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

Percentage Accurate: 85.1% → 91.0%

Time: 33.6s

Precision: binary64

Cost: 28612

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

• 51.2% of points produce a very large (infinite) output. You may want to add a precondition.

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

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))
          (* (* x 4.0) i))))
   (if (<= t_1 5e+294)
     (- t_1 (* (* j 27.0) k))
     (fma
      x
      (fma 18.0 (* t (* y z)) (* i -4.0))
      (fma t (* a -4.0) (fma b c (* k (* j -27.0))))))))

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)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 5e+294) {
		tmp = t_1 - ((j * 27.0) * k);
	} else {
		tmp = fma(x, fma(18.0, (t * (y * z)), (i * -4.0)), fma(t, (a * -4.0), fma(b, c, (k * (j * -27.0)))));
	}
	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(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= 5e+294)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(x, fma(18.0, Float64(t * Float64(y * z)), Float64(i * -4.0)), fma(t, Float64(a * -4.0), fma(b, c, Float64(k * Float64(j * -27.0)))));
	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]

↓

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[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+294], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision] + N[(b * c + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	85.1%
Target	88.7%
Herbie	91.0%

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

Derivation

1. Split input into 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)) < 4.9999999999999999e294

   1. Initial program 97.1%

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

   if 4.9999999999999999e294 < (-.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 58.2%

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

   2. Simplified 85.6%

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

      [Start] 58.2%	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 58.2%	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      +-commutative [=>] 58.2%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 58.2%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+l+ [=>] 58.2%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+r+ [=>] 58.2%	\[ \color{blue}{\left(\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      associate--l+ [=>] 58.2%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [<=] 58.2%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]
      sub-neg [<=] 58.2%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(x \cdot 4\right) \cdot i\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.0%
Cost	28612

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	91.1%
Cost	28612

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	89.4%
Cost	9796

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

Alternative 4
Accuracy	91.6%
Cost	4036

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

Alternative 5
Accuracy	82.2%
Cost	2636

\[\begin{array}{l} t_1 := b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 6
Accuracy	81.8%
Cost	2636

\[\begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - t_1\right) - t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+232}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 7
Accuracy	86.0%
Cost	1988

\[\begin{array}{l} \mathbf{if}\;z \leq 5.7 \cdot 10^{+209}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	32.7%
Cost	1764

\[\begin{array}{l} t_1 := \left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 9
Accuracy	32.8%
Cost	1764

\[\begin{array}{l} t_1 := \left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-306}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+76}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(y \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 10
Accuracy	32.6%
Cost	1764

\[\begin{array}{l} t_1 := \left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -1.1 \cdot 10^{+51}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-306}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot 18\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 11
Accuracy	82.2%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+123} \lor \neg \left(a \leq 1.65 \cdot 10^{-36}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	84.5%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-91} \lor \neg \left(t \leq 2.65 \cdot 10^{-70}\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	75.1%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-81} \lor \neg \left(z \leq 8 \cdot 10^{+209}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 14
Accuracy	32.7%
Cost	1368

\[\begin{array}{l} t_1 := 18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;j \leq -5.5 \cdot 10^{+54}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.35 \cdot 10^{-307}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 15
Accuracy	50.0%
Cost	1364

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-158}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-46}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(y \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 16
Accuracy	57.6%
Cost	1360

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-211}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	58.1%
Cost	1360

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	76.9%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -350000000 \lor \neg \left(x \leq 1.8 \cdot 10^{+40}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 19
Accuracy	73.1%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 20
Accuracy	31.9%
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -5.8 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Accuracy	31.8%
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;j \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 22
Accuracy	42.8%
Cost	1104

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(y \cdot \left(18 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-191}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 23
Accuracy	50.1%
Cost	972

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-155}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Accuracy	31.9%
Cost	848

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+37}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Accuracy	33.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{+55} \lor \neg \left(j \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 26
Accuracy	23.6%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023271 
(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)))