Jmat.Real.dawson

Average Error: 29.8 → 0.0

Time: 4.0s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := x \cdot {x}^{3}\\ t_1 := \frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\\ t_2 := {t_0}^{2}\\ t_3 := \left(x \cdot x\right) \cdot t_2\\ \mathbf{if}\;x \leq -32495593.19127476:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 39972596664.81059:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(0.0001789971, t_3, \mathsf{fma}\left(0.0005064034, t_2, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, t_0, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right) \cdot \frac{1}{\mathsf{fma}\left(0.0003579942, {t_0}^{3}, \mathsf{fma}\left(t_3, 0.0008327945, \mathsf{fma}\left(t_2, 0.0140005442, \mathsf{fma}\left({\left(x \cdot x\right)}^{3}, 0.0694555761, \mathsf{fma}\left(t_0, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (pow x 3.0)))
        (t_1 (+ (/ 0.5 x) (/ 0.2514179000665374 (pow x 3.0))))
        (t_2 (pow t_0 2.0))
        (t_3 (* (* x x) t_2)))
   (if (<= x -32495593.19127476)
     t_1
     (if (<= x 39972596664.81059)
       (*
        x
        (*
         (fma
          0.0001789971
          t_3
          (fma
           0.0005064034
           t_2
           (fma
            0.0072644182
            (pow x 6.0)
            (fma 0.0424060604 t_0 (fma 0.1049934947 (* x x) 1.0)))))
         (/
          1.0
          (fma
           0.0003579942
           (pow t_0 3.0)
           (fma
            t_3
            0.0008327945
            (fma
             t_2
             0.0140005442
             (fma
              (pow (* x x) 3.0)
              0.0694555761
              (fma t_0 0.2909738639 (fma (* x x) 0.7715471019 1.0)))))))))
       t_1))))

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 * pow(x, 3.0);
	double t_1 = (0.5 / x) + (0.2514179000665374 / pow(x, 3.0));
	double t_2 = pow(t_0, 2.0);
	double t_3 = (x * x) * t_2;
	double tmp;
	if (x <= -32495593.19127476) {
		tmp = t_1;
	} else if (x <= 39972596664.81059) {
		tmp = x * (fma(0.0001789971, t_3, fma(0.0005064034, t_2, fma(0.0072644182, pow(x, 6.0), fma(0.0424060604, t_0, fma(0.1049934947, (x * x), 1.0))))) * (1.0 / fma(0.0003579942, pow(t_0, 3.0), fma(t_3, 0.0008327945, fma(t_2, 0.0140005442, fma(pow((x * x), 3.0), 0.0694555761, fma(t_0, 0.2909738639, fma((x * x), 0.7715471019, 1.0))))))));
	} else {
		tmp = t_1;
	}
	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 * (x ^ 3.0))
	t_1 = Float64(Float64(0.5 / x) + Float64(0.2514179000665374 / (x ^ 3.0)))
	t_2 = t_0 ^ 2.0
	t_3 = Float64(Float64(x * x) * t_2)
	tmp = 0.0
	if (x <= -32495593.19127476)
		tmp = t_1;
	elseif (x <= 39972596664.81059)
		tmp = Float64(x * Float64(fma(0.0001789971, t_3, fma(0.0005064034, t_2, fma(0.0072644182, (x ^ 6.0), fma(0.0424060604, t_0, fma(0.1049934947, Float64(x * x), 1.0))))) * Float64(1.0 / fma(0.0003579942, (t_0 ^ 3.0), fma(t_3, 0.0008327945, fma(t_2, 0.0140005442, fma((Float64(x * x) ^ 3.0), 0.0694555761, fma(t_0, 0.2909738639, fma(Float64(x * x), 0.7715471019, 1.0)))))))));
	else
		tmp = t_1;
	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[(x * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.5 / x), $MachinePrecision] + N[(0.2514179000665374 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$0, 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * x), $MachinePrecision] * t$95$2), $MachinePrecision]}, If[LessEqual[x, -32495593.19127476], t$95$1, If[LessEqual[x, 39972596664.81059], N[(x * N[(N[(0.0001789971 * t$95$3 + N[(0.0005064034 * t$95$2 + N[(0.0072644182 * N[Power[x, 6.0], $MachinePrecision] + N[(0.0424060604 * t$95$0 + N[(0.1049934947 * N[(x * x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(0.0003579942 * N[Power[t$95$0, 3.0], $MachinePrecision] + N[(t$95$3 * 0.0008327945 + N[(t$95$2 * 0.0140005442 + N[(N[Power[N[(x * x), $MachinePrecision], 3.0], $MachinePrecision] * 0.0694555761 + N[(t$95$0 * 0.2909738639 + N[(N[(x * x), $MachinePrecision] * 0.7715471019 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -32495593.1912747584 or 39972596664.810593 < x

   1. Initial program 60.5

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

   2. Applied egg-rr 60.5

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

   3. Taylor expanded in x around inf 0.0

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

   4. Simplified 0.0

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

   if -32495593.1912747584 < x < 39972596664.810593

   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

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

   3. Taylor expanded in x around 0 0.0

      \[\leadsto \left(\mathsf{fma}\left(0.0001789971, \left(x \cdot x\right) \cdot {\left({x}^{3} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0005064034, {\left({x}^{3} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0072644182, \color{blue}{{x}^{6}}, \mathsf{fma}\left(0.0424060604, {x}^{3} \cdot x, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right) \cdot \frac{1}{\mathsf{fma}\left(0.0003579942, {\left({x}^{3} \cdot x\right)}^{3}, \mathsf{fma}\left(\left(x \cdot x\right) \cdot {\left({x}^{3} \cdot x\right)}^{2}, 0.0008327945, \mathsf{fma}\left({\left({x}^{3} \cdot x\right)}^{2}, 0.0140005442, \mathsf{fma}\left({\left(x \cdot x\right)}^{3}, 0.0694555761, \mathsf{fma}\left({x}^{3} \cdot x, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}\right) \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32495593.19127476:\\ \;\;\;\;\frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\\ \mathbf{elif}\;x \leq 39972596664.81059:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(0.0001789971, \left(x \cdot x\right) \cdot {\left(x \cdot {x}^{3}\right)}^{2}, \mathsf{fma}\left(0.0005064034, {\left(x \cdot {x}^{3}\right)}^{2}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, x \cdot {x}^{3}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right) \cdot \frac{1}{\mathsf{fma}\left(0.0003579942, {\left(x \cdot {x}^{3}\right)}^{3}, \mathsf{fma}\left(\left(x \cdot x\right) \cdot {\left(x \cdot {x}^{3}\right)}^{2}, 0.0008327945, \mathsf{fma}\left({\left(x \cdot {x}^{3}\right)}^{2}, 0.0140005442, \mathsf{fma}\left({\left(x \cdot x\right)}^{3}, 0.0694555761, \mathsf{fma}\left(x \cdot {x}^{3}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022138 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
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