Jmat.Real.dawson

Average Error: 28.8 → 0.0

Time: 6.4s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\\ \mathbf{if}\;x \leq -3.453551448985941 \cdot 10^{+22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 632.6517676106561:\\ \;\;\;\;\begin{array}{l} t_1 := \sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}\\ \left(x \cdot \frac{1}{t_1}\right) \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{t_1} \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.15298196345929074}{{x}^{5}}\\ \end{array} \]

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 (+ (/ 0.5 x) (/ 0.2514179000665374 (pow x 3.0)))))
   (if (<= x -3.453551448985941e+22)
     t_0
     (if (<= x 632.6517676106561)
       (let* ((t_1
               (sqrt
                (fma
                 0.0003579942
                 (pow x 12.0)
                 (fma
                  (pow x 10.0)
                  0.0008327945
                  (fma
                   (pow x 8.0)
                   0.0140005442
                   (fma
                    (pow x 6.0)
                    0.0694555761
                    (fma
                     (pow x 4.0)
                     0.2909738639
                     (fma (* x x) 0.7715471019 1.0)))))))))
         (*
          (* x (/ 1.0 t_1))
          (/
           (fma
            0.0001789971
            (pow x 10.0)
            (fma
             0.0005064034
             (pow x 8.0)
             (fma
              0.0072644182
              (pow x 6.0)
              (fma 0.0424060604 (pow x 4.0) (fma 0.1049934947 (* x x) 1.0)))))
           t_1)))
       (+ t_0 (/ 0.15298196345929074 (pow x 5.0)))))))

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 = (0.5 / x) + (0.2514179000665374 / pow(x, 3.0));
	double tmp;
	if (x <= -3.453551448985941e+22) {
		tmp = t_0;
	} else if (x <= 632.6517676106561) {
		double t_1 = sqrt(fma(0.0003579942, pow(x, 12.0), fma(pow(x, 10.0), 0.0008327945, fma(pow(x, 8.0), 0.0140005442, fma(pow(x, 6.0), 0.0694555761, fma(pow(x, 4.0), 0.2909738639, fma((x * x), 0.7715471019, 1.0)))))));
		tmp = (x * (1.0 / t_1)) * (fma(0.0001789971, pow(x, 10.0), fma(0.0005064034, pow(x, 8.0), fma(0.0072644182, pow(x, 6.0), fma(0.0424060604, pow(x, 4.0), fma(0.1049934947, (x * x), 1.0))))) / t_1);
	} else {
		tmp = t_0 + (0.15298196345929074 / pow(x, 5.0));
	}
	return tmp;
}

Error

Bits error versus x

Derivation

1. Split input into 3 regimes

2. if x < -3.4535514489859412e22

   1. Initial program 63.2

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

   2. Simplified 63.2

      \[\leadsto \color{blue}{x \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}} \]

   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

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

   if -3.4535514489859412e22 < x < 632.651767610656066

   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. Simplified 0.0

      \[\leadsto \color{blue}{x \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}} \]

   3. Applied add-sqr-sqrt_binary64 0.1

      \[\leadsto x \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\color{blue}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)} \cdot \sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}}} \]

   4. Applied *-un-lft-identity_binary64 0.1

      \[\leadsto x \cdot \frac{\color{blue}{1 \cdot \mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)} \cdot \sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}} \]

   5. Applied times-frac_binary64 0.1

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}} \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}}\right)} \]

   6. Applied associate-*r*_binary64 0.1

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}}\right) \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}}} \]

   if 632.651767610656066 < x

   1. Initial program 59.7

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

   2. Simplified 59.7

      \[\leadsto \color{blue}{x \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}} \]

   3. Taylor expanded in x around inf 0.0

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

   4. Simplified 0.0

      \[\leadsto \color{blue}{\left(\frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\right) + \frac{0.15298196345929074}{{x}^{5}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.453551448985941 \cdot 10^{+22}:\\ \;\;\;\;\frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\\ \mathbf{elif}\;x \leq 632.6517676106561:\\ \;\;\;\;\left(x \cdot \frac{1}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}}\right) \cdot \frac{\mathsf{fma}\left(0.0001789971, {x}^{10}, \mathsf{fma}\left(0.0005064034, {x}^{8}, \mathsf{fma}\left(0.0072644182, {x}^{6}, \mathsf{fma}\left(0.0424060604, {x}^{4}, \mathsf{fma}\left(0.1049934947, x \cdot x, 1\right)\right)\right)\right)\right)}{\sqrt{\mathsf{fma}\left(0.0003579942, {x}^{12}, \mathsf{fma}\left({x}^{10}, 0.0008327945, \mathsf{fma}\left({x}^{8}, 0.0140005442, \mathsf{fma}\left({x}^{6}, 0.0694555761, \mathsf{fma}\left({x}^{4}, 0.2909738639, \mathsf{fma}\left(x \cdot x, 0.7715471019, 1\right)\right)\right)\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{x} + \frac{0.2514179000665374}{{x}^{3}}\right) + \frac{0.15298196345929074}{{x}^{5}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022125 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
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