Average Error: 29.1 → 0.1
Time: 3.3s
Precision: binary64
\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
↓
\[\begin{array}{l} t_0 := {\left(x \cdot x\right)}^{5}\\ t_1 := \frac{0.2514179000665374}{{x}^{3}} + \frac{0.5}{x}\\ \mathbf{if}\;x \leq -74599.29493635755:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.128404978934228:\\ \;\;\;\;x \cdot \frac{\mathsf{fma}\left(0.0001789971, t_0, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.1049934947, x \cdot x, \mathsf{fma}\left(0.0424060604, {x}^{4}, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(t_0, 0.0008327945, \mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left(x, x \cdot 0.7715471019, \mathsf{fma}\left({x}^{4}, 0.2909738639, 1\right)\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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 (pow (* x x) 5.0))
        (t_1 (+ (/ 0.2514179000665374 (pow x 3.0)) (/ 0.5 x))))
   (if (<= x -74599.29493635755)
     t_1
     (if (<= x 4.128404978934228)
       (*
        x
        (/
         (fma
          0.0001789971
          t_0
          (fma
           0.0005064034
           (pow x 8.0)
           (fma
            0.0072644182
            (pow x 6.0)
            (fma 0.1049934947 (* x x) (fma 0.0424060604 (pow x 4.0) 1.0)))))
         (fma
          t_0
          0.0008327945
          (fma
           0.0003579942
           (pow x 12.0)
           (fma
            (pow x 6.0)
            0.0694555761
            (fma
             (pow x 8.0)
             0.0140005442
             (fma
              x
              (* x 0.7715471019)
              (fma (pow x 4.0) 0.2909738639 1.0))))))))
       t_1))))
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 = pow((x * x), 5.0);
	double t_1 = (0.2514179000665374 / pow(x, 3.0)) + (0.5 / x);
	double tmp;
	if (x <= -74599.29493635755) {
		tmp = t_1;
	} else if (x <= 4.128404978934228) {
		tmp = x * (fma(0.0001789971, t_0, fma(0.0005064034, pow(x, 8.0), fma(0.0072644182, pow(x, 6.0), fma(0.1049934947, (x * x), fma(0.0424060604, pow(x, 4.0), 1.0))))) / fma(t_0, 0.0008327945, fma(0.0003579942, pow(x, 12.0), fma(pow(x, 6.0), 0.0694555761, fma(pow(x, 8.0), 0.0140005442, fma(x, (x * 0.7715471019), fma(pow(x, 4.0), 0.2909738639, 1.0)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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) ^ 5.0
	t_1 = Float64(Float64(0.2514179000665374 / (x ^ 3.0)) + Float64(0.5 / x))
	tmp = 0.0
	if (x <= -74599.29493635755)
		tmp = t_1;
	elseif (x <= 4.128404978934228)
		tmp = Float64(x * Float64(fma(0.0001789971, t_0, fma(0.0005064034, (x ^ 8.0), fma(0.0072644182, (x ^ 6.0), fma(0.1049934947, Float64(x * x), fma(0.0424060604, (x ^ 4.0), 1.0))))) / fma(t_0, 0.0008327945, fma(0.0003579942, (x ^ 12.0), fma((x ^ 6.0), 0.0694555761, fma((x ^ 8.0), 0.0140005442, fma(x, Float64(x * 0.7715471019), fma((x ^ 4.0), 0.2909738639, 1.0))))))));
	else
		tmp = t_1;
	end
	return tmp
end

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[Power[N[(x * x), $MachinePrecision], 5.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.2514179000665374 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(0.5 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -74599.29493635755], t$95$1, If[LessEqual[x, 4.128404978934228], N[(x * N[(N[(0.0001789971 * t$95$0 + N[(0.0005064034 * N[Power[x, 8.0], $MachinePrecision] + N[(0.0072644182 * N[Power[x, 6.0], $MachinePrecision] + N[(0.1049934947 * N[(x * x), $MachinePrecision] + N[(0.0424060604 * N[Power[x, 4.0], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * 0.0008327945 + N[(0.0003579942 * N[Power[x, 12.0], $MachinePrecision] + N[(N[Power[x, 6.0], $MachinePrecision] * 0.0694555761 + N[(N[Power[x, 8.0], $MachinePrecision] * 0.0140005442 + N[(x * N[(x * 0.7715471019), $MachinePrecision] + N[(N[Power[x, 4.0], $MachinePrecision] * 0.2909738639 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$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
↓
\begin{array}{l}
t_0 := {\left(x \cdot x\right)}^{5}\\
t_1 := \frac{0.2514179000665374}{{x}^{3}} + \frac{0.5}{x}\\
\mathbf{if}\;x \leq -74599.29493635755:\\
\;\;\;\;t_1\\

\mathbf{elif}\;x \leq 4.128404978934228:\\
\;\;\;\;x \cdot \frac{\mathsf{fma}\left(0.0001789971, t_0, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.1049934947, x \cdot x, \mathsf{fma}\left(0.0424060604, {x}^{4}, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(t_0, 0.0008327945, \mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left(x, x \cdot 0.7715471019, \mathsf{fma}\left({x}^{4}, 0.2909738639, 1\right)\right)\right)\right)\right)\right)}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if x < -74599.2949363575462 or 4.1284049789342276 < x

    1. Initial program 59.3

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

    2. Taylor expanded in x around inf 0.1

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

    3. Simplified0.1

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

    if -74599.2949363575462 < x < 4.1284049789342276

    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. Simplified0.0

      \[\leadsto \color{blue}{x \cdot \frac{\mathsf{fma}\left(0.0001789971, {\left(x \cdot x\right)}^{5}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.1049934947, x \cdot x, \mathsf{fma}\left(0.0424060604, {x}^{4}, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left({\left(x \cdot x\right)}^{5}, 0.0008327945, \mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left(x, x \cdot 0.7715471019, \mathsf{fma}\left({x}^{4}, 0.2909738639, 1\right)\right)\right)\right)\right)\right)}} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -74599.29493635755:\\ \;\;\;\;\frac{0.2514179000665374}{{x}^{3}} + \frac{0.5}{x}\\ \mathbf{elif}\;x \leq 4.128404978934228:\\ \;\;\;\;x \cdot \frac{\mathsf{fma}\left(0.0001789971, {\left(x \cdot x\right)}^{5}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.1049934947, x \cdot x, \mathsf{fma}\left(0.0424060604, {x}^{4}, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left({\left(x \cdot x\right)}^{5}, 0.0008327945, \mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left(x, x \cdot 0.7715471019, \mathsf{fma}\left({x}^{4}, 0.2909738639, 1\right)\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.2514179000665374}{{x}^{3}} + \frac{0.5}{x}\\ \end{array} \]

Reproduce

herbie shell --seed 2022212 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
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