Jmat.Real.dawson

Average Error: 29.2 → 0.0

Time: 17.7s

Precision: binary64

Cost: 5832

Math

\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]

↓

\[\begin{array}{l} t_0 := x \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -100000000:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{x + \left(0.1049934947 + \left(0.0424060604 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(0.0005064034 + x \cdot \frac{x}{5586.682689272619}\right)\right) + 0.0072644182\right)\right)\right) \cdot \left(x \cdot x\right)\right) \cdot t_0}{0.5 \cdot \left(2 + x \cdot \frac{x \cdot \left(0.7715471019 + \left(x \cdot \left(\left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot t_0\right)\right) + 0.2909738639\right) \cdot x\right) + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0694555761 + \frac{x \cdot x}{71.4257950058827}\right)\right)\right)\right)\right)}{0.5}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (/
   (+
    (+
     (+
      (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x))))
      (* 0.0072644182 (* (* (* x x) (* x x)) (* x x))))
     (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x))))
    (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x))))
   (+
    (+
     (+
      (+
       (+
        (+ 1.0 (* 0.7715471019 (* x x)))
        (* 0.2909738639 (* (* x x) (* x x))))
       (* 0.0694555761 (* (* (* x x) (* x x)) (* x x))))
      (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x))))
     (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x))))
    (*
     (* 2.0 0.0001789971)
     (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
  x))

↓

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (* x x))))
   (if (<= x -100000000.0)
     (/ 0.5 x)
     (if (<= x 100000000.0)
       (/
        (+
         x
         (*
          (+
           0.1049934947
           (*
            (+
             0.0424060604
             (*
              x
              (*
               x
               (+
                (* x (* x (+ 0.0005064034 (* x (/ x 5586.682689272619)))))
                0.0072644182))))
            (* x x)))
          t_0))
        (*
         0.5
         (+
          2.0
          (*
           x
           (/
            (*
             x
             (+
              0.7715471019
              (+
               (*
                x
                (*
                 (+
                  (*
                   (+ 0.0008327945 (* x (* x 0.0003579942)))
                   (* x (* (* x x) t_0)))
                  0.2909738639)
                 x))
               (*
                x
                (*
                 x
                 (* (* x x) (+ 0.0694555761 (/ (* x x) 71.4257950058827))))))))
            0.5)))))
       (/ 0.5 x)))))

C

double code(double x) {
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * ((x * x) * (x * x)))) + (0.0072644182 * (((x * x) * (x * x)) * (x * x)))) + (0.0005064034 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0001789971 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * ((x * x) * (x * x)))) + (0.0694555761 * (((x * x) * (x * x)) * (x * x)))) + (0.0140005442 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0008327945 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) + ((2.0 * 0.0001789971) * ((((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)) * (x * x))))) * x;
}

↓

double code(double x) {
	double t_0 = x * (x * x);
	double tmp;
	if (x <= -100000000.0) {
		tmp = 0.5 / x;
	} else if (x <= 100000000.0) {
		tmp = (x + ((0.1049934947 + ((0.0424060604 + (x * (x * ((x * (x * (0.0005064034 + (x * (x / 5586.682689272619))))) + 0.0072644182)))) * (x * x))) * t_0)) / (0.5 * (2.0 + (x * ((x * (0.7715471019 + ((x * ((((0.0008327945 + (x * (x * 0.0003579942))) * (x * ((x * x) * t_0))) + 0.2909738639) * x)) + (x * (x * ((x * x) * (0.0694555761 + ((x * x) / 71.4257950058827)))))))) / 0.5))));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((((((1.0d0 + (0.1049934947d0 * (x * x))) + (0.0424060604d0 * ((x * x) * (x * x)))) + (0.0072644182d0 * (((x * x) * (x * x)) * (x * x)))) + (0.0005064034d0 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0001789971d0 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) / ((((((1.0d0 + (0.7715471019d0 * (x * x))) + (0.2909738639d0 * ((x * x) * (x * x)))) + (0.0694555761d0 * (((x * x) * (x * x)) * (x * x)))) + (0.0140005442d0 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0008327945d0 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) + ((2.0d0 * 0.0001789971d0) * ((((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)) * (x * x))))) * x
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (x * x)
    if (x <= (-100000000.0d0)) then
        tmp = 0.5d0 / x
    else if (x <= 100000000.0d0) then
        tmp = (x + ((0.1049934947d0 + ((0.0424060604d0 + (x * (x * ((x * (x * (0.0005064034d0 + (x * (x / 5586.682689272619d0))))) + 0.0072644182d0)))) * (x * x))) * t_0)) / (0.5d0 * (2.0d0 + (x * ((x * (0.7715471019d0 + ((x * ((((0.0008327945d0 + (x * (x * 0.0003579942d0))) * (x * ((x * x) * t_0))) + 0.2909738639d0) * x)) + (x * (x * ((x * x) * (0.0694555761d0 + ((x * x) / 71.4257950058827d0)))))))) / 0.5d0))))
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * ((x * x) * (x * x)))) + (0.0072644182 * (((x * x) * (x * x)) * (x * x)))) + (0.0005064034 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0001789971 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * ((x * x) * (x * x)))) + (0.0694555761 * (((x * x) * (x * x)) * (x * x)))) + (0.0140005442 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0008327945 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) + ((2.0 * 0.0001789971) * ((((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)) * (x * x))))) * x;
}

↓

public static double code(double x) {
	double t_0 = x * (x * x);
	double tmp;
	if (x <= -100000000.0) {
		tmp = 0.5 / x;
	} else if (x <= 100000000.0) {
		tmp = (x + ((0.1049934947 + ((0.0424060604 + (x * (x * ((x * (x * (0.0005064034 + (x * (x / 5586.682689272619))))) + 0.0072644182)))) * (x * x))) * t_0)) / (0.5 * (2.0 + (x * ((x * (0.7715471019 + ((x * ((((0.0008327945 + (x * (x * 0.0003579942))) * (x * ((x * x) * t_0))) + 0.2909738639) * x)) + (x * (x * ((x * x) * (0.0694555761 + ((x * x) / 71.4257950058827)))))))) / 0.5))));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x):
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * ((x * x) * (x * x)))) + (0.0072644182 * (((x * x) * (x * x)) * (x * x)))) + (0.0005064034 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0001789971 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * ((x * x) * (x * x)))) + (0.0694555761 * (((x * x) * (x * x)) * (x * x)))) + (0.0140005442 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0008327945 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) + ((2.0 * 0.0001789971) * ((((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)) * (x * x))))) * x

↓

def code(x):
	t_0 = x * (x * x)
	tmp = 0
	if x <= -100000000.0:
		tmp = 0.5 / x
	elif x <= 100000000.0:
		tmp = (x + ((0.1049934947 + ((0.0424060604 + (x * (x * ((x * (x * (0.0005064034 + (x * (x / 5586.682689272619))))) + 0.0072644182)))) * (x * x))) * t_0)) / (0.5 * (2.0 + (x * ((x * (0.7715471019 + ((x * ((((0.0008327945 + (x * (x * 0.0003579942))) * (x * ((x * x) * t_0))) + 0.2909738639) * x)) + (x * (x * ((x * x) * (0.0694555761 + ((x * x) / 71.4257950058827)))))))) / 0.5))))
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.1049934947 * Float64(x * x))) + Float64(0.0424060604 * Float64(Float64(x * x) * Float64(x * x)))) + Float64(0.0072644182 * Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)))) + Float64(0.0005064034 * Float64(Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)))) + Float64(0.0001789971 * Float64(Float64(Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)))) / Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.7715471019 * Float64(x * x))) + Float64(0.2909738639 * Float64(Float64(x * x) * Float64(x * x)))) + Float64(0.0694555761 * Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)))) + Float64(0.0140005442 * Float64(Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)))) + Float64(0.0008327945 * Float64(Float64(Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)))) + Float64(Float64(2.0 * 0.0001789971) * Float64(Float64(Float64(Float64(Float64(Float64(x * x) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)) * Float64(x * x)) * Float64(x * x))))) * x)
end

↓

function code(x)
	t_0 = Float64(x * Float64(x * x))
	tmp = 0.0
	if (x <= -100000000.0)
		tmp = Float64(0.5 / x);
	elseif (x <= 100000000.0)
		tmp = Float64(Float64(x + Float64(Float64(0.1049934947 + Float64(Float64(0.0424060604 + Float64(x * Float64(x * Float64(Float64(x * Float64(x * Float64(0.0005064034 + Float64(x * Float64(x / 5586.682689272619))))) + 0.0072644182)))) * Float64(x * x))) * t_0)) / Float64(0.5 * Float64(2.0 + Float64(x * Float64(Float64(x * Float64(0.7715471019 + Float64(Float64(x * Float64(Float64(Float64(Float64(0.0008327945 + Float64(x * Float64(x * 0.0003579942))) * Float64(x * Float64(Float64(x * x) * t_0))) + 0.2909738639) * x)) + Float64(x * Float64(x * Float64(Float64(x * x) * Float64(0.0694555761 + Float64(Float64(x * x) / 71.4257950058827)))))))) / 0.5)))));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

function tmp = code(x)
	tmp = ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * ((x * x) * (x * x)))) + (0.0072644182 * (((x * x) * (x * x)) * (x * x)))) + (0.0005064034 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0001789971 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * ((x * x) * (x * x)))) + (0.0694555761 * (((x * x) * (x * x)) * (x * x)))) + (0.0140005442 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))) + (0.0008327945 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))) + ((2.0 * 0.0001789971) * ((((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)) * (x * x))))) * x;
end

↓

function tmp_2 = code(x)
	t_0 = x * (x * x);
	tmp = 0.0;
	if (x <= -100000000.0)
		tmp = 0.5 / x;
	elseif (x <= 100000000.0)
		tmp = (x + ((0.1049934947 + ((0.0424060604 + (x * (x * ((x * (x * (0.0005064034 + (x * (x / 5586.682689272619))))) + 0.0072644182)))) * (x * x))) * t_0)) / (0.5 * (2.0 + (x * ((x * (0.7715471019 + ((x * ((((0.0008327945 + (x * (x * 0.0003579942))) * (x * ((x * x) * t_0))) + 0.2909738639) * x)) + (x * (x * ((x * x) * (0.0694555761 + ((x * x) / 71.4257950058827)))))))) / 0.5))));
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(1.0 + N[(0.1049934947 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0424060604 * N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0072644182 * N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0005064034 * N[(N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0001789971 * N[(N[(N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(1.0 + N[(0.7715471019 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.2909738639 * N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0694555761 * N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * N[(N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0008327945 * N[(N[(N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(N[(N[(N[(N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

↓

code[x_] := Block[{t$95$0 = N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -100000000.0], N[(0.5 / x), $MachinePrecision], If[LessEqual[x, 100000000.0], N[(N[(x + N[(N[(0.1049934947 + N[(N[(0.0424060604 + N[(x * N[(x * N[(N[(x * N[(x * N[(0.0005064034 + N[(x * N[(x / 5586.682689272619), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.0072644182), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(0.5 * N[(2.0 + N[(x * N[(N[(x * N[(0.7715471019 + N[(N[(x * N[(N[(N[(N[(0.0008327945 + N[(x * N[(x * 0.0003579942), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x * N[(N[(x * x), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.2909738639), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * N[(N[(x * x), $MachinePrecision] * N[(0.0694555761 + N[(N[(x * x), $MachinePrecision] / 71.4257950058827), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1e8 or 1e8 < x

   1. Initial program 60.3

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]

   2. Simplified 60.3

      \[\leadsto \color{blue}{x \cdot \frac{1 + \left(\left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot 0.0072644182 + \left(0.1049934947 + \left(x \cdot x\right) \cdot 0.0424060604\right)\right)\right)}{\left(x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.0694555761 + \left(x \cdot x\right) \cdot 0.0140005442\right) + \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right) \cdot \left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) + \left(1 + \left(x \cdot x\right) \cdot \left(0.7715471019 + x \cdot \left(x \cdot 0.2909738639\right)\right)\right)\right)}} \]
      Proof

      [Start] 60.3

      \[ \frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]

      rational.json-simplify-39 [=>] 60.3

      \[ \color{blue}{x \cdot \frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}} \]

   3. Taylor expanded in x around inf 0

      \[\leadsto \color{blue}{\frac{0.5}{x}} \]

   if -1e8 < x < 1e8

   1. Initial program 0.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]

   2. Simplified 0.0

      \[\leadsto \color{blue}{x \cdot \frac{1 + \left(\left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot 0.0072644182 + \left(0.1049934947 + \left(x \cdot x\right) \cdot 0.0424060604\right)\right)\right)}{\left(x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.0694555761 + \left(x \cdot x\right) \cdot 0.0140005442\right) + \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right) \cdot \left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) + \left(1 + \left(x \cdot x\right) \cdot \left(0.7715471019 + x \cdot \left(x \cdot 0.2909738639\right)\right)\right)\right)}} \]
      Proof

      [Start] 0.0

      \[ \frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]

      rational.json-simplify-39 [=>] 0.0

      \[ \color{blue}{x \cdot \frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}} \]

   3. Applied egg-rr 0.0

      \[\leadsto \color{blue}{\frac{x + x \cdot \left(\left(x \cdot x\right) \cdot \left(\left(0.1049934947 + \left(x \cdot x\right) \cdot \left(0.0424060604 + \left(x \cdot x\right) \cdot 0.0072644182\right)\right) + \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right)}{x \cdot \left(\left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.0694555761 + x \cdot \left(x \cdot 0.0140005442\right)\right)\right) + \left(1 + \left(x \cdot x\right) \cdot \left(\left(0.7715471019 + x \cdot \left(x \cdot 0.2909738639\right)\right) + \left(x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right)\right)\right)}} \]

   4. Applied egg-rr 0.0

      \[\leadsto \color{blue}{\frac{x}{1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(\left(0.0694555761 + x \cdot \left(x \cdot 0.0140005442\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right) + x \cdot \left(\left(0.7715471019 + \left(x \cdot x\right) \cdot 0.2909738639\right) + \left(x \cdot x\right) \cdot \left(\left(0.0008327945 + \frac{x}{\frac{2793.3413446363097}{x}}\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right)\right)} \cdot \left(x \cdot \left(x \cdot \left(0.1049934947 + \left(x \cdot x\right) \cdot \left(\left(0.0005064034 + \left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right) + \left(0.0424060604 + \left(x \cdot x\right) \cdot 0.0072644182\right)\right)\right)\right) + 1\right)} \]

   5. Applied egg-rr 0.0

      \[\leadsto \color{blue}{\frac{\frac{x + x \cdot \left(\left(x \cdot x\right) \cdot \left(0.1049934947 + x \cdot \left(x \cdot \left(0.0424060604 + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right)\right) + x \cdot 0.0072644182\right)\right)\right)\right)\right)}{2 + \frac{x \cdot \left(x \cdot \left(\left(0.7715471019 + \left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot \left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + 0.2909738639\right)\right) + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(0.0694555761 + \frac{x}{\frac{71.4257950058827}{x}}\right)\right)\right)\right)\right)}{0.5}}}{0.5}} \]

   6. Simplified 0.0

      \[\leadsto \color{blue}{\frac{x + \left(0.1049934947 + \left(0.0424060604 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(0.0005064034 + x \cdot \frac{x}{5586.682689272619}\right)\right) + 0.0072644182\right)\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)}{0.5 \cdot \left(2 + x \cdot \frac{x \cdot \left(0.7715471019 + \left(x \cdot \left(\left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right) + 0.2909738639\right) \cdot x\right) + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0694555761 + \frac{x \cdot x}{71.4257950058827}\right)\right)\right)\right)\right)}{0.5}\right)}} \]
      Proof

      [Start] 0.0	\[ \frac{\frac{x + x \cdot \left(\left(x \cdot x\right) \cdot \left(0.1049934947 + x \cdot \left(x \cdot \left(0.0424060604 + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right)\right) + x \cdot 0.0072644182\right)\right)\right)\right)\right)}{2 + \frac{x \cdot \left(x \cdot \left(\left(0.7715471019 + \left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot \left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + 0.2909738639\right)\right) + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(0.0694555761 + \frac{x}{\frac{71.4257950058827}{x}}\right)\right)\right)\right)\right)}{0.5}}}{0.5} \]
      rational.json-simplify-7 [=>] 0.0	\[ \color{blue}{\frac{\frac{x + x \cdot \left(\left(x \cdot x\right) \cdot \left(0.1049934947 + x \cdot \left(x \cdot \left(0.0424060604 + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right)\right) + x \cdot 0.0072644182\right)\right)\right)\right)\right)}{0.5}}{2 + \frac{x \cdot \left(x \cdot \left(\left(0.7715471019 + \left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot \left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + 0.2909738639\right)\right) + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(0.0694555761 + \frac{x}{\frac{71.4257950058827}{x}}\right)\right)\right)\right)\right)}{0.5}}} \]
      rational.json-simplify-16 [=>] 0.0	\[ \color{blue}{\frac{x + x \cdot \left(\left(x \cdot x\right) \cdot \left(0.1049934947 + x \cdot \left(x \cdot \left(0.0424060604 + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0005064034 + x \cdot \left(x \cdot 0.0001789971\right)\right)\right) + x \cdot 0.0072644182\right)\right)\right)\right)\right)}{0.5 \cdot \left(2 + \frac{x \cdot \left(x \cdot \left(\left(0.7715471019 + \left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot \left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + 0.2909738639\right)\right) + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(0.0694555761 + \frac{x}{\frac{71.4257950058827}{x}}\right)\right)\right)\right)\right)}{0.5}\right)}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -100000000:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{x + \left(0.1049934947 + \left(0.0424060604 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(0.0005064034 + x \cdot \frac{x}{5586.682689272619}\right)\right) + 0.0072644182\right)\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)}{0.5 \cdot \left(2 + x \cdot \frac{x \cdot \left(0.7715471019 + \left(x \cdot \left(\left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right) + 0.2909738639\right) \cdot x\right) + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(0.0694555761 + \frac{x \cdot x}{71.4257950058827}\right)\right)\right)\right)\right)}{0.5}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.2
Cost	5448

\[\begin{array}{l} \mathbf{if}\;x \leq -100000000:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{x + x \cdot \left(\left(x \cdot x\right) \cdot \left(0.1049934947 + x \cdot \left(x \cdot \left(0.0424060604 + x \cdot \left(\left(\left(x \cdot x\right) \cdot \left(0.0005064034 + 0.0001789971 \cdot \left(x \cdot x\right)\right) + 0.0072644182\right) \cdot x\right)\right)\right)\right)\right)}{1 + x \cdot \left(x \cdot \left(0.7715471019 + x \cdot \left(x \cdot \left(0.2909738639 + x \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.0008327945 + x \cdot \frac{x}{2793.3413446363097}\right)\right)\right)\right)\right) + \left(x \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 2
Error	0.0
Cost	5320

\[\begin{array}{l} \mathbf{if}\;x \leq -5000000000000:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 150000000:\\ \;\;\;\;\frac{x}{1 + \left(x \cdot x\right) \cdot \left(0.7715471019 + \left(x \cdot x\right) \cdot \left(\left(0.2909738639 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(\left(0.0008327945 + x \cdot \left(x \cdot 0.0003579942\right)\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(0.0694555761 - x \cdot \left(x \cdot -0.0140005442\right)\right)\right)\right)} \cdot \left(\left(x \cdot x\right) \cdot \left(0.1049934947 + x \cdot \left(x \cdot \left(0.0424060604 + \left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot \left(0.0005064034 + x \cdot \frac{x}{5586.682689272619}\right)\right) + 0.0072644182\right)\right)\right)\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 3
Error	0.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.7:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 0.71:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 4
Error	31.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023066 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))