Jmat.Real.dawson

Average Error: 29.3 → 0.0

Time: 9.7s

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 -698637805588.42065 \lor \neg \left(x \le 682.61274732817924\right):\\ \;\;\;\;\mathsf{fma}\left(0.251417900066537248, \frac{1}{{x}^{3}}, \mathsf{fma}\left(0.1529819634592924, \frac{1}{{x}^{5}}, 0.5 \cdot \frac{1}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \left(x \cdot \mathsf{fma}\left(2 \cdot 1.789971 \cdot 10^{-4}, {x}^{8} \cdot {x}^{4}, -\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + x \cdot \left(\left(-{x}^{2}\right) \cdot \mathsf{fma}\left(0.014000544199999999, {x}^{6}, {x}^{8} \cdot 8.32794500000000044 \cdot 10^{-4}\right)\right)\right)\\ \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 VAR;
	if (((x <= -698637805588.4207) || !(x <= 682.6127473281792))) {
		VAR = fma(0.25141790006653725, (1.0 / pow(x, 3.0)), fma(0.15298196345929238, (1.0 / pow(x, 5.0)), (0.5 * (1.0 / x))));
	} else {
		VAR = ((-fma((0.0001789971 * pow(x, 6.0)), pow(x, 4.0), fma((0.0005064034 * pow(x, 7.0)), x, fma(0.0072644182, pow(x, 6.0), fma(0.0424060604, pow(x, 4.0), fma((0.1049934947 * x), x, 1.0))))) / (((-fma(0.0694555761, pow(x, 6.0), fma(0.2909738639, pow(x, 4.0), fma((0.7715471019 * x), x, 1.0))) + -fma((0.0140005442 * (((x * x) * (x * x)) * (x * x))), pow(x, 2.0), (0.0008327945 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x))))) * (-fma(0.0694555761, pow(x, 6.0), fma(0.2909738639, pow(x, 4.0), fma((0.7715471019 * x), x, 1.0))) + -fma((0.0140005442 * (((x * x) * (x * x)) * (x * x))), pow(x, 2.0), (0.0008327945 * (((((x * x) * (x * x)) * (x * x)) * (x * x)) * (x * x)))))) - ((((2.0 * 0.0001789971) * pow(x, 8.0)) * pow(x, 4.0)) * (((2.0 * 0.0001789971) * pow(x, 8.0)) * pow(x, 4.0))))) * ((x * fma((2.0 * 0.0001789971), (pow(x, 8.0) * pow(x, 4.0)), -fma(0.0694555761, pow(x, 6.0), fma(0.2909738639, pow(x, 4.0), fma((0.7715471019 * x), x, 1.0))))) + (x * (-pow(x, 2.0) * fma(0.0140005442, pow(x, 6.0), (pow(x, 8.0) * 0.0008327945))))));
	}
	return VAR;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -698637805588.4207 or 682.6127473281792 < x

   1. Initial program 59.7

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

   3. Applied frac-2neg 59.7

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

   4. Simplified 59.8

      \[\leadsto \frac{\color{blue}{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}}{-\left(\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)} \cdot x\]

   5. Simplified 59.6

      \[\leadsto \frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\color{blue}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right) - \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}}} \cdot x\]
   6. Using strategy rm

   7. Applied flip-- 62.6

      \[\leadsto \frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\color{blue}{\frac{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) + \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}}}} \cdot x\]

   8. Applied associate-/r/ 62.6

      \[\leadsto \color{blue}{\left(\frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \left(\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) + \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)\right)} \cdot x\]

   9. Applied associate-*l* 62.6

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \left(\left(\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) + \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot x\right)}\]

   10. Simplified 62.6

       \[\leadsto \frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(2 \cdot 1.789971 \cdot 10^{-4}, {x}^{8} \cdot {x}^{4}, -\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + x \cdot \left(\left(-{x}^{2}\right) \cdot \mathsf{fma}\left(0.014000544199999999, {x}^{6}, {x}^{8} \cdot 8.32794500000000044 \cdot 10^{-4}\right)\right)\right)}\]

   11. Taylor expanded around inf 0.0

       \[\leadsto \color{blue}{0.251417900066537248 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592924 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

   12. Simplified 0.0

       \[\leadsto \color{blue}{\mathsf{fma}\left(0.251417900066537248, \frac{1}{{x}^{3}}, \mathsf{fma}\left(0.1529819634592924, \frac{1}{{x}^{5}}, 0.5 \cdot \frac{1}{x}\right)\right)}\]

   if -698637805588.4207 < x < 682.6127473281792

   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 frac-2neg 0.0

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

   4. Simplified 0.0

      \[\leadsto \frac{\color{blue}{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}}{-\left(\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)} \cdot x\]

   5. Simplified 0.0

      \[\leadsto \frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\color{blue}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)\right)\right) - \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}}} \cdot x\]
   6. Using strategy rm

   7. Applied flip-- 0.0

      \[\leadsto \frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\color{blue}{\frac{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) + \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}}}} \cdot x\]

   8. Applied associate-/r/ 0.0

      \[\leadsto \color{blue}{\left(\frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \left(\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) + \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)\right)} \cdot x\]

   9. Applied associate-*l* 0.0

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \left(\left(\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) + \left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot x\right)}\]

   10. Simplified 0.0

       \[\leadsto \frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(2 \cdot 1.789971 \cdot 10^{-4}, {x}^{8} \cdot {x}^{4}, -\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + x \cdot \left(\left(-{x}^{2}\right) \cdot \mathsf{fma}\left(0.014000544199999999, {x}^{6}, {x}^{8} \cdot 8.32794500000000044 \cdot 10^{-4}\right)\right)\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -698637805588.42065 \lor \neg \left(x \le 682.61274732817924\right):\\ \;\;\;\;\mathsf{fma}\left(0.251417900066537248, \frac{1}{{x}^{3}}, \mathsf{fma}\left(0.1529819634592924, \frac{1}{{x}^{5}}, 0.5 \cdot \frac{1}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{6}, {x}^{4}, \mathsf{fma}\left(5.0640340000000002 \cdot 10^{-4} \cdot {x}^{7}, x, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left(0.042406060400000001, {x}^{4}, \mathsf{fma}\left(0.1049934947 \cdot x, x, 1\right)\right)\right)\right)\right)}{\left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) \cdot \left(\left(-\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + \left(-\mathsf{fma}\left(0.014000544199999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right), {x}^{2}, 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)\right)\right) - \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right) \cdot \left(\left(\left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot {x}^{8}\right) \cdot {x}^{4}\right)} \cdot \left(x \cdot \mathsf{fma}\left(2 \cdot 1.789971 \cdot 10^{-4}, {x}^{8} \cdot {x}^{4}, -\mathsf{fma}\left(0.069455576099999999, {x}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right)\right)\right) + x \cdot \left(\left(-{x}^{2}\right) \cdot \mathsf{fma}\left(0.014000544199999999, {x}^{6}, {x}^{8} \cdot 8.32794500000000044 \cdot 10^{-4}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(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))