Jmat.Real.dawson

Average Error: 29.1 → 0.0

Time: 3.1s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.2514179000665374, {x}^{-3}, \frac{0.5}{x}\right)\\ t_1 := {\left(x \cdot x\right)}^{2}\\ t_2 := {\left(x \cdot x\right)}^{3}\\ t_3 := \left(x \cdot x\right) \cdot t_2\\ t_4 := t_2 \cdot t_1\\ \mathbf{if}\;x \leq -10000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6000:\\ \;\;\;\;\frac{x \cdot \left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(0.0424060604 \cdot {x}^{4} + 0.0072644182 \cdot t_2\right)\right) + \left(0.0005064034 \cdot t_3 + 0.0001789971 \cdot t_4\right)\right)}{\left(\left(1 + \left(\left(x \cdot x\right) \cdot 0.7715471019 + t_1 \cdot 0.2909738639\right)\right) + \left(t_2 \cdot 0.0694555761 + t_3 \cdot 0.0140005442\right)\right) + \left(t_4 \cdot 0.0008327945 + 0.0003579942 \cdot \left(t_3 \cdot t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 (fma 0.2514179000665374 (pow x -3.0) (/ 0.5 x)))
        (t_1 (pow (* x x) 2.0))
        (t_2 (pow (* x x) 3.0))
        (t_3 (* (* x x) t_2))
        (t_4 (* t_2 t_1)))
   (if (<= x -10000.0)
     t_0
     (if (<= x 6000.0)
       (/
        (*
         x
         (+
          (+
           (+ 1.0 (* 0.1049934947 (* x x)))
           (+ (* 0.0424060604 (pow x 4.0)) (* 0.0072644182 t_2)))
          (+ (* 0.0005064034 t_3) (* 0.0001789971 t_4))))
        (+
         (+
          (+ 1.0 (+ (* (* x x) 0.7715471019) (* t_1 0.2909738639)))
          (+ (* t_2 0.0694555761) (* t_3 0.0140005442)))
         (+ (* t_4 0.0008327945) (* 0.0003579942 (* t_3 t_1)))))
       t_0))))

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 = fma(0.2514179000665374, pow(x, -3.0), (0.5 / x));
	double t_1 = pow((x * x), 2.0);
	double t_2 = pow((x * x), 3.0);
	double t_3 = (x * x) * t_2;
	double t_4 = t_2 * t_1;
	double tmp;
	if (x <= -10000.0) {
		tmp = t_0;
	} else if (x <= 6000.0) {
		tmp = (x * (((1.0 + (0.1049934947 * (x * x))) + ((0.0424060604 * pow(x, 4.0)) + (0.0072644182 * t_2))) + ((0.0005064034 * t_3) + (0.0001789971 * t_4)))) / (((1.0 + (((x * x) * 0.7715471019) + (t_1 * 0.2909738639))) + ((t_2 * 0.0694555761) + (t_3 * 0.0140005442))) + ((t_4 * 0.0008327945) + (0.0003579942 * (t_3 * t_1))));
	} else {
		tmp = t_0;
	}
	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 = fma(0.2514179000665374, (x ^ -3.0), Float64(0.5 / x))
	t_1 = Float64(x * x) ^ 2.0
	t_2 = Float64(x * x) ^ 3.0
	t_3 = Float64(Float64(x * x) * t_2)
	t_4 = Float64(t_2 * t_1)
	tmp = 0.0
	if (x <= -10000.0)
		tmp = t_0;
	elseif (x <= 6000.0)
		tmp = Float64(Float64(x * Float64(Float64(Float64(1.0 + Float64(0.1049934947 * Float64(x * x))) + Float64(Float64(0.0424060604 * (x ^ 4.0)) + Float64(0.0072644182 * t_2))) + Float64(Float64(0.0005064034 * t_3) + Float64(0.0001789971 * t_4)))) / Float64(Float64(Float64(1.0 + Float64(Float64(Float64(x * x) * 0.7715471019) + Float64(t_1 * 0.2909738639))) + Float64(Float64(t_2 * 0.0694555761) + Float64(t_3 * 0.0140005442))) + Float64(Float64(t_4 * 0.0008327945) + Float64(0.0003579942 * Float64(t_3 * t_1)))));
	else
		tmp = t_0;
	end
	return 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[(0.2514179000665374 * N[Power[x, -3.0], $MachinePrecision] + N[(0.5 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(x * x), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(x * x), $MachinePrecision], 3.0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * x), $MachinePrecision] * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 * t$95$1), $MachinePrecision]}, If[LessEqual[x, -10000.0], t$95$0, If[LessEqual[x, 6000.0], N[(N[(x * N[(N[(N[(1.0 + N[(0.1049934947 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0424060604 * N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] + N[(0.0072644182 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0005064034 * t$95$3), $MachinePrecision] + N[(0.0001789971 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 + N[(N[(N[(x * x), $MachinePrecision] * 0.7715471019), $MachinePrecision] + N[(t$95$1 * 0.2909738639), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * 0.0694555761), $MachinePrecision] + N[(t$95$3 * 0.0140005442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 * 0.0008327945), $MachinePrecision] + N[(0.0003579942 * N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -1e4 or 6e3 < x

   1. Initial program 59.1

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

   2. Taylor expanded in x around inf 0.0

      \[\leadsto \color{blue}{0.5 \cdot \frac{1}{x} + 0.2514179000665374 \cdot \frac{1}{{x}^{3}}} \]

   3. Simplified 0.0

      \[\leadsto \color{blue}{\frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}} \]

   4. Applied egg-rr 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.2514179000665374, {x}^{-3}, \frac{0.5}{x}\right)} \]

   if -1e4 < x < 6e3

   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. Applied egg-rr 0.0

      \[\leadsto \color{blue}{\frac{\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(0.0424060604 \cdot {\left(x \cdot x\right)}^{2} + 0.0072644182 \cdot {\left(x \cdot x\right)}^{3}\right)\right) + \left(0.0005064034 \cdot \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) + 0.0001789971 \cdot \left({\left(x \cdot x\right)}^{3} \cdot {\left(x \cdot x\right)}^{2}\right)\right)\right) \cdot x}{\left(\left(1 + \left(\left(x \cdot x\right) \cdot 0.7715471019 + {\left(x \cdot x\right)}^{2} \cdot 0.2909738639\right)\right) + \left({\left(x \cdot x\right)}^{3} \cdot 0.0694555761 + \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) \cdot 0.0140005442\right)\right) + \left(\left({\left(x \cdot x\right)}^{3} \cdot {\left(x \cdot x\right)}^{2}\right) \cdot 0.0008327945 + 0.0003579942 \cdot \left(\left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) \cdot {\left(x \cdot x\right)}^{2}\right)\right)}} \]

   3. Taylor expanded in x around 0 0.0

      \[\leadsto \frac{\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(0.0424060604 \cdot \color{blue}{{x}^{4}} + 0.0072644182 \cdot {\left(x \cdot x\right)}^{3}\right)\right) + \left(0.0005064034 \cdot \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) + 0.0001789971 \cdot \left({\left(x \cdot x\right)}^{3} \cdot {\left(x \cdot x\right)}^{2}\right)\right)\right) \cdot x}{\left(\left(1 + \left(\left(x \cdot x\right) \cdot 0.7715471019 + {\left(x \cdot x\right)}^{2} \cdot 0.2909738639\right)\right) + \left({\left(x \cdot x\right)}^{3} \cdot 0.0694555761 + \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) \cdot 0.0140005442\right)\right) + \left(\left({\left(x \cdot x\right)}^{3} \cdot {\left(x \cdot x\right)}^{2}\right) \cdot 0.0008327945 + 0.0003579942 \cdot \left(\left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) \cdot {\left(x \cdot x\right)}^{2}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10000:\\ \;\;\;\;\mathsf{fma}\left(0.2514179000665374, {x}^{-3}, \frac{0.5}{x}\right)\\ \mathbf{elif}\;x \leq 6000:\\ \;\;\;\;\frac{x \cdot \left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(0.0424060604 \cdot {x}^{4} + 0.0072644182 \cdot {\left(x \cdot x\right)}^{3}\right)\right) + \left(0.0005064034 \cdot \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) + 0.0001789971 \cdot \left({\left(x \cdot x\right)}^{3} \cdot {\left(x \cdot x\right)}^{2}\right)\right)\right)}{\left(\left(1 + \left(\left(x \cdot x\right) \cdot 0.7715471019 + {\left(x \cdot x\right)}^{2} \cdot 0.2909738639\right)\right) + \left({\left(x \cdot x\right)}^{3} \cdot 0.0694555761 + \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) \cdot 0.0140005442\right)\right) + \left(\left({\left(x \cdot x\right)}^{3} \cdot {\left(x \cdot x\right)}^{2}\right) \cdot 0.0008327945 + 0.0003579942 \cdot \left(\left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}\right) \cdot {\left(x \cdot x\right)}^{2}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.2514179000665374, {x}^{-3}, \frac{0.5}{x}\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022165 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
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