Jmat.Real.dawson

Average Error: 28.8 → 0.0

Time: 17.2s

Precision: 64

Math

\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -860.66640155127811 \lor \neg \left(x \le 820.60219200991969\right):\\ \;\;\;\;0.25141790006653753 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592933 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right)\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.069455576099999999 + 1\right) + {x}^{2} \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.32794500000000044 \cdot 10^{-4} \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)}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}} \cdot x\\ \end{array}\]

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 temp;
	if (((x <= -860.6664015512781) || !(x <= 820.6021920099197))) {
		temp = ((0.2514179000665375 * (1.0 / pow(x, 3.0))) + ((0.15298196345929327 * (1.0 / pow(x, 5.0))) + (0.5 * (1.0 / x))));
	} else {
		temp = ((1.0 / ((((((pow(x, 2.0) * (pow(x, 2.0) * (pow(x, 2.0) * (pow(x, 2.0) * (x * pow(x, 3.0)))))) * (2.0 * 0.0001789971)) + ((((pow(x, 2.0) * (x * pow(x, 3.0))) * 0.0694555761) + 1.0) + (pow(x, 2.0) * (0.7715471019 + (0.2909738639 * pow(x, 2.0)))))) + (pow(x, 2.0) * ((0.0140005442 * (((x * x) * x) * ((x * x) * x))) + (0.0008327945 * ((((x * x) * (x * x)) * (x * x)) * (x * x)))))) / sqrt(((((pow(x, 2.0) * (pow(x, 2.0) * (pow(x, 2.0) * (x * pow(x, 3.0))))) * 0.0001789971) + ((((pow(x, 2.0) * (x * pow(x, 3.0))) * 0.0072644182) + 1.0) + (pow(x, 2.0) * (0.1049934947 + (0.0424060604 * pow(x, 2.0)))))) + ((pow(x, 2.0) * (pow(x, 2.0) * (x * pow(x, 3.0)))) * 0.0005064034)))) / sqrt(((((pow(x, 2.0) * (pow(x, 2.0) * (pow(x, 2.0) * (x * pow(x, 3.0))))) * 0.0001789971) + ((((pow(x, 2.0) * (x * pow(x, 3.0))) * 0.0072644182) + 1.0) + (pow(x, 2.0) * (0.1049934947 + (0.0424060604 * pow(x, 2.0)))))) + ((pow(x, 2.0) * (pow(x, 2.0) * (x * pow(x, 3.0)))) * 0.0005064034))))) * x);
	}
	return temp;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -860.6664015512781 or 820.6021920099197 < x

   1. Initial program 59.1

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

   2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{0.25141790006653753 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592933 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

   if -860.6664015512781 < x < 820.6021920099197

   1. Initial program 0.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
   2. Using strategy rm

   3. Applied clear-num 0.0

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}}} \cdot x\]

   4. Simplified 0.0

      \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right)\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.069455576099999999 + 1\right) + {x}^{2} \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}} \cdot x\]
   5. Using strategy rm

   6. Applied add-sqr-sqrt 0.0

      \[\leadsto \frac{1}{\frac{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right)\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.069455576099999999 + 1\right) + {x}^{2} \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}{\color{blue}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}} \cdot \sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}}} \cdot x\]

   7. Applied associate-/r* 0.0

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right)\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.069455576099999999 + 1\right) + {x}^{2} \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}}} \cdot x\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -860.66640155127811 \lor \neg \left(x \le 820.60219200991969\right):\\ \;\;\;\;0.25141790006653753 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592933 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right)\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.069455576099999999 + 1\right) + {x}^{2} \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.32794500000000044 \cdot 10^{-4} \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)}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}}{\sqrt{\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.00726441819999999999 + 1\right) + {x}^{2} \cdot \left(0.1049934947 + 0.042406060400000001 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.0640340000000002 \cdot 10^{-4}}}} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 1 (* 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 (* 0.7715471019 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))