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

Average Error: 5.8 → 0.9

Time: 38.5s

Precision: binary64

Cost: 5321

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+306}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

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
 (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 1e+306)))
     (+
      (+ (* 18.0 (* y (* z (* x t)))) (* b c))
      (+ (* x (* i -4.0)) (* j (* k -27.0))))
     (+ t_1 (* 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)) + (i * (x * -4.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+306)) {
		tmp = ((18.0 * (y * (z * (x * t)))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	} else {
		tmp = t_1 + (k * (j * -27.0));
	}
	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 <= 1e+306)) {
		tmp = ((18.0 * (y * (z * (x * t)))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	} else {
		tmp = t_1 + (k * (j * -27.0));
	}
	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 <= 1e+306):
		tmp = ((18.0 * (y * (z * (x * t)))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)))
	else:
		tmp = t_1 + (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(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 <= 1e+306))
		tmp = Float64(Float64(Float64(18.0 * Float64(y * Float64(z * Float64(x * t)))) + Float64(b * c)) + Float64(Float64(x * Float64(i * -4.0)) + Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(t_1 + Float64(k * Float64(j * -27.0)));
	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 <= 1e+306)))
		tmp = ((18.0 * (y * (z * (x * t)))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	else
		tmp = t_1 + (k * (j * -27.0));
	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, 1e+306]], $MachinePrecision]], N[(N[(N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	5.8
Target	1.6
Herbie	0.9

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

Derivation

1. Split input into 2 regimes

2. if (-.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 1.00000000000000002e306 < (-.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 61.9

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

   2. Simplified 41.6

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

      [Start] 61.9	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 61.9	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 61.9	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 61.9	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 61.9	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 41.6	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 41.6	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 41.6	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 15.6

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

   4. Simplified 7.1

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

      [Start] 15.6	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 15.6	\[ \left(18 \cdot \left(y \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*l* [=>] 7.1	\[ \left(18 \cdot \left(y \cdot \color{blue}{\left(z \cdot \left(x \cdot t\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   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)) < 1.00000000000000002e306

   1. Initial program 0.3

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 10^{+306}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	6.1
Cost	2386

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;z \leq -45000000000 \lor \neg \left(z \leq 3 \cdot 10^{+123} \lor \neg \left(z \leq 1.35 \cdot 10^{+217}\right) \land z \leq 1.7 \cdot 10^{+263}\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + t_1\\ \end{array} \]

Alternative 2
Error	4.5
Cost	2249

\[\begin{array}{l} \mathbf{if}\;z \leq -100000000 \lor \neg \left(z \leq 9.8 \cdot 10^{+64}\right):\\ \;\;\;\;\left(\left(\left(18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right) + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 3
Error	33.9
Cost	2153

\[\begin{array}{l} t_1 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) + i \cdot -4\right)\\ t_3 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_4 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;t_4 + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-280}:\\ \;\;\;\;t_4 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-20} \lor \neg \left(x \leq 9.5 \cdot 10^{+57}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	33.5
Cost	2153

\[\begin{array}{l} t_1 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;t_3 + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-280}:\\ \;\;\;\;t_3 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-22} \lor \neg \left(x \leq 1.55 \cdot 10^{+59}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 5
Error	11.6
Cost	2130

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+51} \lor \neg \left(x \leq -4.2 \cdot 10^{-28}\right) \land \left(x \leq -6.4 \cdot 10^{-106} \lor \neg \left(x \leq 6.2 \cdot 10^{-147}\right)\right):\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right) + b \cdot c\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \end{array} \]

Alternative 6
Error	35.4
Cost	2028

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2900:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	33.2
Cost	1760

\[\begin{array}{l} t_1 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := t_2 + i \cdot \left(x \cdot -4\right)\\ t_4 := t_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+27}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1850:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	8.6
Cost	1737

\[\begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+15} \lor \neg \left(t \leq 6.9 \cdot 10^{+112}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 9
Error	8.5
Cost	1736

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t \leq -50000000000000:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+112}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + t_1\\ \end{array} \]

Alternative 10
Error	44.5
Cost	1640

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -4.35 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-217}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-164}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 11
Error	44.9
Cost	1640

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;c \leq -3.35 \cdot 10^{-65}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.05 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-141}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 12
Error	44.9
Cost	1640

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;c \leq -1.16 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-217}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 13
Error	34.5
Cost	1626

\[\begin{array}{l} t_1 := x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-279}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-151} \lor \neg \left(x \leq 3.2 \cdot 10^{-87}\right) \land \left(x \leq 10^{-19} \lor \neg \left(x \leq 9 \cdot 10^{+58}\right)\right):\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	18.4
Cost	1488

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)\\ t_3 := t_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 15
Error	18.5
Cost	1488

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-70}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+118}:\\ \;\;\;\;t_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 16
Error	10.3
Cost	1476

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;y \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(t_1 + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17
Error	35.6
Cost	1368

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2900:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+37}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	22.2
Cost	1357

\[\begin{array}{l} \mathbf{if}\;x \leq -5.4:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-19} \lor \neg \left(x \leq 6 \cdot 10^{+57}\right):\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 19
Error	45.3
Cost	848

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;c \leq -7.2 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20
Error	45.3
Cost	848

\[\begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-287}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 1.44 \cdot 10^{-207}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21
Error	45.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+78}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Error	48.7
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023054 
(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)))