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

Average Error: 5.5 → 0.9

Time: 48.5s

Precision: binary64

Cost: 6088

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

Math

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

↓

\[\begin{array}{l} t_1 := b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ t_2 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+288}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
         (+
          (* b c)
          (+
           (* x (+ (* 18.0 (* y (* z t))) (* i -4.0)))
           (+ (* -27.0 (* j k)) (* -4.0 (* t a))))))
        (t_2
         (+
          (+
           (+ (+ (* (* (* (* x 18.0) y) z) t) (* t (* a -4.0))) (* b c))
           (* i (* x -4.0)))
          (* k (* j -27.0)))))
   (if (<= t_2 -5e+307) t_1 (if (<= t_2 1e+288) t_2 t_1))))

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 = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-27.0 * (j * k)) + (-4.0 * (t * a))));
	double t_2 = (((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))) + (k * (j * -27.0));
	double tmp;
	if (t_2 <= -5e+307) {
		tmp = t_1;
	} else if (t_2 <= 1e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((x * ((18.0d0 * (y * (z * t))) + (i * (-4.0d0)))) + (((-27.0d0) * (j * k)) + ((-4.0d0) * (t * a))))
    t_2 = (((((((x * 18.0d0) * y) * z) * t) + (t * (a * (-4.0d0)))) + (b * c)) + (i * (x * (-4.0d0)))) + (k * (j * (-27.0d0)))
    if (t_2 <= (-5d+307)) then
        tmp = t_1
    else if (t_2 <= 1d+288) then
        tmp = t_2
    else
        tmp = t_1
    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 = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-27.0 * (j * k)) + (-4.0 * (t * a))));
	double t_2 = (((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))) + (k * (j * -27.0));
	double tmp;
	if (t_2 <= -5e+307) {
		tmp = t_1;
	} else if (t_2 <= 1e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-27.0 * (j * k)) + (-4.0 * (t * a))))
	t_2 = (((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))) + (k * (j * -27.0))
	tmp = 0
	if t_2 <= -5e+307:
		tmp = t_1
	elif t_2 <= 1e+288:
		tmp = t_2
	else:
		tmp = t_1
	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(b * c) + Float64(Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(-4.0 * Float64(t * a)))))
	t_2 = Float64(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))) + Float64(k * Float64(j * -27.0)))
	tmp = 0.0
	if (t_2 <= -5e+307)
		tmp = t_1;
	elseif (t_2 <= 1e+288)
		tmp = t_2;
	else
		tmp = t_1;
	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 = (b * c) + ((x * ((18.0 * (y * (z * t))) + (i * -4.0))) + ((-27.0 * (j * k)) + (-4.0 * (t * a))));
	t_2 = (((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0))) + (k * (j * -27.0));
	tmp = 0.0;
	if (t_2 <= -5e+307)
		tmp = t_1;
	elseif (t_2 <= 1e+288)
		tmp = t_2;
	else
		tmp = t_1;
	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[(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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+307], t$95$1, If[LessEqual[t$95$2, 1e+288], t$95$2, t$95$1]]]]

Target

Original	5.5
Target	1.7
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 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < -5e307 or 1e288 < (-.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 44.7

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

   2. Simplified 30.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(t, \mathsf{fma}\left(x, y \cdot \left(18 \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)\right)} \]
      Proof
      (fma.f64 j (*.f64 k -27) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (*.f64 k (Rewrite<= metadata-eval (neg.f64 27))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 k 27))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 27 k))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y 18) z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 8 points increase in error, 1 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 18 y)) z) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (*.f64 18 y) z) (*.f64 a (Rewrite<= metadata-eval (neg.f64 4)))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (*.f64 18 y) z) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4)))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (*.f64 (*.f64 18 y) z)) (*.f64 a 4))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (*.f64 18 y)) z)) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 6 points increase in error, 16 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 18) y)) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 5 points increase in error, 3 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x (Rewrite<= metadata-eval (neg.f64 4))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x 4))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (*.f64 x 4)) i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (Rewrite=> distribute-lft-neg-out_binary64 (neg.f64 (*.f64 (*.f64 x 4) i)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i))))): 2 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4))) (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (+.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i)))): 1 points increase in error, 1 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (Rewrite<= associate--l+_binary64 (-.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)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j (neg.f64 (*.f64 27 k))) (-.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 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 j (*.f64 27 k)))) (-.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))): 0 points increase in error, 0 points decrease in error
      (+.f64 (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 j 27) k))) (-.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))): 7 points increase in error, 11 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 (*.f64 j 27)) k)) (-.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))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.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 (neg.f64 (*.f64 j 27)) k))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.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))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in x around 0 6.0

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

   if -5e307 < (-.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)) < 1e288

   1. Initial program 0.2

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right) \leq -5 \cdot 10^{+307}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right) \leq 10^{+288}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	34.8
Cost	2416

\[\begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_2 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_4 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_5 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+261}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+210}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.089379414470121 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.2475071275885702 \cdot 10^{-12}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5.837230394585687 \cdot 10^{-39}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -3.9358362708218385 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5.689457138403514 \cdot 10^{-164}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2.338065975660128 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -6.15285377002527 \cdot 10^{-243}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 1.5186122346564503 \cdot 10^{-202}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 5.070926388794882 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	22.7
Cost	2408

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := b \cdot c + \left(t_1 + t_2\right)\\ t_4 := -27 \cdot \left(j \cdot k\right)\\ t_5 := b \cdot c + \left(t_4 + t_1\right)\\ t_6 := \left(b \cdot c + t_4\right) + 18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ t_7 := b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -1.3300945887105373 \cdot 10^{+50}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq -1.2479039387333071 \cdot 10^{+35}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -1.3346172155382868 \cdot 10^{-139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.3274400452495188 \cdot 10^{-203}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7.280519497060109 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.0253493235353304 \cdot 10^{-260}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.7151422118308668 \cdot 10^{-250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.5618883450361816 \cdot 10^{-94}:\\ \;\;\;\;b \cdot c + \left(t_4 + t_2\right)\\ \mathbf{elif}\;y \leq 7.557885996997852 \cdot 10^{-32}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 3
Error	22.7
Cost	2408

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ t_4 := b \cdot c + \left(t_3 + t_1\right)\\ t_5 := -27 \cdot \left(j \cdot k\right)\\ t_6 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + \left(b \cdot c + t_5\right)\\ t_7 := b \cdot c + \left(t_5 + t_3\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -1.3300945887105373 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -318694010182942850:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -1.3346172155382868 \cdot 10^{-139}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.3274400452495188 \cdot 10^{-203}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq -7.280519497060109 \cdot 10^{-296}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.0253493235353304 \cdot 10^{-260}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 1.7151422118308668 \cdot 10^{-250}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.5618883450361816 \cdot 10^{-94}:\\ \;\;\;\;b \cdot c + \left(t_5 + t_1\right)\\ \mathbf{elif}\;y \leq 7.557885996997852 \cdot 10^{-32}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	42.2
Cost	2292

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -1.1746694792575402 \cdot 10^{-92}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.2525494290774822 \cdot 10^{-185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.561830548323779 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.600439207818842 \cdot 10^{-250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.9100602165879 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.71913559163847 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7680225290615362 \cdot 10^{-140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7965577364570656 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+248}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	11.3
Cost	2264

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c + \left(\left(t_2 + t_1\right) + -4 \cdot \left(x \cdot i\right)\right)\\ t_4 := b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + t_1\right)\\ t_5 := \left(b \cdot c + t_2\right) + t \cdot \left(a \cdot -4 + x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{if}\;k \leq -4.440992676133738 \cdot 10^{-60}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.8051363152623117 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 6.941202772505252 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.972555320320189 \cdot 10^{-18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+135}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	11.1
Cost	2264

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c + \left(\left(t_2 + t_1\right) + -4 \cdot \left(x \cdot i\right)\right)\\ t_4 := b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + t_1\right)\\ t_5 := b \cdot c + t_2\\ \mathbf{if}\;k \leq -4.440992676133738 \cdot 10^{-60}:\\ \;\;\;\;t_5 + t \cdot \left(a \cdot -4 + x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.8051363152623117 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 6.941202772505252 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.972555320320189 \cdot 10^{-18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+135}:\\ \;\;\;\;t_5 + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	4.3
Cost	2120

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+110}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + t_1\\ \mathbf{elif}\;t \leq 10^{+130}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(t_2 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t_2\right) + t_1\\ \end{array} \]

Alternative 8
Error	3.6
Cost	2120

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -2.0971039707181842 \cdot 10^{-109}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 10^{+130}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t_1\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 9
Error	10.5
Cost	2000

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + t_1\right)\\ t_3 := b \cdot c + \left(\left(-27 \cdot \left(j \cdot k\right) + t_1\right) + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{if}\;k \leq -9.408728255807257 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.8051363152623117 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 6.941202772505252 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.972555320320189 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	10.6
Cost	1868

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+156}:\\ \;\;\;\;b \cdot c + \left(18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + \left(t_3 + t_1\right)\right)\\ \mathbf{elif}\;y \leq -4.424244069670175 \cdot 10^{+20}:\\ \;\;\;\;\left(b \cdot c + t_3\right) + \left(t_2 + t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.557885996997852 \cdot 10^{-32}:\\ \;\;\;\;b \cdot c + \left(\left(t_3 + t_2\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t_1\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 11
Error	24.0
Cost	1752

\[\begin{array}{l} t_1 := b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + -4 \cdot \left(x \cdot i\right)\right)\\ t_2 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -1.351910994505921 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3.2911751416111834 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9.14610175426866 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+271}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	11.0
Cost	1740

\[\begin{array}{l} t_1 := b \cdot c + \left(\left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(t \cdot a\right)\right) + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{if}\;x \leq -7.128337935195698 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6969636311997928 \cdot 10^{-43}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 13
Error	19.5
Cost	1620

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + \left(t_1 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{if}\;x \leq -7.128337935195698 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6969636311997928 \cdot 10^{-43}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.2959986989544993 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c + \left(-27 \cdot \left(j \cdot k\right) + t_1\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 14
Error	19.4
Cost	1620

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ t_4 := b \cdot c + \left(t_1 + t_2\right)\\ \mathbf{if}\;x \leq -7.128337935195698 \cdot 10^{-30}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.6969636311997928 \cdot 10^{-43}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.3693532390286414 \cdot 10^{-115}:\\ \;\;\;\;b \cdot c + \left(t_3 + t_2\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c + \left(t_3 + t_1\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+139}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 15
Error	44.6
Cost	1508

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;c \leq -3.5566105585802774 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -3.2847652847888362 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.746606404811424 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.8053493483924187 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.2691760968675628 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.025 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.8205865950576546 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.3814162945490598 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+133}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 16
Error	34.8
Cost	1500

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;x \leq -7.128337935195698 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.6969636311997928 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3693532390286414 \cdot 10^{-115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 7.726520200948153 \cdot 10^{-142}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	34.7
Cost	1500

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ \mathbf{if}\;x \leq -7.128337935195698 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6969636311997928 \cdot 10^{-43}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.3693532390286414 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.726520200948153 \cdot 10^{-142}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(y \cdot \left(18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	32.5
Cost	1500

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ \mathbf{if}\;x \leq -7.128337935195698 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6969636311997928 \cdot 10^{-43}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.3693532390286414 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.726520200948153 \cdot 10^{-142}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(y \cdot \left(18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	38.6
Cost	1368

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -3.893756785478794 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.047328718456192 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3159823670303794 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.994512641420562 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.258720450795957 \cdot 10^{-140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	34.9
Cost	1368

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;j \leq -1.35 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -3.9358362708218385 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.103906594656376 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.1692734301052103 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.928653646414216 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 21
Error	43.8
Cost	980

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -3.5566105585802774 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -3.2847652847888362 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.746606404811424 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.025 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.244455374443911 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Error	43.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;c \leq -3.5566105585802774 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 1.1158792220813552 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 23
Error	48.6
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2022300 
(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)))