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

Percentage Accurate: 85.3% → 92.5%

Time: 25.3s

Precision: binary64

Cost: 15812

• 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.

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

Math

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

↓

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

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))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY)
     t_1
     (fma j (* k -27.0) (* x (fma -4.0 i (* (* y z) (* 18.0 t))))))))

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)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(j, (k * -27.0), (x * fma(-4.0, i, ((y * z) * (18.0 * t)))));
	}
	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(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(j, Float64(k * -27.0), Float64(x * fma(-4.0, i, Float64(Float64(y * z) * Float64(18.0 * t)))));
	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[(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] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(-4.0 * i + N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	85.3%
Target	89.5%
Herbie	92.5%

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

Derivation

1. Split input into 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

   1. Initial program 97.4%

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

   if +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))

   1. Initial program 0.0%

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

   2. Simplified 69.2%

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

      [Start] 0.0%	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 0.0%	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [=>] 0.0%	\[ \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]
      associate-*l* [=>] 0.0%	\[ \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      distribute-rgt-neg-in [=>] 0.0%	\[ \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      fma-def [=>] 15.4%	\[ \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]
      *-commutative [=>] 15.4%	\[ \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      distribute-rgt-neg-in [=>] 15.4%	\[ \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      metadata-eval [=>] 15.4%	\[ \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]
      sub-neg [=>] 15.4%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]
      +-commutative [=>] 15.4%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]
      associate-*l* [=>] 15.4%	\[ \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]
      distribute-rgt-neg-in [=>] 15.4%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Taylor expanded in x around inf 76.9%

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

   4. Simplified 76.9%

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

      [Start] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + -4 \cdot i\right) \cdot x\right) \]
      *-commutative [=>] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + -4 \cdot i\right)}\right) \]
      +-commutative [=>] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]
      fma-def [=>] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, x \cdot \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]
      *-commutative [=>] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot 18}\right)\right) \]
      *-commutative [=>] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, x \cdot \mathsf{fma}\left(-4, i, \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot 18\right)\right) \]
      associate-*l* [<=] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right)\right) \]
      associate-*l* [=>] 76.9%	\[ \mathsf{fma}\left(j, k \cdot -27, x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot 18\right)}\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 95.3%

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

Alternatives

Alternative 1
Accuracy	92.5%
Cost	15812

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

Alternative 2
Accuracy	91.7%
Cost	4036

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

Alternative 3
Accuracy	87.9%
Cost	1988

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+237}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	70.1%
Cost	1884

\[\begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(\left(-a \cdot 4\right) - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-57}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - t_1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	57.3%
Cost	1756

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_3 := b \cdot c + t_1\\ t_4 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+103}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-259}:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Accuracy	57.3%
Cost	1756

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_3 := b \cdot c + t_1\\ t_4 := x \cdot \left(y \cdot \left(18 \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+102}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-250}:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Accuracy	82.3%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-11} \lor \neg \left(a \leq 9.2 \cdot 10^{+73}\right):\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(-27 \cdot \left(j \cdot k\right) + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	84.3%
Cost	1737

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{-57} \lor \neg \left(t \leq 2.15 \cdot 10^{-44}\right):\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 + -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - t_1\\ \end{array} \]

Alternative 9
Accuracy	80.9%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+108} \lor \neg \left(t \leq 3.5 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4 + -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 10
Accuracy	69.3%
Cost	1488

\[\begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(y \cdot \left(18 \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-167}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(\left(-a \cdot 4\right) - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+105}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	47.8%
Cost	1370

\[\begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(-x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-168} \lor \neg \left(x \leq -4.4 \cdot 10^{-203}\right) \land \left(x \leq 1.7 \cdot 10^{-200} \lor \neg \left(x \leq 7 \cdot 10^{-168}\right) \land x \leq 7.5 \cdot 10^{-72}\right):\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]

Alternative 12
Accuracy	48.0%
Cost	1369

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + t_1\\ \mathbf{if}\;x \leq -1.86 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(-x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-250}:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-200} \lor \neg \left(x \leq 2.5 \cdot 10^{-169}\right) \land x \leq 4.1 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]

Alternative 13
Accuracy	76.6%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-18} \lor \neg \left(t \leq 3.7 \cdot 10^{-44}\right):\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4 + -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	59.1%
Cost	1292

\[\begin{array}{l} t_1 := t \cdot \left(\left(-a \cdot 4\right) - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-102}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	51.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-10} \lor \neg \left(a \leq 3.3 \cdot 10^{+104}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 16
Accuracy	29.4%
Cost	649

\[\begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+132} \lor \neg \left(a \leq 4.2 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \left(-a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 17
Accuracy	31.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;i \leq -45000 \lor \neg \left(i \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 18
Accuracy	38.4%
Cost	576

\[-4 \cdot \left(x \cdot i + t \cdot a\right) \]

Alternative 19
Accuracy	23.6%
Cost	320

\[-27 \cdot \left(j \cdot k\right) \]

Reproduce

herbie shell --seed 2023243 
(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)))