Jmat.Real.dawson

Average Error: 29.6 → 0.0

Time: 22.2s

Precision: binary64

Cost: 150984

Math

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

↓

\[\begin{array}{l} t_0 := {\left({x}^{4}\right)}^{2}\\ t_1 := {\left(x \cdot x\right)}^{3}\\ t_2 := {\left({x}^{3}\right)}^{3} \cdot x\\ \mathbf{if}\;x \leq -46000000:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 20000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.0001789971, t_2, \mathsf{fma}\left(t_0, 0.0005064034, \mathsf{fma}\left(t_1, 0.0072644182, \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(x \cdot x, 0.0424060604, 0.1049934947\right), 1\right)\right)\right)\right)}{\mathsf{fma}\left(0.0003579942, {\left({x}^{4}\right)}^{3}, \mathsf{fma}\left(t_2, 0.0008327945, \mathsf{fma}\left(t_0, 0.0140005442, \mathsf{fma}\left(t_1, 0.0694555761, \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right), 1\right)\right)\right)\right)\right)} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

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 (pow (pow x 4.0) 2.0))
        (t_1 (pow (* x x) 3.0))
        (t_2 (* (pow (pow x 3.0) 3.0) x)))
   (if (<= x -46000000.0)
     (/ 0.5 x)
     (if (<= x 20000000.0)
       (*
        (/
         (fma
          0.0001789971
          t_2
          (fma
           t_0
           0.0005064034
           (fma
            t_1
            0.0072644182
            (fma (* x x) (fma (* x x) 0.0424060604 0.1049934947) 1.0))))
         (fma
          0.0003579942
          (pow (pow x 4.0) 3.0)
          (fma
           t_2
           0.0008327945
           (fma
            t_0
            0.0140005442
            (fma
             t_1
             0.0694555761
             (fma (* x x) (fma (* 0.2909738639 x) x 0.7715471019) 1.0))))))
        x)
       (/ 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 = pow(pow(x, 4.0), 2.0);
	double t_1 = pow((x * x), 3.0);
	double t_2 = pow(pow(x, 3.0), 3.0) * x;
	double tmp;
	if (x <= -46000000.0) {
		tmp = 0.5 / x;
	} else if (x <= 20000000.0) {
		tmp = (fma(0.0001789971, t_2, fma(t_0, 0.0005064034, fma(t_1, 0.0072644182, fma((x * x), fma((x * x), 0.0424060604, 0.1049934947), 1.0)))) / fma(0.0003579942, pow(pow(x, 4.0), 3.0), fma(t_2, 0.0008327945, fma(t_0, 0.0140005442, fma(t_1, 0.0694555761, fma((x * x), fma((0.2909738639 * x), x, 0.7715471019), 1.0)))))) * x;
	} 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 = (x ^ 4.0) ^ 2.0
	t_1 = Float64(x * x) ^ 3.0
	t_2 = Float64(((x ^ 3.0) ^ 3.0) * x)
	tmp = 0.0
	if (x <= -46000000.0)
		tmp = Float64(0.5 / x);
	elseif (x <= 20000000.0)
		tmp = Float64(Float64(fma(0.0001789971, t_2, fma(t_0, 0.0005064034, fma(t_1, 0.0072644182, fma(Float64(x * x), fma(Float64(x * x), 0.0424060604, 0.1049934947), 1.0)))) / fma(0.0003579942, ((x ^ 4.0) ^ 3.0), fma(t_2, 0.0008327945, fma(t_0, 0.0140005442, fma(t_1, 0.0694555761, fma(Float64(x * x), fma(Float64(0.2909738639 * x), x, 0.7715471019), 1.0)))))) * x);
	else
		tmp = Float64(0.5 / x);
	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[Power[N[Power[x, 4.0], $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(x * x), $MachinePrecision], 3.0], $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[N[Power[x, 3.0], $MachinePrecision], 3.0], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -46000000.0], N[(0.5 / x), $MachinePrecision], If[LessEqual[x, 20000000.0], N[(N[(N[(0.0001789971 * t$95$2 + N[(t$95$0 * 0.0005064034 + N[(t$95$1 * 0.0072644182 + N[(N[(x * x), $MachinePrecision] * N[(N[(x * x), $MachinePrecision] * 0.0424060604 + 0.1049934947), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.0003579942 * N[Power[N[Power[x, 4.0], $MachinePrecision], 3.0], $MachinePrecision] + N[(t$95$2 * 0.0008327945 + N[(t$95$0 * 0.0140005442 + N[(t$95$1 * 0.0694555761 + N[(N[(x * x), $MachinePrecision] * N[(N[(0.2909738639 * x), $MachinePrecision] * x + 0.7715471019), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e7 or 2e7 < 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. Taylor expanded in x around inf 0.0

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

   if -4.6e7 < x < 2e7

   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

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

   3. Simplified 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	11336

\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ t_1 := t_0 \cdot \left(x \cdot x\right)\\ t_2 := t_1 \cdot \left(x \cdot x\right)\\ t_3 := t_2 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -20000000000000:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot t_0\right) + 0.0072644182 \cdot t_1\right) + 0.0005064034 \cdot t_2\right) + 0.0001789971 \cdot t_3}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot t_0\right) + 0.0694555761 \cdot t_1\right) + 0.0140005442 \cdot t_2\right) + 0.0008327945 \cdot t_3\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(t_3 \cdot \left(x \cdot x\right)\right)} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 2
Error	0.4
Cost	968

\[\begin{array}{l} \mathbf{if}\;x \leq -0.78:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 0.95:\\ \;\;\;\;\left(x \cdot \left(-0.6665536072 \cdot x\right)\right) \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.2514179000665374}{x \cdot x}}{x} + \frac{0.5}{x}\\ \end{array} \]

Alternative 3
Error	0.5
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -0.78:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;\left(x \cdot \left(-0.6665536072 \cdot x\right)\right) \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 4
Error	0.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.7:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;x \leq 0.72:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 5
Error	31.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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))