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

Percentage Accurate: 85.5% → 91.1%

Time: 34.7s

Precision: binary64

Cost: 28996

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

• 50.2% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

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))
          (* (* j 27.0) k))))
   (if (<= t_1 2e+267)
     t_1
     (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)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= 2e+267) {
		tmp = t_1;
	} 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(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 <= 2e+267)
		tmp = t_1;
	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[(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, 2e+267], t$95$1, 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	85.5%
Target	89.4%
Herbie	91.1%

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

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)) < 1.9999999999999999e267

   1. Initial program 97.9%

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

   if 1.9999999999999999e267 < (-.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 60.6%

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

   2. Simplified 87.5%

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

      [Start] 60.6%	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 60.6%	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      +-commutative [=>] 60.6%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 60.6%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+l+ [=>] 60.6%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+r+ [=>] 60.6%	\[ \color{blue}{\left(\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      associate--l+ [=>] 60.6%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [<=] 60.6%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]
      sub-neg [<=] 60.6%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(x \cdot 4\right) \cdot i\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+267}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.1%
Cost	28996

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	89.0%
Cost	3652

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+267}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	70.5%
Cost	2512

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + \left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	82.8%
Cost	2249

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-76} \lor \neg \left(t_1 \leq 5 \cdot 10^{+23}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	88.7%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-112} \lor \neg \left(t \leq 2.5 \cdot 10^{-113}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 6
Accuracy	59.8%
Cost	1756

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := -4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ t_3 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	70.3%
Cost	1625

\[\begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 0.019:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+49} \lor \neg \left(t \leq 4.2 \cdot 10^{+261}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Accuracy	71.6%
Cost	1625

\[\begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c + t \cdot \left(t_2 - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+45} \lor \neg \left(t \leq 3.55 \cdot 10^{+261}\right):\\ \;\;\;\;t \cdot \left(t_2 + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Accuracy	74.2%
Cost	1618

\[\begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-23} \lor \neg \left(x \leq 5.9 \cdot 10^{-148} \lor \neg \left(x \leq 2.85 \cdot 10^{-46}\right) \land x \leq 7.1 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 10
Accuracy	56.3%
Cost	1493

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(i \cdot -4 + \left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;x \leq -350000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-147}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-46} \lor \neg \left(x \leq 6 \cdot 10^{+52}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	60.1%
Cost	1492

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := -4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ t_3 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -4.35 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Accuracy	80.3%
Cost	1480

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c + t \cdot \left(t_1 - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+261}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t_1 + a \cdot -4\right)\\ \end{array} \]

Alternative 13
Accuracy	58.8%
Cost	1360

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-288}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 0.0013:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	45.3%
Cost	1236

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-156}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-258}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{+158}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	46.4%
Cost	1232

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-289}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 16
Accuracy	40.5%
Cost	1104

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;j \leq -3.9 \cdot 10^{+261}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 17
Accuracy	31.2%
Cost	980

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-234}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	29.3%
Cost	848

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -4.75 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-289}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-209}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Accuracy	44.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-9} \lor \neg \left(z \leq 6.5 \cdot 10^{+84}\right):\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 20
Accuracy	44.4%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-9}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 21
Accuracy	33.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;c \leq -1.08 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+161}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Accuracy	24.2%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023272 
(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)))