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

Average Error: 5.7 → 2.8

Time: 52.2s

Precision: binary64

Cost: 5320

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

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t_1\right) + b \cdot c\right) + t_2\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{elif}\;t_3 \leq 10^{+215}:\\ \;\;\;\;t_3 + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right) + t_1\right)\right) + t_2\right) + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

↓

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0)))
        (t_2 (* i (* x -4.0)))
        (t_3 (+ (+ (+ (* (* (* (* x 18.0) y) z) t) t_1) (* b c)) t_2)))
   (if (<= t_3 -2e+256)
     (+
      (* b c)
      (+
       (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
       (+ (* -27.0 (* k j)) (* -4.0 (* t a)))))
     (if (<= t_3 1e+215)
       (+ t_3 (* j (* -27.0 k)))
       (+
        (+ (+ (* b c) (+ (* (* 18.0 y) (* t (* x z))) t_1)) t_2)
        (* k (* -27.0 j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = i * (x * -4.0);
	double t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	double tmp;
	if (t_3 <= -2e+256) {
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) - (4.0 * i))) + ((-27.0 * (k * j)) + (-4.0 * (t * a))));
	} else if (t_3 <= 1e+215) {
		tmp = t_3 + (j * (-27.0 * k));
	} else {
		tmp = (((b * c) + (((18.0 * y) * (t * (x * z))) + t_1)) + t_2) + (k * (-27.0 * j));
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = i * (x * (-4.0d0))
    t_3 = ((((((x * 18.0d0) * y) * z) * t) + t_1) + (b * c)) + t_2
    if (t_3 <= (-2d+256)) then
        tmp = (b * c) + ((x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))) + (((-27.0d0) * (k * j)) + ((-4.0d0) * (t * a))))
    else if (t_3 <= 1d+215) then
        tmp = t_3 + (j * ((-27.0d0) * k))
    else
        tmp = (((b * c) + (((18.0d0 * y) * (t * (x * z))) + t_1)) + t_2) + (k * ((-27.0d0) * j))
    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 = t * (a * -4.0);
	double t_2 = i * (x * -4.0);
	double t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	double tmp;
	if (t_3 <= -2e+256) {
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) - (4.0 * i))) + ((-27.0 * (k * j)) + (-4.0 * (t * a))));
	} else if (t_3 <= 1e+215) {
		tmp = t_3 + (j * (-27.0 * k));
	} else {
		tmp = (((b * c) + (((18.0 * y) * (t * (x * z))) + t_1)) + t_2) + (k * (-27.0 * j));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = i * (x * -4.0)
	t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2
	tmp = 0
	if t_3 <= -2e+256:
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) - (4.0 * i))) + ((-27.0 * (k * j)) + (-4.0 * (t * a))))
	elif t_3 <= 1e+215:
		tmp = t_3 + (j * (-27.0 * k))
	else:
		tmp = (((b * c) + (((18.0 * y) * (t * (x * z))) + t_1)) + t_2) + (k * (-27.0 * j))
	return tmp

Julia

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

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(i * Float64(x * -4.0))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) + t_1) + Float64(b * c)) + t_2)
	tmp = 0.0
	if (t_3 <= -2e+256)
		tmp = Float64(Float64(b * c) + Float64(Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i))) + Float64(Float64(-27.0 * Float64(k * j)) + Float64(-4.0 * Float64(t * a)))));
	elseif (t_3 <= 1e+215)
		tmp = Float64(t_3 + Float64(j * Float64(-27.0 * k)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(Float64(18.0 * y) * Float64(t * Float64(x * z))) + t_1)) + t_2) + Float64(k * Float64(-27.0 * j)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = i * (x * -4.0);
	t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	tmp = 0.0;
	if (t_3 <= -2e+256)
		tmp = (b * c) + ((x * ((18.0 * (y * (z * t))) - (4.0 * i))) + ((-27.0 * (k * j)) + (-4.0 * (t * a))));
	elseif (t_3 <= 1e+215)
		tmp = t_3 + (j * (-27.0 * k));
	else
		tmp = (((b * c) + (((18.0 * y) * (t * (x * z))) + t_1)) + t_2) + (k * (-27.0 * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+256], N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+215], N[(t$95$3 + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(18.0 * y), $MachinePrecision] * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	5.7
Target	1.7
Herbie	2.8

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

Derivation

1. Split input into 3 regimes

2. if (-.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)) < -2.0000000000000001e256

   1. Initial program 23.3

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

   2. Simplified 17.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(t, \mathsf{fma}\left(x, y \cdot \left(18 \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)\right)} \]
      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))))): 5 points increase in error, 7 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))))): 0 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))))): 20 points increase in error, 14 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, 5 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))))): 0 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)))): 0 points increase in error, 2 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)))): 0 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))): 12 points increase in error, 8 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 8.2

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

   if -2.0000000000000001e256 < (-.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)) < 9.99999999999999907e214

   1. Initial program 0.5

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

   2. Applied egg-rr 0.4

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{\left(0 + j \cdot \left(27 \cdot k\right)\right)} \]

   if 9.99999999999999907e214 < (-.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 15.7

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

   2. Taylor expanded in x around 0 9.1

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

   3. Simplified 9.2

      \[\leadsto \left(\left(\left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      Proof
      (*.f64 (*.f64 18 y) (*.f64 t (*.f64 z x))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))): 29 points increase in error, 29 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 2.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -2 \cdot 10^{+256}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 10^{+215}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.9
Cost	5320

\[\begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t_2\right) + b \cdot c\right) + t_1\\ t_4 := k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{elif}\;t_3 \leq 10^{+215}:\\ \;\;\;\;t_3 + t_4\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right) + t_2\right)\right) + t_1\right) + t_4\\ \end{array} \]

Alternative 2
Error	21.3
Cost	2536

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ t_4 := b \cdot c + \left(t_2 + t_3\right)\\ t_5 := k \cdot \left(-27 \cdot j\right)\\ t_6 := t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + t_5\\ t_7 := t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) + t_5\\ \mathbf{if}\;k \leq -6.802042838440591 \cdot 10^{-166}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;k \leq -2.068908669017389 \cdot 10^{-231}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -5.244983443103124 \cdot 10^{-261}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 4.291486458929159 \cdot 10^{-93}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 5.9421199609552476 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + t_5\\ \mathbf{elif}\;k \leq 2.6590707446205607 \cdot 10^{+23}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.1889833467776455 \cdot 10^{+43}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 10^{+75}:\\ \;\;\;\;b \cdot c + \left(t_1 + t_2\right)\\ \mathbf{elif}\;k \leq 10^{+213}:\\ \;\;\;\;b \cdot c + \left(t_1 + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 3
Error	21.3
Cost	2532

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ t_4 := b \cdot c + \left(t_2 + t_3\right)\\ t_5 := b \cdot c + \left(t_1 + t_3\right)\\ t_6 := k \cdot \left(-27 \cdot j\right)\\ t_7 := t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) + t_6\\ \mathbf{if}\;k \leq -6.802042838440591 \cdot 10^{-166}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;k \leq 4.291486458929159 \cdot 10^{-93}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 5.9421199609552476 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + t_6\\ \mathbf{elif}\;k \leq 2.6590707446205607 \cdot 10^{+23}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.1889833467776455 \cdot 10^{+43}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 10^{+75}:\\ \;\;\;\;b \cdot c + \left(t_1 + t_2\right)\\ \mathbf{elif}\;k \leq 10^{+213}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 10^{+250}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right) + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) + t_6\\ \mathbf{elif}\;k \leq 10^{+265}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_6\\ \end{array} \]

Alternative 4
Error	10.9
Cost	2392

\[\begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ t_4 := t_2 + t_3\\ t_5 := b \cdot c + \left(t_1 + t_4\right)\\ t_6 := -4 \cdot \left(t \cdot a\right)\\ t_7 := b \cdot c + \left(t_3 + \left(t_2 + t_6\right)\right)\\ t_8 := \left(t_6 + \left(b \cdot c + t_1\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;z \leq -4.8717768017048215 \cdot 10^{-180}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.3198806172699913 \cdot 10^{+21}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+169}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+235}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+288}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Error	17.7
Cost	2272

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ t_3 := b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + t_1\right)\\ t_4 := b \cdot c + \left(-27 \cdot \left(k \cdot j\right) + t_1\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3900000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.96896215848375 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.617314034178887 \cdot 10^{-118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.6013193188952992 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.0468241876495105 \cdot 10^{-91}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+147}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	4.5
Cost	2248

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := \left(\left(b \cdot c + \left(x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right) + t_1\\ \mathbf{if}\;x \leq -1.581866271344682 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.844162147443089 \cdot 10^{-108}:\\ \;\;\;\;\left(-4 \cdot \left(t \cdot a\right) + \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	2.5
Cost	2248

\[\begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ t_2 := k \cdot \left(-27 \cdot j\right)\\ t_3 := t \cdot \left(a \cdot -4\right)\\ t_4 := \left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) + t_3\right)\right) + t_1\right) + t_2\\ \mathbf{if}\;t \leq -1 \cdot 10^{+70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.36217368199067 \cdot 10^{-150}:\\ \;\;\;\;\left(\left(b \cdot c + \left(x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right) + t_3\right)\right) + t_1\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	11.6
Cost	2136

\[\begin{array}{l} t_1 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ t_2 := k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;c \leq -1.9729815707505964 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1206484229411452 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) + t_2\\ \mathbf{elif}\;c \leq 8.985057292044785 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2810534749623624 \cdot 10^{-64}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_2\\ \mathbf{elif}\;c \leq 9.518615768318511 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+106}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right) + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	11.7
Cost	2132

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(-27 \cdot j\right)\\ t_3 := \left(b \cdot c + t_1\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+260}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+150}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_1 + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	4.3
Cost	2120

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + \left(x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + t_1\right)\right)\\ \mathbf{if}\;x \leq -1.581866271344682 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.844162147443089 \cdot 10^{-108}:\\ \;\;\;\;\left(t_1 + \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	32.2
Cost	1884

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_1\\ t_3 := b \cdot c + t_1\\ t_4 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;c \leq -1.9729815707505964 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -6.251712401354935 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.46748433822703 \cdot 10^{-197}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 2.0818713116522193 \cdot 10^{-297}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;c \leq 3.1771548960533514 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_1\\ \mathbf{elif}\;c \leq 3.337334407490117 \cdot 10^{-168}:\\ \;\;\;\;t_4 + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;c \leq 4.635033529675212 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	20.1
Cost	1884

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ t_4 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ t_5 := b \cdot c + \left(t_2 + t_3\right)\\ t_6 := b \cdot c + \left(t_1 + t_3\right)\\ \mathbf{if}\;a \leq -1.6952152457018643 \cdot 10^{+58}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.655562005293923 \cdot 10^{-64}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -2.4757605765989217 \cdot 10^{-106}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.8081731129491497 \cdot 10^{-151}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.0046806058249516 \cdot 10^{-265}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 4.815861572188123 \cdot 10^{-275}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 0.0003275362092823611:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_1 + t_2\right)\\ \end{array} \]

Alternative 13
Error	8.1
Cost	1864

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(t_1 + \left(b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.143533249374503 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	17.8
Cost	1736

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+82}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + t_2\\ \mathbf{elif}\;t_1 \leq 10^{+105}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_2\\ \end{array} \]

Alternative 15
Error	16.4
Cost	1736

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+82}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(-27 \cdot \left(k \cdot j\right) + t_1\right)\\ \end{array} \]

Alternative 16
Error	31.6
Cost	1628

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := x \cdot \left(i \cdot -4\right) + t_1\\ t_3 := b \cdot c + t_1\\ t_4 := t \cdot \left(a \cdot -4\right)\\ t_5 := t_4 + j \cdot \left(-27 \cdot k\right)\\ \mathbf{if}\;c \leq -1.389632219016263 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.0818713116522193 \cdot 10^{-297}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;c \leq 3.1771548960533514 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.337334407490117 \cdot 10^{-168}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 1.2810534749623624 \cdot 10^{-64}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) + t_1\\ \mathbf{elif}\;c \leq 1.9688014648329185 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.169612305212714 \cdot 10^{+53}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	44.8
Cost	1244

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.1597725186522744 \cdot 10^{-30}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.9517219881960524 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.022848106644386 \cdot 10^{-205}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \leq -7.326999233691244 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.946405197912242 \cdot 10^{-175}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18
Error	31.3
Cost	1232

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := t \cdot \left(a \cdot -4\right) + t_1\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.1597725186522744 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.504700611327034 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	30.7
Cost	1232

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := t \cdot \left(a \cdot -4\right) + t_1\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;c \leq -1.389632219016263 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.0818713116522193 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.9688014648329185 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_1\\ \mathbf{elif}\;c \leq 5.169612305212714 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	30.7
Cost	1232

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;c \leq -1.389632219016263 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.0818713116522193 \cdot 10^{-297}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;c \leq 1.9688014648329185 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_1\\ \mathbf{elif}\;c \leq 5.169612305212714 \cdot 10^{+53}:\\ \;\;\;\;t_2 + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	33.7
Cost	708

\[\begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]

Alternative 22
Error	43.2
Cost	584

\[\begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;k \leq -4380430975313292300:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4.836739620247888 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	43.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;k \leq -4380430975313292300:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \leq 4.836739620247888 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \end{array} \]

Alternative 24
Error	48.4
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2022291 
(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)))