Jmat.Real.dawson

Average Error: 29.3 → 0.0

Time: 7.2m

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -11921922.1905300114 \lor \neg \left(x \le 341298.60975052114\right):\\ \;\;\;\;0.2514179000665369 \cdot \frac{1}{{x}^{3}} + \left(0.152981963459283 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}\\ \end{array}\]

C

double f(double x) {
        double r1528155 = 1.0;
        double r1528156 = 0.1049934947;
        double r1528157 = x;
        double r1528158 = r1528157 * r1528157;
        double r1528159 = r1528156 * r1528158;
        double r1528160 = r1528155 + r1528159;
        double r1528161 = 0.0424060604;
        double r1528162 = r1528158 * r1528158;
        double r1528163 = r1528161 * r1528162;
        double r1528164 = r1528160 + r1528163;
        double r1528165 = 0.0072644182;
        double r1528166 = r1528162 * r1528158;
        double r1528167 = r1528165 * r1528166;
        double r1528168 = r1528164 + r1528167;
        double r1528169 = 0.0005064034;
        double r1528170 = r1528166 * r1528158;
        double r1528171 = r1528169 * r1528170;
        double r1528172 = r1528168 + r1528171;
        double r1528173 = 0.0001789971;
        double r1528174 = r1528170 * r1528158;
        double r1528175 = r1528173 * r1528174;
        double r1528176 = r1528172 + r1528175;
        double r1528177 = 0.7715471019;
        double r1528178 = r1528177 * r1528158;
        double r1528179 = r1528155 + r1528178;
        double r1528180 = 0.2909738639;
        double r1528181 = r1528180 * r1528162;
        double r1528182 = r1528179 + r1528181;
        double r1528183 = 0.0694555761;
        double r1528184 = r1528183 * r1528166;
        double r1528185 = r1528182 + r1528184;
        double r1528186 = 0.0140005442;
        double r1528187 = r1528186 * r1528170;
        double r1528188 = r1528185 + r1528187;
        double r1528189 = 0.0008327945;
        double r1528190 = r1528189 * r1528174;
        double r1528191 = r1528188 + r1528190;
        double r1528192 = 2.0;
        double r1528193 = r1528192 * r1528173;
        double r1528194 = r1528174 * r1528158;
        double r1528195 = r1528193 * r1528194;
        double r1528196 = r1528191 + r1528195;
        double r1528197 = r1528176 / r1528196;
        double r1528198 = r1528197 * r1528157;
        return r1528198;
}

↓

double f(double x) {
        double r1528199 = x;
        double r1528200 = -11921922.190530011;
        bool r1528201 = r1528199 <= r1528200;
        double r1528202 = 341298.60975052114;
        bool r1528203 = r1528199 <= r1528202;
        double r1528204 = !r1528203;
        bool r1528205 = r1528201 || r1528204;
        double r1528206 = 0.25141790006653686;
        double r1528207 = 1.0;
        double r1528208 = 3.0;
        double r1528209 = pow(r1528199, r1528208);
        double r1528210 = r1528207 / r1528209;
        double r1528211 = r1528206 * r1528210;
        double r1528212 = 0.1529819634592826;
        double r1528213 = 5.0;
        double r1528214 = pow(r1528199, r1528213);
        double r1528215 = r1528207 / r1528214;
        double r1528216 = r1528212 * r1528215;
        double r1528217 = 0.5;
        double r1528218 = r1528207 / r1528199;
        double r1528219 = r1528217 * r1528218;
        double r1528220 = r1528216 + r1528219;
        double r1528221 = r1528211 + r1528220;
        double r1528222 = r1528199 * r1528199;
        double r1528223 = pow(r1528222, r1528208);
        double r1528224 = r1528223 * r1528209;
        double r1528225 = r1528199 * r1528224;
        double r1528226 = 0.0008327945;
        double r1528227 = 2.0;
        double r1528228 = 0.0001789971;
        double r1528229 = r1528227 * r1528228;
        double r1528230 = r1528222 * r1528229;
        double r1528231 = r1528226 + r1528230;
        double r1528232 = r1528225 * r1528231;
        double r1528233 = 0.7715471019;
        double r1528234 = 0.2909738639;
        double r1528235 = r1528234 * r1528222;
        double r1528236 = r1528233 + r1528235;
        double r1528237 = r1528222 * r1528236;
        double r1528238 = 1.0;
        double r1528239 = r1528237 + r1528238;
        double r1528240 = r1528232 + r1528239;
        double r1528241 = 6.0;
        double r1528242 = pow(r1528199, r1528241);
        double r1528243 = 0.0694555761;
        double r1528244 = 0.0140005442;
        double r1528245 = r1528222 * r1528244;
        double r1528246 = r1528243 + r1528245;
        double r1528247 = r1528242 * r1528246;
        double r1528248 = r1528240 + r1528247;
        double r1528249 = r1528199 / r1528248;
        double r1528250 = 4.0;
        double r1528251 = pow(r1528222, r1528250);
        double r1528252 = 0.0005064034;
        double r1528253 = r1528222 * r1528228;
        double r1528254 = r1528252 + r1528253;
        double r1528255 = r1528251 * r1528254;
        double r1528256 = 0.1049934947;
        double r1528257 = r1528256 * r1528222;
        double r1528258 = r1528238 + r1528257;
        double r1528259 = r1528255 + r1528258;
        double r1528260 = pow(r1528199, r1528250);
        double r1528261 = 0.0424060604;
        double r1528262 = 0.0072644182;
        double r1528263 = r1528222 * r1528262;
        double r1528264 = r1528261 + r1528263;
        double r1528265 = r1528260 * r1528264;
        double r1528266 = r1528259 + r1528265;
        double r1528267 = r1528207 / r1528266;
        double r1528268 = r1528249 / r1528267;
        double r1528269 = r1528205 ? r1528221 : r1528268;
        return r1528269;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -11921922.190530011 or 341298.60975052114 < x

   1. Initial program 59.8

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

   2. Simplified 59.8

      \[\leadsto \color{blue}{\frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}}\]
   3. Using strategy rm

   4. Applied div-inv 59.8

      \[\leadsto \frac{x}{\color{blue}{\left(\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)\right) \cdot \frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}}\]

   5. Applied associate-/r* 59.8

      \[\leadsto \color{blue}{\frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}}\]
   6. Using strategy rm

   7. Applied flip3-+ 59.8

      \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \color{blue}{\frac{{0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}}{0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)}}}}\]

   8. Applied associate-*r/ 59.8

      \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + \color{blue}{\frac{{x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)}{0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)}}}}\]

   9. Applied flip-+ 59.8

      \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \color{blue}{\frac{1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)}{1 - 0.1049934947 \cdot \left(x \cdot x\right)}}\right) + \frac{{x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)}{0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)}}}\]

   10. Applied flip3-+ 59.8

       \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \color{blue}{\frac{{\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}}{5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)}} + \frac{1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)}{1 - 0.1049934947 \cdot \left(x \cdot x\right)}\right) + \frac{{x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)}{0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)}}}\]

   11. Applied associate-*r/ 60.5

       \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left(\color{blue}{\frac{{\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)}{5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)}} + \frac{1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)}{1 - 0.1049934947 \cdot \left(x \cdot x\right)}\right) + \frac{{x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)}{0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)}}}\]

   12. Applied frac-add 61.1

       \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\color{blue}{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)}{\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)}} + \frac{{x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)}{0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)}}}\]

   13. Applied frac-add 62.0

       \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\color{blue}{\frac{\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)}{\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)}}}}\]

   14. Applied associate-/r/ 62.0

       \[\leadsto \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\color{blue}{\frac{1}{\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)} \cdot \left(\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)\right)}}\]

   15. Applied *-un-lft-identity 62.0

       \[\leadsto \frac{\frac{x}{\color{blue}{1 \cdot \left(\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)\right)}}}{\frac{1}{\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)} \cdot \left(\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)\right)}\]

   16. Applied *-un-lft-identity 62.0

       \[\leadsto \frac{\frac{\color{blue}{1 \cdot x}}{1 \cdot \left(\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)\right)}}{\frac{1}{\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)} \cdot \left(\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)\right)}\]

   17. Applied times-frac 62.0

       \[\leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}}{\frac{1}{\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)} \cdot \left(\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)\right)}\]

   18. Applied times-frac 62.1

       \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{1}{\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)}} \cdot \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)}}\]

   19. Simplified 62.1

       \[\leadsto \color{blue}{\left(\left(\left({\left(x \cdot x\right)}^{4} \cdot \left({\left( 5.0640340000000002 \cdot 10^{-4} \right)}^{3} + {\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)}^{3}\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right) + \left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 \cdot 1 - \left(0.1049934947 \cdot \left(x \cdot x\right)\right) \cdot \left(0.1049934947 \cdot \left(x \cdot x\right)\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right) + \left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left({x}^{4} \cdot \left({0.042406060400000001}^{3} + {\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)}^{3}\right)\right)\right)} \cdot \frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\left(\left(5.0640340000000002 \cdot 10^{-4} \cdot 5.0640340000000002 \cdot 10^{-4} + \left(\left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) - 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right)\right)\right) \cdot \left(1 - 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.042406060400000001 \cdot 0.042406060400000001 + \left(\left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right) - 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot 0.00726441819999999999\right)\right)\right)}\]

   20. Taylor expanded around inf 0.0

       \[\leadsto \color{blue}{0.2514179000665369 \cdot \frac{1}{{x}^{3}} + \left(0.152981963459283 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

   if -11921922.190530011 < x < 341298.60975052114

   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. Simplified 0.0

      \[\leadsto \color{blue}{\frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}}\]
   3. Using strategy rm

   4. Applied div-inv 0.0

      \[\leadsto \frac{x}{\color{blue}{\left(\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)\right) \cdot \frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}}\]

   5. Applied associate-/r* 0.0

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

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -11921922.1905300114 \lor \neg \left(x \le 341298.60975052114\right):\\ \;\;\;\;0.2514179000665369 \cdot \frac{1}{{x}^{3}} + \left(0.152981963459283 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.32794500000000044 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.069455576099999999 + \left(x \cdot x\right) \cdot 0.014000544199999999\right)}}{\frac{1}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.042406060400000001 + \left(x \cdot x\right) \cdot 0.00726441819999999999\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))