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

Average Accuracy: 91.0% → 98.6%

Time: 30.3s

Precision: binary64

Cost: 5321

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 4 \cdot 10^{+295}\right):\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]

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))
          (* i (* x -4.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+295)))
     (+
      (* b c)
      (+
       (* x (+ (* 18.0 (* y (* z t))) (* i -4.0)))
       (+ (* -4.0 (* t a)) (* -27.0 (* k j)))))
     (+ t_1 (* k (* -27.0 j))))))

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)) + (i * (x * -4.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+295)) {
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-4.0 * (t * a)) + (-27.0 * (k * j))));
	} else {
		tmp = t_1 + (k * (-27.0 * j));
	}
	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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+295)) {
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-4.0 * (t * a)) + (-27.0 * (k * j))));
	} else {
		tmp = t_1 + (k * (-27.0 * j));
	}
	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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+295):
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-4.0 * (t * a)) + (-27.0 * (k * j))))
	else:
		tmp = t_1 + (k * (-27.0 * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) + Float64(t * Float64(a * -4.0))) + Float64(b * c)) + Float64(i * Float64(x * -4.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+295))
		tmp = Float64(Float64(b * c) + Float64(Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0))) + Float64(Float64(-4.0 * Float64(t * a)) + Float64(-27.0 * Float64(k * j)))));
	else
		tmp = Float64(t_1 + Float64(k * Float64(-27.0 * j)));
	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 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+295)))
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-4.0 * (t * a)) + (-27.0 * (k * j))));
	else
		tmp = t_1 + (k * (-27.0 * j));
	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[(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[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+295]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	91.0%
Target	97.6%
Herbie	98.6%

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < -inf.0 or 3.9999999999999999e295 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))

   1. Initial program 14.3%

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

   2. Simplified 45.1%

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

      [Start] 14.3	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 14.3	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate--l+ [=>] 14.3	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]
      distribute-rgt-out-- [=>] 14.3	\[ \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      fma-def [=>] 14.3	\[ \color{blue}{\mathsf{fma}\left(t, \left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]
      associate-*l* [=>] 14.4	\[ \mathsf{fma}\left(t, \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z - a \cdot 4, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      associate-*l* [=>] 45.1	\[ \mathsf{fma}\left(t, \color{blue}{x \cdot \left(\left(18 \cdot y\right) \cdot z\right)} - a \cdot 4, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      fma-neg [=>] 45.1	\[ \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(x, \left(18 \cdot y\right) \cdot z, -a \cdot 4\right)}, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      *-commutative [=>] 45.1	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, \color{blue}{z \cdot \left(18 \cdot y\right)}, -a \cdot 4\right), b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      distribute-rgt-neg-in [=>] 45.1	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), \color{blue}{a \cdot \left(-4\right)}\right), b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      metadata-eval [=>] 45.1	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot \color{blue}{-4}\right), b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]
      fma-neg [=>] 45.1	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot -4\right), \color{blue}{\mathsf{fma}\left(b, c, -\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)}\right) \]
      distribute-neg-in [=>] 45.1	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot -4\right), \mathsf{fma}\left(b, c, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)}\right)\right) \]
      associate-*l* [=>] 45.3	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot -4\right), \mathsf{fma}\left(b, c, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(-\left(j \cdot 27\right) \cdot k\right)\right)\right) \]
      distribute-rgt-neg-in [=>] 45.3	\[ \mathsf{fma}\left(t, \mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot -4\right), \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(-\left(j \cdot 27\right) \cdot k\right)\right)\right) \]

   3. Taylor expanded in x around 0 91.2%

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

   if -inf.0 < (-.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)) < 3.9999999999999999e295

   1. Initial program 99.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 4 \cdot 10^{+295}\right):\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	59.1%
Cost	2280

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ t_3 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_4 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_5 := -27 \cdot \left(k \cdot j\right)\\ t_6 := b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + t_5\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+64}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-88}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-155}:\\ \;\;\;\;t_5 + t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-287}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-188}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-174}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 2
Accuracy	48.7%
Cost	2157

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t_1\\ t_4 := -27 \cdot \left(k \cdot j\right)\\ t_5 := b \cdot c + t_2\\ t_6 := t_4 + t_1\\ t_7 := t_2 + t_4\\ \mathbf{if}\;i \leq -4 \cdot 10^{+218}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{+37}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.62 \cdot 10^{-301}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-281}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-150}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-118}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+83} \lor \neg \left(i \leq 8.4 \cdot 10^{+105}\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Accuracy	52.6%
Cost	2152

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + t_1\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ t_4 := -27 \cdot \left(k \cdot j\right)\\ t_5 := t_1 + t_4\\ t_6 := b \cdot c + t_4\\ t_7 := t_4 + t_3\\ \mathbf{if}\;x \leq -1.38 \cdot 10^{-31}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-240}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-141}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-112}:\\ \;\;\;\;b \cdot c + t_3\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-51}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 27000000000000:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+109}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 4
Accuracy	84.6%
Cost	2128

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := x \cdot \left(i \cdot -4\right) + j \cdot \left(-27 \cdot k\right)\\ t_3 := b \cdot c + \left(\left(-4 \cdot \left(t \cdot a\right) + t_1\right) + \frac{x}{\frac{-0.25}{i}}\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 10^{-188}:\\ \;\;\;\;b \cdot c + \left(t_1 + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+178}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_2\\ \end{array} \]

Alternative 5
Accuracy	92.9%
Cost	2121

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-75} \lor \neg \left(x \leq 9.5 \cdot 10^{-191}\right):\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-4 \cdot \left(t \cdot a\right) + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_1 + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	97.2%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-60} \lor \neg \left(t \leq 50\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(-27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	29.4%
Cost	1772

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-182}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-24}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	84.8%
Cost	1736

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c + \left(\left(-4 \cdot \left(t \cdot a\right) + t_1\right) + \frac{x}{\frac{-0.25}{i}}\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-192}:\\ \;\;\;\;b \cdot c + \left(t_1 + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(-27 \cdot k\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	69.5%
Cost	1621

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+21}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-73} \lor \neg \left(t \leq 6.2 \cdot 10^{+63}\right):\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(-27 \cdot k\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	51.7%
Cost	1500

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ t_3 := t_1 + t_2\\ t_4 := b \cdot c + t_2\\ t_5 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+149}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -8400000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-162}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Accuracy	80.3%
Cost	1476

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;b \cdot c + \left(t_1 + y \cdot \left(18 \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(-4 \cdot \left(t \cdot a\right) + t_1\right) + \frac{x}{\frac{-0.25}{i}}\right)\\ \end{array} \]

Alternative 12
Accuracy	51.7%
Cost	1368

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + -27 \cdot \left(k \cdot j\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Accuracy	44.8%
Cost	1105

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;c \leq -2.05 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+149} \lor \neg \left(c \leq 5 \cdot 10^{+161}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 14
Accuracy	31.0%
Cost	848

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;k \leq -7.4 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.95 \cdot 10^{-280}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{-150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	31.0%
Cost	848

\[\begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{-131}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \leq -8.2 \cdot 10^{-280}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 16
Accuracy	52.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;k \leq -2.65 \cdot 10^{-114} \lor \neg \left(k \leq 5.5 \cdot 10^{-70}\right):\\ \;\;\;\;b \cdot c + -27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 17
Accuracy	31.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;k \leq -4.2 \cdot 10^{-131} \lor \neg \left(k \leq 10^{+70}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18
Accuracy	23.9%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023129 
(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)))