Jmat.Real.dawson

Average Error: 29.3 → 0.0

Time: 4.0m

Precision: 64

Math

\[\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \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) + 1.789971000000000009994005623070734145585 \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \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 1.789971000000000009994005623070734145585 \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\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -811566251180947968 \lor \neg \left(x \le 8094.733051485990472428966313600540161133\right):\\ \;\;\;\;0.2514179000665375252054900556686334311962 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592932686700805788859724998474 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x \cdot \left(\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.007264418199999999985194687468492702464573 + 1\right) + {x}^{2} \cdot \left(0.1049934946999999951788851149103720672429 + 0.04240606040000000076517494562722276896238 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right)}{\left(2 \cdot \left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot {x}^{3}\right)\right)\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.06945557609999999937322456844412954524159 + 1\right) + {x}^{2} \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.01400054419999999938406531896362139377743 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}^{1}\\ \end{array}\]

C

double f(double x) {
        double r215295 = 1.0;
        double r215296 = 0.1049934947;
        double r215297 = x;
        double r215298 = r215297 * r215297;
        double r215299 = r215296 * r215298;
        double r215300 = r215295 + r215299;
        double r215301 = 0.0424060604;
        double r215302 = r215298 * r215298;
        double r215303 = r215301 * r215302;
        double r215304 = r215300 + r215303;
        double r215305 = 0.0072644182;
        double r215306 = r215302 * r215298;
        double r215307 = r215305 * r215306;
        double r215308 = r215304 + r215307;
        double r215309 = 0.0005064034;
        double r215310 = r215306 * r215298;
        double r215311 = r215309 * r215310;
        double r215312 = r215308 + r215311;
        double r215313 = 0.0001789971;
        double r215314 = r215310 * r215298;
        double r215315 = r215313 * r215314;
        double r215316 = r215312 + r215315;
        double r215317 = 0.7715471019;
        double r215318 = r215317 * r215298;
        double r215319 = r215295 + r215318;
        double r215320 = 0.2909738639;
        double r215321 = r215320 * r215302;
        double r215322 = r215319 + r215321;
        double r215323 = 0.0694555761;
        double r215324 = r215323 * r215306;
        double r215325 = r215322 + r215324;
        double r215326 = 0.0140005442;
        double r215327 = r215326 * r215310;
        double r215328 = r215325 + r215327;
        double r215329 = 0.0008327945;
        double r215330 = r215329 * r215314;
        double r215331 = r215328 + r215330;
        double r215332 = 2.0;
        double r215333 = r215332 * r215313;
        double r215334 = r215314 * r215298;
        double r215335 = r215333 * r215334;
        double r215336 = r215331 + r215335;
        double r215337 = r215316 / r215336;
        double r215338 = r215337 * r215297;
        return r215338;
}

↓

double f(double x) {
        double r215339 = x;
        double r215340 = -8.11566251180948e+17;
        bool r215341 = r215339 <= r215340;
        double r215342 = 8094.7330514859905;
        bool r215343 = r215339 <= r215342;
        double r215344 = !r215343;
        bool r215345 = r215341 || r215344;
        double r215346 = 0.2514179000665375;
        double r215347 = 1.0;
        double r215348 = 3.0;
        double r215349 = pow(r215339, r215348);
        double r215350 = r215347 / r215349;
        double r215351 = r215346 * r215350;
        double r215352 = 0.15298196345929327;
        double r215353 = 5.0;
        double r215354 = pow(r215339, r215353);
        double r215355 = r215347 / r215354;
        double r215356 = r215352 * r215355;
        double r215357 = 0.5;
        double r215358 = r215347 / r215339;
        double r215359 = r215357 * r215358;
        double r215360 = r215356 + r215359;
        double r215361 = r215351 + r215360;
        double r215362 = 2.0;
        double r215363 = pow(r215339, r215362);
        double r215364 = r215339 * r215349;
        double r215365 = r215363 * r215364;
        double r215366 = r215363 * r215365;
        double r215367 = r215363 * r215366;
        double r215368 = 0.0001789971;
        double r215369 = r215367 * r215368;
        double r215370 = 0.0072644182;
        double r215371 = r215365 * r215370;
        double r215372 = 1.0;
        double r215373 = r215371 + r215372;
        double r215374 = 0.1049934947;
        double r215375 = 0.0424060604;
        double r215376 = r215375 * r215363;
        double r215377 = r215374 + r215376;
        double r215378 = r215363 * r215377;
        double r215379 = r215373 + r215378;
        double r215380 = r215369 + r215379;
        double r215381 = 0.0005064034;
        double r215382 = r215366 * r215381;
        double r215383 = r215380 + r215382;
        double r215384 = r215339 * r215383;
        double r215385 = 2.0;
        double r215386 = r215339 * r215339;
        double r215387 = r215386 * r215386;
        double r215388 = r215387 * r215386;
        double r215389 = r215388 * r215386;
        double r215390 = r215389 * r215364;
        double r215391 = r215368 * r215390;
        double r215392 = r215385 * r215391;
        double r215393 = 0.0694555761;
        double r215394 = r215365 * r215393;
        double r215395 = r215394 + r215372;
        double r215396 = 0.7715471019;
        double r215397 = 0.2909738639;
        double r215398 = r215397 * r215363;
        double r215399 = r215396 + r215398;
        double r215400 = r215363 * r215399;
        double r215401 = r215395 + r215400;
        double r215402 = r215392 + r215401;
        double r215403 = 0.0140005442;
        double r215404 = r215386 * r215339;
        double r215405 = r215404 * r215404;
        double r215406 = r215403 * r215405;
        double r215407 = 0.0008327945;
        double r215408 = r215407 * r215389;
        double r215409 = r215406 + r215408;
        double r215410 = r215363 * r215409;
        double r215411 = r215402 + r215410;
        double r215412 = r215384 / r215411;
        double r215413 = pow(r215412, r215347);
        double r215414 = r215345 ? r215361 : r215413;
        return r215414;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -8.11566251180948e+17 or 8094.7330514859905 < x

   1. Initial program 60.9

      \[\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \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) + 1.789971000000000009994005623070734145585 \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \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 1.789971000000000009994005623070734145585 \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

      \[\leadsto \color{blue}{0.2514179000665375252054900556686334311962 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592932686700805788859724998474 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

   if -8.11566251180948e+17 < x < 8094.7330514859905

   1. Initial program 0.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \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) + 1.789971000000000009994005623070734145585 \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \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 1.789971000000000009994005623070734145585 \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 pow1 0.0

      \[\leadsto \frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \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) + 1.789971000000000009994005623070734145585 \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \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 1.789971000000000009994005623070734145585 \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 \color{blue}{{x}^{1}}\]

   4. Applied pow1 0.0

      \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \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) + 1.789971000000000009994005623070734145585 \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \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 1.789971000000000009994005623070734145585 \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)}^{1}} \cdot {x}^{1}\]

   5. Applied pow-prod-down 0.0

      \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \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) + 1.789971000000000009994005623070734145585 \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \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 1.789971000000000009994005623070734145585 \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\right)}^{1}}\]

   6. Simplified 0.0

      \[\leadsto {\color{blue}{\left(\frac{x \cdot \left(\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.007264418199999999985194687468492702464573 + 1\right) + {x}^{2} \cdot \left(0.1049934946999999951788851149103720672429 + 0.04240606040000000076517494562722276896238 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right)}{\left(2 \cdot \left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot {x}^{3}\right)\right)\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.06945557609999999937322456844412954524159 + 1\right) + {x}^{2} \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.01400054419999999938406531896362139377743 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -811566251180947968 \lor \neg \left(x \le 8094.733051485990472428966313600540161133\right):\\ \;\;\;\;0.2514179000665375252054900556686334311962 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592932686700805788859724998474 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x \cdot \left(\left(\left({x}^{2} \cdot \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right)\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4} + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.007264418199999999985194687468492702464573 + 1\right) + {x}^{2} \cdot \left(0.1049934946999999951788851149103720672429 + 0.04240606040000000076517494562722276896238 \cdot {x}^{2}\right)\right)\right) + \left({x}^{2} \cdot \left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right)\right) \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right)}{\left(2 \cdot \left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot {x}^{3}\right)\right)\right) + \left(\left(\left({x}^{2} \cdot \left(x \cdot {x}^{3}\right)\right) \cdot 0.06945557609999999937322456844412954524159 + 1\right) + {x}^{2} \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot {x}^{2}\right)\right)\right) + {x}^{2} \cdot \left(0.01400054419999999938406531896362139377743 \cdot \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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))