \left(x \leq 1.9 \cdot 10^{+264}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 8
Error	48.87%
Cost	1501

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -2.6 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-41} \lor \neg \left(k \leq 5.1 \cdot 10^{+16}\right) \land k \leq 2.05 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	48.77%
Cost	1501

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;k \leq -1.05 \cdot 10^{-120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.65 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-42} \lor \neg \left(k \leq 2.3 \cdot 10^{+17}\right) \land k \leq 7.6 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	50.98%
Cost	1496

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := -4 \cdot \left(t \cdot a\right) - t_2\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-101}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_2\\ \end{array} \]

Alternative 11
Error	15.22%
Cost	1476

\[\begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 12
Error	27.01%
Cost	1225

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-6} \lor \neg \left(x \leq 1.1 \cdot 10^{-27}\right):\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 13
Error	27.05%
Cost	1224

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-57}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2050000:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 14
Error	68.85%
Cost	1112

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 15
Error	68.97%
Cost	1112

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-88}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 16
Error	68.92%
Cost	1112

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.52 \cdot 10^{-87}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17
Error	49.47%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+173} \lor \neg \left(i \leq 1.05 \cdot 10^{-46}\right) \land \left(i \leq 4.5 \cdot 10^{-24} \lor \neg \left(i \leq 4.2 \cdot 10^{+26}\right)\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 18
Error	68.46%
Cost	585

\[\begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+47} \lor \neg \left(b \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 19
Error	75.85%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023115 
(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)))