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

Percentage Accurate: 84.8% → 90.7%

Time: 33.7s

Precision: binary64

Cost: 27076

• Unsound rule application detected in e-graph. Results may not be sound.

• 50.9% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

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)))

↓

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t 1e-111)
   (fma
    x
    (fma 18.0 (* t (* y z)) (* i -4.0))
    (fma t (* -4.0 a) (fma b c (* k (* j -27.0)))))
   (fma
    j
    (* k -27.0)
    (fma x (* i -4.0) (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (* b c))))))

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);
}

↓

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= 1e-111) {
		tmp = fma(x, fma(18.0, (t * (y * z)), (i * -4.0)), fma(t, (-4.0 * a), fma(b, c, (k * (j * -27.0)))));
	} else {
		tmp = fma(j, (k * -27.0), fma(x, (i * -4.0), fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), (b * c))));
	}
	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

↓

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= 1e-111)
		tmp = fma(x, fma(18.0, Float64(t * Float64(y * z)), Float64(i * -4.0)), fma(t, Float64(-4.0 * a), fma(b, c, Float64(k * Float64(j * -27.0)))));
	else
		tmp = fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), Float64(b * c))));
	end
	return 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]

↓

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, 1e-111], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision] + N[(b * c + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	84.8%
Target	89.1%
Herbie	90.7%

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

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000009e-111

   1. Initial program 83.7%

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

   2. Simplified 92.2%

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

      [Start] 83.7%	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 83.7%	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      +-commutative [=>] 83.7%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 83.7%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+l+ [=>] 83.7%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+r+ [=>] 83.7%	\[ \color{blue}{\left(\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      associate--l+ [=>] 83.7%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [<=] 83.7%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]
      sub-neg [<=] 83.7%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(x \cdot 4\right) \cdot i\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]

   if 1.00000000000000009e-111 < t

   1. Initial program 85.8%

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

   2. Simplified 95.9%

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

      [Start] 85.8%	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 85.8%	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [=>] 85.8%	\[ \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]
      associate-*l* [=>] 85.8%	\[ \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      distribute-rgt-neg-in [=>] 85.8%	\[ \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      fma-def [=>] 90.1%	\[ \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]
      *-commutative [=>] 90.1%	\[ \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      distribute-rgt-neg-in [=>] 90.1%	\[ \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      metadata-eval [=>] 90.1%	\[ \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      sub-neg [=>] 90.1%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]
      +-commutative [=>] 90.1%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]
      associate-*l* [=>] 90.1%	\[ \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]
      distribute-rgt-neg-in [=>] 90.1%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	90.7%
Cost	27076

\[\begin{array}{l} \mathbf{if}\;t \leq 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	89.8%
Cost	27076

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+235}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	91.2%
Cost	4036

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

Alternative 4
Accuracy	82.5%
Cost	3025

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \left(-4 \cdot a - t_1 \cdot -18\right) - t_2\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-5} \lor \neg \left(t_2 \leq 5 \cdot 10^{+119}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 5
Accuracy	79.9%
Cost	2128

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := -27 \cdot \left(k \cdot j\right) + \left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)\\ t_3 := x \cdot i + t \cdot a\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-211}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot t_3\right) - t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-29}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-12}:\\ \;\;\;\;-4 \cdot t_3 - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	80.9%
Cost	2120

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 7
Accuracy	80.5%
Cost	2000

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\right) - t_2\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - t_2\right) - t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right) + \left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot a - y \cdot \left(z \cdot \left(x \cdot -18\right)\right)\right) - t_1\\ \end{array} \]

Alternative 8
Accuracy	77.7%
Cost	1745

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(-4 \cdot a - \left(y \cdot \left(x \cdot z\right)\right) \cdot -18\right) - t_1\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-49}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+45} \lor \neg \left(t \leq 3 \cdot 10^{+111}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 9
Accuracy	77.7%
Cost	1745

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(-4 \cdot a - y \cdot \left(z \cdot \left(x \cdot -18\right)\right)\right) - t_1\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+42} \lor \neg \left(t \leq 1.05 \cdot 10^{+111}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 10
Accuracy	77.1%
Cost	1744

\[\begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+82}:\\ \;\;\;\;x \cdot t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t_1 - i \cdot 4\right)\\ \end{array} \]

Alternative 11
Accuracy	77.1%
Cost	1744

\[\begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;x \leq -3.65 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{+57}:\\ \;\;\;\;t_2 - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+158}:\\ \;\;\;\;t_2 - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t_1 - i \cdot 4\right)\\ \end{array} \]

Alternative 12
Accuracy	62.7%
Cost	1620

\[\begin{array}{l} t_1 := x \cdot i + t \cdot a\\ t_2 := -4 \cdot t_1 - k \cdot \left(j \cdot 27\right)\\ t_3 := b \cdot c - 4 \cdot t_1\\ t_4 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+56}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.12 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 13
Accuracy	45.0%
Cost	1500

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ t_2 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-69}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	45.0%
Cost	1500

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := b \cdot c - t_2\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-220}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-172}:\\ \;\;\;\;t_1 - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-70}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+76}:\\ \;\;\;\;t_1 - t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+145}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	69.5%
Cost	1488

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6200000:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+244}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	69.4%
Cost	1488

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7500000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+244}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	45.7%
Cost	1364

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(18 \cdot y\right) \cdot \left(z \cdot \left(t \cdot x\right)\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 18
Accuracy	45.7%
Cost	1364

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(18 \cdot y\right) \cdot \left(z \cdot \left(t \cdot x\right)\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 19
Accuracy	62.4%
Cost	1360

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Accuracy	71.2%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+29} \lor \neg \left(t \leq 7200000\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 21
Accuracy	45.7%
Cost	1105

\[\begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+34}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(z \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-63}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+168} \lor \neg \left(t \leq 3.5 \cdot 10^{+244}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 22
Accuracy	35.2%
Cost	1104

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;k \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-139}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 23
Accuracy	35.8%
Cost	1104

\[\begin{array}{l} t_1 := \left(18 \cdot y\right) \cdot \left(z \cdot \left(t \cdot x\right)\right)\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{+53}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \leq 3.65 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-139}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 24
Accuracy	57.4%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+19} \lor \neg \left(t \leq 1.8 \cdot 10^{-66}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 25
Accuracy	46.4%
Cost	972

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+240}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+89}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 26
Accuracy	33.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 15000000:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 27
Accuracy	30.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+45}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-37}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 28
Accuracy	23.6%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023167 
(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)))