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

Average Error: 5.2 → 4.4

Time: 41.2s

Precision: binary64

Cost: 2248

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

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-125}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-66}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(\left(b \cdot c + \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right)\\ \end{array} \]

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 (* i -4.0)) (* j (* k -27.0)))))
   (if (<= t -1.85e-125)
     (+ (+ (* b c) (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))) t_1)
     (if (<= t 2.25e-66)
       (+ (+ (* b c) (* 18.0 (* x (* z (* y t))))) t_1)
       (+
        (* k (* j -27.0))
        (+
         (+ (* b c) (+ (* (* z (* x y)) (* 18.0 t)) (* t (* a -4.0))))
         (* i (* x -4.0))))))))

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 * (i * -4.0)) + (j * (k * -27.0));
	double tmp;
	if (t <= -1.85e-125) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) + (a * -4.0)))) + t_1;
	} else if (t <= 2.25e-66) {
		tmp = ((b * c) + (18.0 * (x * (z * (y * t))))) + t_1;
	} else {
		tmp = (k * (j * -27.0)) + (((b * c) + (((z * (x * y)) * (18.0 * t)) + (t * (a * -4.0)))) + (i * (x * -4.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

↓

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (i * (-4.0d0))) + (j * (k * (-27.0d0)))
    if (t <= (-1.85d-125)) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0))))) + t_1
    else if (t <= 2.25d-66) then
        tmp = ((b * c) + (18.0d0 * (x * (z * (y * t))))) + t_1
    else
        tmp = (k * (j * (-27.0d0))) + (((b * c) + (((z * (x * y)) * (18.0d0 * t)) + (t * (a * (-4.0d0))))) + (i * (x * (-4.0d0))))
    end if
    code = tmp
end function

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 * (i * -4.0)) + (j * (k * -27.0));
	double tmp;
	if (t <= -1.85e-125) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) + (a * -4.0)))) + t_1;
	} else if (t <= 2.25e-66) {
		tmp = ((b * c) + (18.0 * (x * (z * (y * t))))) + t_1;
	} else {
		tmp = (k * (j * -27.0)) + (((b * c) + (((z * (x * y)) * (18.0 * t)) + (t * (a * -4.0)))) + (i * (x * -4.0)));
	}
	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 * (i * -4.0)) + (j * (k * -27.0))
	tmp = 0
	if t <= -1.85e-125:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) + (a * -4.0)))) + t_1
	elif t <= 2.25e-66:
		tmp = ((b * c) + (18.0 * (x * (z * (y * t))))) + t_1
	else:
		tmp = (k * (j * -27.0)) + (((b * c) + (((z * (x * y)) * (18.0 * t)) + (t * (a * -4.0)))) + (i * (x * -4.0)))
	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(x * Float64(i * -4.0)) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (t <= -1.85e-125)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)))) + t_1);
	elseif (t <= 2.25e-66)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(x * Float64(z * Float64(y * t))))) + t_1);
	else
		tmp = Float64(Float64(k * Float64(j * -27.0)) + Float64(Float64(Float64(b * c) + Float64(Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t)) + Float64(t * Float64(a * -4.0)))) + Float64(i * Float64(x * -4.0))));
	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 * (i * -4.0)) + (j * (k * -27.0));
	tmp = 0.0;
	if (t <= -1.85e-125)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) + (a * -4.0)))) + t_1;
	elseif (t <= 2.25e-66)
		tmp = ((b * c) + (18.0 * (x * (z * (y * t))))) + t_1;
	else
		tmp = (k * (j * -27.0)) + (((b * c) + (((z * (x * y)) * (18.0 * t)) + (t * (a * -4.0)))) + (i * (x * -4.0)));
	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[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e-125], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 2.25e-66], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	5.2
Target	1.6
Herbie	4.4

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

Derivation

1. Split input into 3 regimes

2. if t < -1.85e-125

   1. Initial program 3.0

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

   2. Simplified 3.7

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

      [Start] 3.0	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 3.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 3.0	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 3.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 3.0	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 3.6	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 3.6	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 3.7	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   if -1.85e-125 < t < 2.2499999999999999e-66

   1. Initial program 8.1

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

   2. Simplified 9.3

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

      [Start] 8.1	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 8.1	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 8.1	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 8.1	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 8.1	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 9.3	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 9.3	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 9.3	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 9.6

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

   4. Simplified 5.8

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

      [Start] 9.6	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 9.5	\[ \left(18 \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot x\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      associate-*r* [=>] 5.8	\[ \left(18 \cdot \color{blue}{\left(\left(\left(y \cdot t\right) \cdot z\right) \cdot x\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      *-commutative [=>] 5.8	\[ \left(18 \cdot \left(\left(\color{blue}{\left(t \cdot y\right)} \cdot z\right) \cdot x\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if 2.2499999999999999e-66 < t

   1. Initial program 2.6

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

   2. Taylor expanded in x around 0 5.0

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

   3. Simplified 2.5

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

      [Start] 5.0	\[ \left(\left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 5.0	\[ \left(\left(\left(18 \cdot \left(y \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*r* [=>] 2.4	\[ \left(\left(\left(18 \cdot \color{blue}{\left(\left(y \cdot \left(z \cdot x\right)\right) \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*l* [<=] 2.4	\[ \left(\left(\left(\color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right)\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 2.4	\[ \left(\left(\left(\color{blue}{\left(\left(y \cdot \left(z \cdot x\right)\right) \cdot 18\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*l* [=>] 2.4	\[ \left(\left(\left(\color{blue}{\left(y \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 2.4	\[ \left(\left(\left(\color{blue}{\left(\left(z \cdot x\right) \cdot y\right)} \cdot \left(18 \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*l* [=>] 2.5	\[ \left(\left(\left(\color{blue}{\left(z \cdot \left(x \cdot y\right)\right)} \cdot \left(18 \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [<=] 2.5	\[ \left(\left(\left(\left(z \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot \left(18 \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Recombined 3 regimes into one program.

4. Final simplification 4.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-125}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-66}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(\left(b \cdot c + \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	3.9
Cost	5320

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_1\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 2
Error	37.2
Cost	2552

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_4 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-169}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+20}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+281}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot y\right)\\ \end{array} \]

Alternative 3
Error	36.3
Cost	2412

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c + t_2\\ t_4 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_5 := t_2 + t_1\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-271}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-168}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+25}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+273}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_1\\ \end{array} \]

Alternative 4
Error	21.2
Cost	2412

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(x \cdot i\right) \cdot -4\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := t_3 + \left(b \cdot c + t_1\right)\\ t_5 := \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) + t_3\\ t_6 := b \cdot c + \left(t_1 + t_2\right)\\ t_7 := t_3 + \left(b \cdot c + t_2\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-113}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-218}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 60000000000:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+196}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+265}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 5
Error	36.2
Cost	2285

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_4 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-168}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+178} \lor \neg \left(z \leq 1.5 \cdot 10^{+269}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	11.4
Cost	2265

\[\begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot i\right) \cdot -4\\ t_2 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{if}\;k \leq -3.6 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.82 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-77}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-15} \lor \neg \left(k \leq 7.8 \cdot 10^{+54}\right) \land k \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	36.6
Cost	2152

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_4 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-169}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+180}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+280}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot y\right)\\ \end{array} \]

Alternative 8
Error	5.0
Cost	2121

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-125} \lor \neg \left(t \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) + t_1\\ \end{array} \]

Alternative 9
Error	44.9
Cost	2028

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;j \leq -7 \cdot 10^{+210}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-112}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-182}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	23.8
Cost	2016

\[\begin{array}{l} t_1 := \left(x \cdot i\right) \cdot -4\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ t_4 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_3\\ t_5 := b \cdot c + \left(t_3 + t_1\right)\\ t_6 := b \cdot c + t_2\\ \mathbf{if}\;k \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 7.4 \cdot 10^{-118}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 7.4 \cdot 10^{-47}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+83}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 6.4 \cdot 10^{+165}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 1.66 \cdot 10^{+192}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \]

Alternative 11
Error	9.0
Cost	1996

\[\begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -0.76:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-164}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ \mathbf{elif}\;t \leq 2050000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right)\\ \end{array} \]

Alternative 12
Error	10.7
Cost	1872

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-67}:\\ \;\;\;\;\left(b \cdot c + t_2\right) + t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+180}:\\ \;\;\;\;t_1 + \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+281}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 13
Error	19.5
Cost	1752

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_1\\ t_3 := k \cdot \left(j \cdot -27\right) + \left(b \cdot c + t_1\right)\\ t_4 := b \cdot c + \left(t_1 + \left(x \cdot i\right) \cdot -4\right)\\ \mathbf{if}\;k \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 45:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 14
Error	19.7
Cost	1752

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(x \cdot i\right) \cdot -4\\ t_3 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_1\\ t_4 := k \cdot \left(j \cdot -27\right)\\ t_5 := b \cdot c + \left(t_1 + t_2\right)\\ \mathbf{if}\;k \leq -4.2 \cdot 10^{-208}:\\ \;\;\;\;t_4 + \left(b \cdot c + t_2\right)\\ \mathbf{elif}\;k \leq 5.1 \cdot 10^{-115}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 7.4 \cdot 10^{-47}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 340:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4 + \left(b \cdot c + t_1\right)\\ \end{array} \]

Alternative 15
Error	10.3
Cost	1608

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-67}:\\ \;\;\;\;\left(b \cdot c + t_1\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+281}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 16
Error	45.1
Cost	1508

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-294}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-176}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2700:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	44.7
Cost	1508

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.82 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-125}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18
Error	44.6
Cost	1508

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-121}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-135}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 19
Error	30.8
Cost	1365

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;a \leq -102000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-111}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-86}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-67} \lor \neg \left(a \leq 9.2 \cdot 10^{-63}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 20
Error	30.6
Cost	1364

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-242}:\\ \;\;\;\;t_1 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	33.8
Cost	1104

\[\begin{array}{l} t_1 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-265}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Error	43.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-135}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 23
Error	48.0
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2022356 
(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)))