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

Average Error: 5.6 → 2.1

Time: 37.4s

Precision: binary64

Cost: 2248

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

Math

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

↓

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t \leq -200000000000:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+68}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right)\\ \end{array} \]

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 (* k (* j -27.0))))
   (if (<= t -200000000000.0)
     (+
      (+ (* t (+ (* (* x 18.0) (* y z)) (* a -4.0))) (* b c))
      (+ (* x (* i -4.0)) (* j (* k -27.0))))
     (if (<= t 5e+68)
       (+
        (+
         (* b c)
         (+ (* x (+ (* y (* t (* 18.0 z))) (* i -4.0))) (* -4.0 (* t a))))
        t_1)
       (+
        t_1
        (+
         (+ (* b c) (+ (* t (* z (* (* x 18.0) y))) (* 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 = k * (j * -27.0);
	double tmp;
	if (t <= -200000000000.0) {
		tmp = ((t * (((x * 18.0) * (y * z)) + (a * -4.0))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	} else if (t <= 5e+68) {
		tmp = ((b * c) + ((x * ((y * (t * (18.0 * z))) + (i * -4.0))) + (-4.0 * (t * a)))) + t_1;
	} else {
		tmp = t_1 + (((b * c) + ((t * (z * ((x * 18.0) * y))) + (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 = k * (j * (-27.0d0))
    if (t <= (-200000000000.0d0)) then
        tmp = ((t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))) + (b * c)) + ((x * (i * (-4.0d0))) + (j * (k * (-27.0d0))))
    else if (t <= 5d+68) then
        tmp = ((b * c) + ((x * ((y * (t * (18.0d0 * z))) + (i * (-4.0d0)))) + ((-4.0d0) * (t * a)))) + t_1
    else
        tmp = t_1 + (((b * c) + ((t * (z * ((x * 18.0d0) * y))) + (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 = k * (j * -27.0);
	double tmp;
	if (t <= -200000000000.0) {
		tmp = ((t * (((x * 18.0) * (y * z)) + (a * -4.0))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	} else if (t <= 5e+68) {
		tmp = ((b * c) + ((x * ((y * (t * (18.0 * z))) + (i * -4.0))) + (-4.0 * (t * a)))) + t_1;
	} else {
		tmp = t_1 + (((b * c) + ((t * (z * ((x * 18.0) * y))) + (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 = k * (j * -27.0)
	tmp = 0
	if t <= -200000000000.0:
		tmp = ((t * (((x * 18.0) * (y * z)) + (a * -4.0))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)))
	elif t <= 5e+68:
		tmp = ((b * c) + ((x * ((y * (t * (18.0 * z))) + (i * -4.0))) + (-4.0 * (t * a)))) + t_1
	else:
		tmp = t_1 + (((b * c) + ((t * (z * ((x * 18.0) * y))) + (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(k * Float64(j * -27.0))
	tmp = 0.0
	if (t <= -200000000000.0)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0))) + Float64(b * c)) + Float64(Float64(x * Float64(i * -4.0)) + Float64(j * Float64(k * -27.0))));
	elseif (t <= 5e+68)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * Float64(Float64(y * Float64(t * Float64(18.0 * z))) + Float64(i * -4.0))) + Float64(-4.0 * Float64(t * a)))) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(Float64(x * 18.0) * y))) + 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 = k * (j * -27.0);
	tmp = 0.0;
	if (t <= -200000000000.0)
		tmp = ((t * (((x * 18.0) * (y * z)) + (a * -4.0))) + (b * c)) + ((x * (i * -4.0)) + (j * (k * -27.0)));
	elseif (t <= 5e+68)
		tmp = ((b * c) + ((x * ((y * (t * (18.0 * z))) + (i * -4.0))) + (-4.0 * (t * a)))) + t_1;
	else
		tmp = t_1 + (((b * c) + ((t * (z * ((x * 18.0) * y))) + (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[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -200000000000.0], N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+68], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(N[(y * N[(t * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	5.6
Target	1.4
Herbie	2.1

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

Derivation

1. Split input into 3 regimes

2. if t < -2e11

   1. Initial program 1.4

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

   2. Simplified 2.7

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
      Proof
      (-.f64 (+.f64 (*.f64 t (-.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) (*.f64 a 4))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 t (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 x 18) y) z)) (*.f64 a 4))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 4 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 4 points decrease in error
      (-.f64 (+.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (neg.f64 (*.f64 (*.f64 a 4) t)))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 (*.f64 (*.f64 a 4) t)) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 15 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 (*.f64 a 4) t))) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 15 points decrease in error
      (-.f64 (+.f64 (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 (*.f64 (*.f64 a 4) t)) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (*.f64 (*.f64 a 4) t))) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (neg.f64 (*.f64 (*.f64 a 4) t)))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> associate-+l-_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 b c)))) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 1 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 b c))) (+.f64 (*.f64 x (*.f64 4 i)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 j 27) k)))): 0 points increase in error, 1 points decrease in error
      (-.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 b c))) (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c))) (+.f64 (*.f64 (*.f64 x 4) i) (*.f64 (*.f64 j 27) k))): 16 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l-_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, 16 points decrease in error

   if -2e11 < t < 5.0000000000000004e68

   1. Initial program 7.4

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

   2. Simplified 8.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)} \]
      Proof
      (-.f64 (+.f64 (*.f64 t (-.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) (*.f64 a 4))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 t (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 x 18) y) z)) (*.f64 a 4))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 4 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 4 points decrease in error
      (-.f64 (+.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (neg.f64 (*.f64 (*.f64 a 4) t)))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 (*.f64 (*.f64 a 4) t)) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 15 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 (*.f64 a 4) t))) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 15 points decrease in error
      (-.f64 (+.f64 (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 (*.f64 (*.f64 a 4) t)) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (*.f64 (*.f64 a 4) t))) (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (neg.f64 (*.f64 (*.f64 a 4) t)))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (*.f64 b c)) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> associate-+l-_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 b c)))) (+.f64 (*.f64 x (*.f64 4 i)) (*.f64 j (*.f64 27 k)))): 1 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 b c))) (+.f64 (*.f64 x (*.f64 4 i)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 j 27) k)))): 0 points increase in error, 1 points decrease in error
      (-.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (-.f64 (*.f64 (*.f64 a 4) t) (*.f64 b c))) (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c))) (+.f64 (*.f64 (*.f64 x 4) i) (*.f64 (*.f64 j 27) k))): 16 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l-_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, 16 points decrease in error

   3. Taylor expanded in x around 0 2.1

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

   4. Applied egg-rr 11.8

      \[\leadsto \left(c \cdot b + \left(\left(\color{blue}{\left(e^{\mathsf{log1p}\left(\left(y \cdot t\right) \cdot \left(z \cdot 18\right)\right)} - 1\right)} + -4 \cdot i\right) \cdot x + -4 \cdot \left(a \cdot t\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

   5. Simplified 2.2

      \[\leadsto \left(c \cdot b + \left(\left(\color{blue}{y \cdot \left(t \cdot \left(18 \cdot z\right)\right)} + -4 \cdot i\right) \cdot x + -4 \cdot \left(a \cdot t\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]
      Proof
      (+.f64 (+.f64 (*.f64 c b) (+.f64 (*.f64 (+.f64 (*.f64 y (*.f64 t (*.f64 18 z))) (*.f64 -4 i)) x) (*.f64 -4 (*.f64 a t)))) (*.f64 k (*.f64 j -27))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 c b) (+.f64 (*.f64 (+.f64 (*.f64 y (*.f64 t (Rewrite<= *-commutative_binary64 (*.f64 z 18)))) (*.f64 -4 i)) x) (*.f64 -4 (*.f64 a t)))) (*.f64 k (*.f64 j -27))): 5 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 c b) (+.f64 (*.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y t) (*.f64 z 18))) (*.f64 -4 i)) x) (*.f64 -4 (*.f64 a t)))) (*.f64 k (*.f64 j -27))): 0 points increase in error, 5 points decrease in error
      (+.f64 (+.f64 (*.f64 c b) (+.f64 (*.f64 (+.f64 (Rewrite<= expm1-log1p_binary64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 y t) (*.f64 z 18))))) (*.f64 -4 i)) x) (*.f64 -4 (*.f64 a t)))) (*.f64 k (*.f64 j -27))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 c b) (+.f64 (*.f64 (+.f64 (Rewrite<= expm1-def_binary64 (-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 y t) (*.f64 z 18)))) 1)) (*.f64 -4 i)) x) (*.f64 -4 (*.f64 a t)))) (*.f64 k (*.f64 j -27))): 5 points increase in error, 0 points decrease in error

   if 5.0000000000000004e68 < t

   1. Initial program 1.0

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

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -200000000000:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+68}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	49.3
Cost	2828

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+37}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-122}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-232}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-285}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-212}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-189}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-124}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-6}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+24}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+128}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+145}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 2
Error	49.8
Cost	2696

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-286}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-212}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-126}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 0.00012:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+24}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+128}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+145}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+277}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 3
Error	33.1
Cost	2156

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + t_1\\ t_3 := b \cdot c + a \cdot \left(t \cdot -4\right)\\ t_4 := -4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ t_5 := x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.12 \cdot 10^{+86}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -800:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-75}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-129}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-209}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-152}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \]

Alternative 4
Error	33.2
Cost	2156

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + t_1\\ t_3 := b \cdot c + a \cdot \left(t \cdot -4\right)\\ t_4 := -4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ t_5 := x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+87}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -13.5:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-73}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-128}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-210}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-151}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \]

Alternative 5
Error	2.1
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -720000 \lor \neg \left(t \leq 10000000000\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right) + b \cdot c\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 6
Error	4.5
Cost	2120

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;\left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+70}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 7
Error	4.6
Cost	2120

\[\begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+139}:\\ \;\;\;\;\left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) + i \cdot -4\right) + -4 \cdot \left(t \cdot a\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 8
Error	9.9
Cost	2002

\[\begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-26} \lor \neg \left(x \leq 2 \cdot 10^{-255}\right) \land \left(x \leq 7 \cdot 10^{-177} \lor \neg \left(x \leq 1.7 \cdot 10^{-63}\right)\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 9
Error	9.7
Cost	1997

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+140}:\\ \;\;\;\;\left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-98} \lor \neg \left(t \leq 2.4 \cdot 10^{+87}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + \left(-4 \cdot \left(t \cdot a\right) + \left(18 \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	23.3
Cost	1753

\[\begin{array}{l} t_1 := \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + a \cdot \left(t \cdot -4\right)\\ t_2 := x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;b \leq -1.95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-231} \lor \neg \left(b \leq 1.08 \cdot 10^{-210}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	21.7
Cost	1752

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_2\\ t_4 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+170}:\\ \;\;\;\;t_4 + y \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-17}:\\ \;\;\;\;t_1 + \left(b \cdot c + t_2\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-31}:\\ \;\;\;\;t_1 + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-164}:\\ \;\;\;\;t_4 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + 18 \cdot \left(y \cdot \left(x \cdot \left(t \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	18.7
Cost	1744

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_3 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + t_1\\ t_4 := k \cdot \left(j \cdot -27\right) + \left(b \cdot c + t_1\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1250000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.05 \cdot 10^{-63}:\\ \;\;\;\;t_2 + y \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+172}:\\ \;\;\;\;t_2 + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 13
Error	31.1
Cost	1633

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_3 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;k \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 0.00047:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+83} \lor \neg \left(k \leq 2.7 \cdot 10^{+114}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	30.9
Cost	1496

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := t_1 - k \cdot \left(j \cdot 27\right)\\ t_3 := b \cdot c + a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-156}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	9.5
Cost	1476

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+263}:\\ \;\;\;\;\left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + y \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 16
Error	37.4
Cost	1369

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.14 \cdot 10^{-296}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-105} \lor \neg \left(b \leq 8.1 \cdot 10^{-84}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 17
Error	45.3
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-301}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-13}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18
Error	30.7
Cost	1236

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := b \cdot c + a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_1\\ \mathbf{elif}\;a \leq -135:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-229}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	16.9
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-72} \lor \neg \left(a \leq 2.8 \cdot 10^{-5}\right):\\ \;\;\;\;\left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 20
Error	30.0
Cost	1104

\[\begin{array}{l} t_1 := b \cdot c + a \cdot \left(t \cdot -4\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-304}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	44.3
Cost	980

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \leq -3.25 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -22.5:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-97}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Error	44.3
Cost	980

\[\begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+83}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq -19.5:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-100}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-13}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 23
Error	43.2
Cost	585

\[\begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{-72} \lor \neg \left(j \leq 1.85 \cdot 10^{-33}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 24
Error	48.7
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2022340 
(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)))