Average Error: 29.3 → 0.0
Time: 3.3s
Precision: binary64
\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
↓
\[\begin{array}{l} t_0 := {\left(x \cdot x\right)}^{2}\\ t_1 := \frac{0.15298196345929074}{{x}^{5}} + \left(\frac{0.5}{x} + \mathsf{fma}\left(0.2514179000665374, {x}^{-3}, 11.259630434457211 \cdot {x}^{-7}\right)\right)\\ t_2 := {\left(x \cdot x\right)}^{3}\\ t_3 := {\left(x \cdot x\right)}^{5}\\ \mathbf{if}\;x \leq -7.047516478362811 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 107.82553502604974:\\ \;\;\;\;x \cdot \frac{\left(1 + x \cdot \left(x \cdot 0.1049934947\right)\right) + \left(\mathsf{fma}\left(0.0424060604, t_0, 0.0072644182 \cdot t_2\right) + \mathsf{fma}\left(0.0005064034, \left(x \cdot x\right) \cdot t_2, 0.0001789971 \cdot t_3\right)\right)}{\left(1 + \mathsf{fma}\left(x \cdot x, 0.7715471019, t_0 \cdot 0.2909738639\right)\right) + \left(\mathsf{fma}\left(t_2, 0.0694555761, \left(x \cdot x\right) \cdot \left(t_2 \cdot 0.0140005442\right)\right) + \mathsf{fma}\left(t_3, 0.0008327945, 0.0003579942 \cdot \left(\left(x \cdot x\right) \cdot t_3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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) 2.0))
        (t_1
         (+
          (/ 0.15298196345929074 (pow x 5.0))
          (+
           (/ 0.5 x)
           (fma
            0.2514179000665374
            (pow x -3.0)
            (* 11.259630434457211 (pow x -7.0))))))
        (t_2 (pow (* x x) 3.0))
        (t_3 (pow (* x x) 5.0)))
   (if (<= x -7.047516478362811e+25)
     t_1
     (if (<= x 107.82553502604974)
       (*
        x
        (/
         (+
          (+ 1.0 (* x (* x 0.1049934947)))
          (+
           (fma 0.0424060604 t_0 (* 0.0072644182 t_2))
           (fma 0.0005064034 (* (* x x) t_2) (* 0.0001789971 t_3))))
         (+
          (+ 1.0 (fma (* x x) 0.7715471019 (* t_0 0.2909738639)))
          (+
           (fma t_2 0.0694555761 (* (* x x) (* t_2 0.0140005442)))
           (fma t_3 0.0008327945 (* 0.0003579942 (* (* x x) t_3)))))))
       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), 2.0);
	double t_1 = (0.15298196345929074 / pow(x, 5.0)) + ((0.5 / x) + fma(0.2514179000665374, pow(x, -3.0), (11.259630434457211 * pow(x, -7.0))));
	double t_2 = pow((x * x), 3.0);
	double t_3 = pow((x * x), 5.0);
	double tmp;
	if (x <= -7.047516478362811e+25) {
		tmp = t_1;
	} else if (x <= 107.82553502604974) {
		tmp = x * (((1.0 + (x * (x * 0.1049934947))) + (fma(0.0424060604, t_0, (0.0072644182 * t_2)) + fma(0.0005064034, ((x * x) * t_2), (0.0001789971 * t_3)))) / ((1.0 + fma((x * x), 0.7715471019, (t_0 * 0.2909738639))) + (fma(t_2, 0.0694555761, ((x * x) * (t_2 * 0.0140005442))) + fma(t_3, 0.0008327945, (0.0003579942 * ((x * x) * t_3))))));
	} 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) ^ 2.0
	t_1 = Float64(Float64(0.15298196345929074 / (x ^ 5.0)) + Float64(Float64(0.5 / x) + fma(0.2514179000665374, (x ^ -3.0), Float64(11.259630434457211 * (x ^ -7.0)))))
	t_2 = Float64(x * x) ^ 3.0
	t_3 = Float64(x * x) ^ 5.0
	tmp = 0.0
	if (x <= -7.047516478362811e+25)
		tmp = t_1;
	elseif (x <= 107.82553502604974)
		tmp = Float64(x * Float64(Float64(Float64(1.0 + Float64(x * Float64(x * 0.1049934947))) + Float64(fma(0.0424060604, t_0, Float64(0.0072644182 * t_2)) + fma(0.0005064034, Float64(Float64(x * x) * t_2), Float64(0.0001789971 * t_3)))) / Float64(Float64(1.0 + fma(Float64(x * x), 0.7715471019, Float64(t_0 * 0.2909738639))) + Float64(fma(t_2, 0.0694555761, Float64(Float64(x * x) * Float64(t_2 * 0.0140005442))) + fma(t_3, 0.0008327945, Float64(0.0003579942 * Float64(Float64(x * x) * t_3)))))));
	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], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.15298196345929074 / N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 / x), $MachinePrecision] + N[(0.2514179000665374 * N[Power[x, -3.0], $MachinePrecision] + N[(11.259630434457211 * N[Power[x, -7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(x * x), $MachinePrecision], 3.0], $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(x * x), $MachinePrecision], 5.0], $MachinePrecision]}, If[LessEqual[x, -7.047516478362811e+25], t$95$1, If[LessEqual[x, 107.82553502604974], N[(x * N[(N[(N[(1.0 + N[(x * N[(x * 0.1049934947), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0424060604 * t$95$0 + N[(0.0072644182 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0005064034 * N[(N[(x * x), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(0.0001789971 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * 0.7715471019 + N[(t$95$0 * 0.2909738639), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * 0.0694555761 + N[(N[(x * x), $MachinePrecision] * N[(t$95$2 * 0.0140005442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * 0.0008327945 + N[(0.0003579942 * N[(N[(x * x), $MachinePrecision] * t$95$3), $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)}^{2}\\
t_1 := \frac{0.15298196345929074}{{x}^{5}} + \left(\frac{0.5}{x} + \mathsf{fma}\left(0.2514179000665374, {x}^{-3}, 11.259630434457211 \cdot {x}^{-7}\right)\right)\\
t_2 := {\left(x \cdot x\right)}^{3}\\
t_3 := {\left(x \cdot x\right)}^{5}\\
\mathbf{if}\;x \leq -7.047516478362811 \cdot 10^{+25}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;x \leq 107.82553502604974:\\
\;\;\;\;x \cdot \frac{\left(1 + x \cdot \left(x \cdot 0.1049934947\right)\right) + \left(\mathsf{fma}\left(0.0424060604, t_0, 0.0072644182 \cdot t_2\right) + \mathsf{fma}\left(0.0005064034, \left(x \cdot x\right) \cdot t_2, 0.0001789971 \cdot t_3\right)\right)}{\left(1 + \mathsf{fma}\left(x \cdot x, 0.7715471019, t_0 \cdot 0.2909738639\right)\right) + \left(\mathsf{fma}\left(t_2, 0.0694555761, \left(x \cdot x\right) \cdot \left(t_2 \cdot 0.0140005442\right)\right) + \mathsf{fma}\left(t_3, 0.0008327945, 0.0003579942 \cdot \left(\left(x \cdot x\right) \cdot t_3\right)\right)\right)}\\

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


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if x < -7.04751647836281076e25 or 107.825535026049735 < x

    1. Initial program 61.4

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

    2. Taylor expanded in x around inf 0.0

      \[\leadsto \color{blue}{0.2514179000665374 \cdot \frac{1}{{x}^{3}} + \left(0.15298196345929074 \cdot \frac{1}{{x}^{5}} + \left(11.259630434457211 \cdot \frac{1}{{x}^{7}} + 0.5 \cdot \frac{1}{x}\right)\right)} \]

    3. Simplified0.0

      \[\leadsto \color{blue}{\frac{0.15298196345929074}{{x}^{5}} + \left(\frac{0.5}{x} + \left(\frac{0.2514179000665374}{{x}^{3}} + \frac{11.259630434457211}{{x}^{7}}\right)\right)} \]

    4. Applied egg-rr0.0

      \[\leadsto \frac{0.15298196345929074}{{x}^{5}} + \left(\frac{0.5}{x} + \color{blue}{\mathsf{fma}\left(0.2514179000665374, {x}^{-3}, 11.259630434457211 \cdot {x}^{-7}\right)}\right) \]

    if -7.04751647836281076e25 < x < 107.825535026049735

    1. Initial program 0.1

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

    2. Applied egg-rr0.1

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

    3. Applied egg-rr0.1

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.047516478362811 \cdot 10^{+25}:\\ \;\;\;\;\frac{0.15298196345929074}{{x}^{5}} + \left(\frac{0.5}{x} + \mathsf{fma}\left(0.2514179000665374, {x}^{-3}, 11.259630434457211 \cdot {x}^{-7}\right)\right)\\ \mathbf{elif}\;x \leq 107.82553502604974:\\ \;\;\;\;x \cdot \frac{\left(1 + x \cdot \left(x \cdot 0.1049934947\right)\right) + \left(\mathsf{fma}\left(0.0424060604, {\left(x \cdot x\right)}^{2}, 0.0072644182 \cdot {\left(x \cdot x\right)}^{3}\right) + \mathsf{fma}\left(0.0005064034, \left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{3}, 0.0001789971 \cdot {\left(x \cdot x\right)}^{5}\right)\right)}{\left(1 + \mathsf{fma}\left(x \cdot x, 0.7715471019, {\left(x \cdot x\right)}^{2} \cdot 0.2909738639\right)\right) + \left(\mathsf{fma}\left({\left(x \cdot x\right)}^{3}, 0.0694555761, \left(x \cdot x\right) \cdot \left({\left(x \cdot x\right)}^{3} \cdot 0.0140005442\right)\right) + \mathsf{fma}\left({\left(x \cdot x\right)}^{5}, 0.0008327945, 0.0003579942 \cdot \left(\left(x \cdot x\right) \cdot {\left(x \cdot x\right)}^{5}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.15298196345929074}{{x}^{5}} + \left(\frac{0.5}{x} + \mathsf{fma}\left(0.2514179000665374, {x}^{-3}, 11.259630434457211 \cdot {x}^{-7}\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022204 
(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))