Jmat.Real.dawson

Average Error: 29.4 → 0.0

Time: 30.6s

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\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -882.4771496533965091657591983675956726074 \lor \neg \left(x \le 699.193619297093619024963118135929107666\right):\\ \;\;\;\;0.2514179000665375252054900556686334311962 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592932686700805788859724998474 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)} \cdot \frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\\ \end{array}\]

C

double f(double x) {
        double r281328 = 1.0;
        double r281329 = 0.1049934947;
        double r281330 = x;
        double r281331 = r281330 * r281330;
        double r281332 = r281329 * r281331;
        double r281333 = r281328 + r281332;
        double r281334 = 0.0424060604;
        double r281335 = r281331 * r281331;
        double r281336 = r281334 * r281335;
        double r281337 = r281333 + r281336;
        double r281338 = 0.0072644182;
        double r281339 = r281335 * r281331;
        double r281340 = r281338 * r281339;
        double r281341 = r281337 + r281340;
        double r281342 = 0.0005064034;
        double r281343 = r281339 * r281331;
        double r281344 = r281342 * r281343;
        double r281345 = r281341 + r281344;
        double r281346 = 0.0001789971;
        double r281347 = r281343 * r281331;
        double r281348 = r281346 * r281347;
        double r281349 = r281345 + r281348;
        double r281350 = 0.7715471019;
        double r281351 = r281350 * r281331;
        double r281352 = r281328 + r281351;
        double r281353 = 0.2909738639;
        double r281354 = r281353 * r281335;
        double r281355 = r281352 + r281354;
        double r281356 = 0.0694555761;
        double r281357 = r281356 * r281339;
        double r281358 = r281355 + r281357;
        double r281359 = 0.0140005442;
        double r281360 = r281359 * r281343;
        double r281361 = r281358 + r281360;
        double r281362 = 0.0008327945;
        double r281363 = r281362 * r281347;
        double r281364 = r281361 + r281363;
        double r281365 = 2.0;
        double r281366 = r281365 * r281346;
        double r281367 = r281347 * r281331;
        double r281368 = r281366 * r281367;
        double r281369 = r281364 + r281368;
        double r281370 = r281349 / r281369;
        double r281371 = r281370 * r281330;
        return r281371;
}

↓

double f(double x) {
        double r281372 = x;
        double r281373 = -882.4771496533965;
        bool r281374 = r281372 <= r281373;
        double r281375 = 699.1936192970936;
        bool r281376 = r281372 <= r281375;
        double r281377 = !r281376;
        bool r281378 = r281374 || r281377;
        double r281379 = 0.2514179000665375;
        double r281380 = 1.0;
        double r281381 = 3.0;
        double r281382 = pow(r281372, r281381);
        double r281383 = r281380 / r281382;
        double r281384 = r281379 * r281383;
        double r281385 = 0.15298196345929327;
        double r281386 = 5.0;
        double r281387 = pow(r281372, r281386);
        double r281388 = r281380 / r281387;
        double r281389 = r281385 * r281388;
        double r281390 = 0.5;
        double r281391 = r281380 / r281372;
        double r281392 = r281390 * r281391;
        double r281393 = r281389 + r281392;
        double r281394 = r281384 + r281393;
        double r281395 = r281372 * r281372;
        double r281396 = 4.0;
        double r281397 = pow(r281395, r281396);
        double r281398 = 0.0005064034;
        double r281399 = 0.0001789971;
        double r281400 = r281395 * r281399;
        double r281401 = r281398 + r281400;
        double r281402 = r281397 * r281401;
        double r281403 = 1.0;
        double r281404 = 0.1049934947;
        double r281405 = r281404 * r281395;
        double r281406 = r281403 + r281405;
        double r281407 = r281402 + r281406;
        double r281408 = pow(r281372, r281396);
        double r281409 = 0.0424060604;
        double r281410 = 0.0072644182;
        double r281411 = r281395 * r281410;
        double r281412 = r281409 + r281411;
        double r281413 = r281408 * r281412;
        double r281414 = r281407 + r281413;
        double r281415 = sqrt(r281414);
        double r281416 = pow(r281395, r281381);
        double r281417 = r281416 * r281382;
        double r281418 = r281372 * r281417;
        double r281419 = 0.0008327945;
        double r281420 = 2.0;
        double r281421 = r281420 * r281399;
        double r281422 = r281395 * r281421;
        double r281423 = r281419 + r281422;
        double r281424 = r281418 * r281423;
        double r281425 = 0.7715471019;
        double r281426 = 0.2909738639;
        double r281427 = r281426 * r281395;
        double r281428 = r281425 + r281427;
        double r281429 = r281395 * r281428;
        double r281430 = r281429 + r281403;
        double r281431 = r281424 + r281430;
        double r281432 = 6.0;
        double r281433 = pow(r281372, r281432);
        double r281434 = 0.0694555761;
        double r281435 = 0.0140005442;
        double r281436 = r281395 * r281435;
        double r281437 = r281434 + r281436;
        double r281438 = r281433 * r281437;
        double r281439 = r281431 + r281438;
        double r281440 = r281439 / r281415;
        double r281441 = r281372 / r281440;
        double r281442 = r281415 * r281441;
        double r281443 = r281378 ? r281394 : r281442;
        return r281443;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -882.4771496533965 or 699.1936192970936 < x

   1. Initial program 59.6

      \[\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. Simplified 59.5

      \[\leadsto \color{blue}{\frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\]

   3. 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 -882.4771496533965 < x < 699.1936192970936

   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. Simplified 0.0

      \[\leadsto \color{blue}{\frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 0.0

      \[\leadsto \frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\color{blue}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)} \cdot \sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}}\]

   5. Applied *-un-lft-identity 0.0

      \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot \left(\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)\right)}}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)} \cdot \sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\]

   6. Applied times-frac 0.0

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}} \cdot \frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}}\]

   7. Applied *-un-lft-identity 0.0

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\frac{1}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}} \cdot \frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\]

   8. Applied times-frac 0.0

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}} \cdot \frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}}\]

   9. Simplified 0.0

      \[\leadsto \color{blue}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}} \cdot \frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -882.4771496533965091657591983675956726074 \lor \neg \left(x \le 699.193619297093619024963118135929107666\right):\\ \;\;\;\;0.2514179000665375252054900556686334311962 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592932686700805788859724998474 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)} \cdot \frac{x}{\frac{\left(\left(x \cdot \left({\left(x \cdot x\right)}^{3} \cdot {x}^{3}\right)\right) \cdot \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} + \left(x \cdot x\right) \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right) + \left(\left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + 0.2909738639000000182122107617033179849386 \cdot \left(x \cdot x\right)\right) + 1\right)\right) + {x}^{6} \cdot \left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right)}{\sqrt{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left(x \cdot x\right) \cdot 0.007264418199999999985194687468492702464573\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019318 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.042406060400000001 (* (* x x) (* x x)))) (* 0.00726441819999999999 (* (* (* x x) (* x x)) (* x x)))) (* 5.0640340000000002e-4 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 1.789971e-4 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.77154710189999998 (* x x))) (* 0.29097386390000002 (* (* x x) (* x x)))) (* 0.069455576099999999 (* (* (* x x) (* x x)) (* x x)))) (* 0.014000544199999999 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 8.32794500000000044e-4 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 1.789971e-4) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))