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

Average Accuracy: 85.8% → 92.9%

Time: 50.7s

Precision: binary64

Cost: 27209

• 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.

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+19} \lor \neg \left(x \leq 5.4 \cdot 10^{-109}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

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
 (if (or (<= x -4e+19) (not (<= x 5.4e-109)))
   (fma
    x
    (fma 18.0 (* t (* y z)) (* i -4.0))
    (fma t (* -4.0 a) (fma b c (* k (* j -27.0)))))
   (-
    (-
     (+ (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* 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 tmp;
	if ((x <= -4e+19) || !(x <= 5.4e-109)) {
		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 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (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)
	tmp = 0.0
	if ((x <= -4e+19) || !(x <= 5.4e-109))
		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 = Float64(Float64(Float64(Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - 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_] := If[Or[LessEqual[x, -4e+19], N[Not[LessEqual[x, 5.4e-109]], $MachinePrecision]], 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[(N[(N[(N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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]]

Target

Original	85.8%
Target	89.6%
Herbie	92.9%

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

Derivation

1. Split input into 2 regimes

2. if x < -4e19 or 5.4000000000000001e-109 < x

   1. Initial program 79.2%

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

   2. Simplified 92.8%

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

      [Start] 79.2	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 79.2	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      +-commutative [=>] 79.2	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 79.2	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+l+ [=>] 79.2	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+r+ [=>] 79.2	\[ \color{blue}{\left(\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      associate--l+ [=>] 79.2	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [<=] 79.2	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]
      sub-neg [<=] 79.2	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(x \cdot 4\right) \cdot i\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]

   if -4e19 < x < 5.4000000000000001e-109

   1. Initial program 95.2%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+19} \lor \neg \left(x \leq 5.4 \cdot 10^{-109}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, -4 \cdot a, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.6%
Cost	27209

\[\begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+17} \lor \neg \left(t \leq 3 \cdot 10^{-23}\right):\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(t \cdot z, x \cdot \left(18 \cdot y\right), t \cdot \left(a \cdot \left(-4\right)\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 2
Accuracy	91.2%
Cost	4036

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

Alternative 3
Accuracy	32.3%
Cost	2160

\[\begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ t_3 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-241}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-287}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-34}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 5000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Accuracy	32.0%
Cost	2160

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := t \cdot \left(-4 \cdot a\right)\\ t_3 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-287}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-34}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 1060000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+121}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	32.3%
Cost	2160

\[\begin{array}{l} t_1 := t \cdot \left(x \cdot z\right)\\ t_2 := 18 \cdot \left(y \cdot t_1\right)\\ t_3 := t \cdot \left(-4 \cdot a\right)\\ t_4 := -27 \cdot \left(k \cdot j\right)\\ t_5 := y \cdot \left(18 \cdot t_1\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+22}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-58}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-243}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-285}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-34}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 12500000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 6
Accuracy	46.8%
Cost	2028

\[\begin{array}{l} t_1 := t \cdot \left(x \cdot z\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := b \cdot c - t_2\\ t_4 := y \cdot \left(18 \cdot t_1\right)\\ t_5 := -4 \cdot \left(t \cdot a\right) - t_2\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-243}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-189}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1700000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+104}:\\ \;\;\;\;18 \cdot \left(y \cdot t_1\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Accuracy	48.8%
Cost	2028

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) - t_1\\ t_3 := t \cdot \left(x \cdot z\right)\\ t_4 := b \cdot c - t_1\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 420000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+78}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;18 \cdot \left(y \cdot t_3\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+183}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(18 \cdot t_3\right)\\ \end{array} \]

Alternative 8
Accuracy	73.5%
Cost	2008

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := k \cdot \left(j \cdot -27\right) + z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ t_4 := t_1 - t_2\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.66 \cdot 10^{+177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - t_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Accuracy	86.5%
Cost	1988

\[\begin{array}{l} \mathbf{if}\;z \leq 6.6 \cdot 10^{+248}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	49.4%
Cost	1892

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := i \cdot \left(x \cdot -4\right) - t_1\\ t_3 := x \cdot \left(i \cdot -4\right) - 27 \cdot \left(k \cdot j\right)\\ t_4 := b \cdot c - t_1\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+140}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+114}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+151}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+227}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	60.2%
Cost	1888

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -2.05 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t_1\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-20}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_1\\ \end{array} \]

Alternative 12
Accuracy	60.6%
Cost	1884

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t_1\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3.65 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-20}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+168}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_1\\ \end{array} \]

Alternative 13
Accuracy	61.4%
Cost	1884

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -1.85 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.65 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-20}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq 5.1 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{+167}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	64.2%
Cost	1884

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -65000000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 10^{-153}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-20}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{+167}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	50.0%
Cost	1628

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c - t_1\\ t_3 := i \cdot \left(x \cdot -4\right) - t_1\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+140}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+114}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+227}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	47.0%
Cost	1368

\[\begin{array}{l} t_1 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ t_2 := z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+115}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	32.2%
Cost	1112

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -7.8 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -5.8 \cdot 10^{-132}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 18
Accuracy	32.3%
Cost	848

\[\begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 19
Accuracy	33.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;k \leq -8 \cdot 10^{+42} \lor \neg \left(k \leq 4.4 \cdot 10^{+50}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20
Accuracy	33.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;k \leq -4.4 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 21
Accuracy	23.5%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023160 
(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)))