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

Percentage Accurate: 85.9% → 91.6%

Time: 31.8s

Precision: binary64

Cost: 4036

• 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.

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

Math

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

↓

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

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

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 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) + (-4.0 * a));
	}
	return tmp;
}

Java

public static 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);
}

↓

public static 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 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) + (-4.0 * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

↓

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * ((18.0 * (y * (x * z))) + (-4.0 * a))
	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(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)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(-4.0 * a)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

↓

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((18.0 * (y * (x * z))) + (-4.0 * a));
	end
	tmp_2 = 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[(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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	85.9%
Target	89.7%
Herbie	91.6%

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

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 94.9%

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

   if +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 44.0%

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

      [Start] 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%	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      +-commutative [=>] 0.0%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 0.0%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+l+ [=>] 0.0%	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+r+ [=>] 0.0%	\[ \color{blue}{\left(\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      associate--l+ [=>] 0.0%	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [<=] 0.0%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]
      sub-neg [<=] 0.0%	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(x \cdot 4\right) \cdot i\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]

   3. Taylor expanded in b around 0 52.0%

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

   4. Taylor expanded in k around 0 56.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + -4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.9%

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

Alternatives

Alternative 1
Accuracy	91.6%
Cost	4036

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

Alternative 2
Accuracy	90.8%
Cost	26944

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

Alternative 3
Accuracy	87.0%
Cost	1988

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+185}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	79.9%
Cost	1865

\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-77} \lor \neg \left(x \leq 10^{-111}\right):\\ \;\;\;\;\left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 5
Accuracy	79.0%
Cost	1864

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;\left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-133}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \end{array} \]

Alternative 6
Accuracy	73.6%
Cost	1744

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := t_2 + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-48}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+264}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+297}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	44.2%
Cost	1633

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right) + b \cdot c\\ t_2 := t \cdot \left(-4 \cdot a\right)\\ t_3 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+217}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+195} \lor \neg \left(t \leq 1.1 \cdot 10^{+247}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	73.6%
Cost	1612

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := -4 \cdot \left(t \cdot a\right) + x \cdot \left(t_1 + i \cdot -4\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-48}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+263}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+297}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t_1 - i \cdot 4\right)\\ \end{array} \]

Alternative 9
Accuracy	58.3%
Cost	1492

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-81}:\\ \;\;\;\;t_2 + b \cdot c\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{-19}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Accuracy	71.4%
Cost	1489

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+264} \lor \neg \left(x \leq 7.2 \cdot 10^{+297}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \end{array} \]

Alternative 11
Accuracy	71.5%
Cost	1361

\[\begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-47}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 9000000000000 \lor \neg \left(x \leq 1.05 \cdot 10^{+87}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 12
Accuracy	32.2%
Cost	1236

\[\begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -3.3 \cdot 10^{-223}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3600000000000:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	32.7%
Cost	1236

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.22 \cdot 10^{-223}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 16500000000000:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	32.4%
Cost	1236

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -6.8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -4 \cdot 10^{-223}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 2020000000000:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(\left(t \cdot z\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	51.2%
Cost	1104

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right) + b \cdot c\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-269}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Accuracy	49.9%
Cost	1104

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right) + b \cdot c\\ \mathbf{if}\;j \leq -5.6 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-154}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	51.4%
Cost	1100

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right) + t_1\\ \mathbf{if}\;j \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-154}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	31.7%
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -4 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-223}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;k \leq 5.4 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Accuracy	34.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;k \leq -2.4 \cdot 10^{+16} \lor \neg \left(k \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20
Accuracy	24.0%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023263 
(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)))