Jmat.Real.dawson

Average Error: 29.1 → 0.0

Time: 24.1s

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 -19828430064280764762030080 \lor \neg \left(x \le 728.9315294198679566761711612343788146973\right):\\ \;\;\;\;\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \left(\frac{0.5}{x} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{\mathsf{fma}\left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}, {\left(x \cdot x\right)}^{6}, \mathsf{fma}\left({\left(x \cdot x\right)}^{4}, \mathsf{fma}\left(8.327945000000000442749725770852364803432 \cdot 10^{-4}, x \cdot x, 0.01400054419999999938406531896362139377743\right), \mathsf{fma}\left(0.06945557609999999937322456844412954524159, {x}^{6}, \mathsf{fma}\left(0.2909738639000000182122107617033179849386, {x}^{4}, \mathsf{fma}\left(x \cdot x, 0.7715471018999999763821051601553335785866, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(0.007264418199999999985194687468492702464573, {x}^{6}, \mathsf{fma}\left(\mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, {x}^{2}, 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right), {\left(x \cdot x\right)}^{4}, \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)\right)}}{\mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, \mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, {x}^{2}, 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) \cdot {\left(x \cdot x\right)}^{4}\right) - \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)} \cdot \left(\mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, {\left(x \cdot x\right)}^{4} \cdot \left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot \left(x \cdot x\right) + 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right)\right) - \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)}\\ \end{array}\]

C

double f(double x) {
        double r106300 = 1.0;
        double r106301 = 0.1049934947;
        double r106302 = x;
        double r106303 = r106302 * r106302;
        double r106304 = r106301 * r106303;
        double r106305 = r106300 + r106304;
        double r106306 = 0.0424060604;
        double r106307 = r106303 * r106303;
        double r106308 = r106306 * r106307;
        double r106309 = r106305 + r106308;
        double r106310 = 0.0072644182;
        double r106311 = r106307 * r106303;
        double r106312 = r106310 * r106311;
        double r106313 = r106309 + r106312;
        double r106314 = 0.0005064034;
        double r106315 = r106311 * r106303;
        double r106316 = r106314 * r106315;
        double r106317 = r106313 + r106316;
        double r106318 = 0.0001789971;
        double r106319 = r106315 * r106303;
        double r106320 = r106318 * r106319;
        double r106321 = r106317 + r106320;
        double r106322 = 0.7715471019;
        double r106323 = r106322 * r106303;
        double r106324 = r106300 + r106323;
        double r106325 = 0.2909738639;
        double r106326 = r106325 * r106307;
        double r106327 = r106324 + r106326;
        double r106328 = 0.0694555761;
        double r106329 = r106328 * r106311;
        double r106330 = r106327 + r106329;
        double r106331 = 0.0140005442;
        double r106332 = r106331 * r106315;
        double r106333 = r106330 + r106332;
        double r106334 = 0.0008327945;
        double r106335 = r106334 * r106319;
        double r106336 = r106333 + r106335;
        double r106337 = 2.0;
        double r106338 = r106337 * r106318;
        double r106339 = r106319 * r106303;
        double r106340 = r106338 * r106339;
        double r106341 = r106336 + r106340;
        double r106342 = r106321 / r106341;
        double r106343 = r106342 * r106302;
        return r106343;
}

↓

double f(double x) {
        double r106344 = x;
        double r106345 = -1.9828430064280765e+25;
        bool r106346 = r106344 <= r106345;
        double r106347 = 728.931529419868;
        bool r106348 = r106344 <= r106347;
        double r106349 = !r106348;
        bool r106350 = r106346 || r106349;
        double r106351 = 0.15298196345929327;
        double r106352 = 5.0;
        double r106353 = pow(r106344, r106352);
        double r106354 = r106351 / r106353;
        double r106355 = 0.5;
        double r106356 = r106355 / r106344;
        double r106357 = 0.2514179000665375;
        double r106358 = 3.0;
        double r106359 = pow(r106344, r106358);
        double r106360 = r106357 / r106359;
        double r106361 = r106356 + r106360;
        double r106362 = r106354 + r106361;
        double r106363 = 2.0;
        double r106364 = 0.0001789971;
        double r106365 = r106363 * r106364;
        double r106366 = r106344 * r106344;
        double r106367 = 6.0;
        double r106368 = pow(r106366, r106367);
        double r106369 = 4.0;
        double r106370 = pow(r106366, r106369);
        double r106371 = 0.0008327945;
        double r106372 = 0.0140005442;
        double r106373 = fma(r106371, r106366, r106372);
        double r106374 = 0.0694555761;
        double r106375 = pow(r106344, r106367);
        double r106376 = 0.2909738639;
        double r106377 = pow(r106344, r106369);
        double r106378 = 0.7715471019;
        double r106379 = 1.0;
        double r106380 = fma(r106366, r106378, r106379);
        double r106381 = fma(r106376, r106377, r106380);
        double r106382 = fma(r106374, r106375, r106381);
        double r106383 = fma(r106370, r106373, r106382);
        double r106384 = fma(r106365, r106368, r106383);
        double r106385 = 0.0072644182;
        double r106386 = 2.0;
        double r106387 = pow(r106344, r106386);
        double r106388 = 0.0005064034;
        double r106389 = fma(r106364, r106387, r106388);
        double r106390 = 0.0424060604;
        double r106391 = 0.1049934947;
        double r106392 = fma(r106366, r106391, r106379);
        double r106393 = fma(r106377, r106390, r106392);
        double r106394 = fma(r106389, r106370, r106393);
        double r106395 = fma(r106385, r106375, r106394);
        double r106396 = r106384 / r106395;
        double r106397 = r106389 * r106370;
        double r106398 = fma(r106375, r106385, r106397);
        double r106399 = r106398 - r106393;
        double r106400 = r106396 / r106399;
        double r106401 = r106364 * r106366;
        double r106402 = r106401 + r106388;
        double r106403 = r106370 * r106402;
        double r106404 = fma(r106375, r106385, r106403);
        double r106405 = r106404 - r106393;
        double r106406 = r106400 * r106405;
        double r106407 = r106344 / r106406;
        double r106408 = r106350 ? r106362 : r106407;
        return r106408;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -1.9828430064280765e+25 or 728.931529419868 < x

   1. Initial program 61.5

      \[\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 61.5

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

   3. Taylor expanded around inf 0.0

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

   4. Simplified 0.0

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

   if -1.9828430064280765e+25 < x < 728.931529419868

   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

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

   4. Applied flip-+ 0.9

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

   5. Applied associate-/r/ 0.9

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

   6. Simplified 0.0

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

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -19828430064280764762030080 \lor \neg \left(x \le 728.9315294198679566761711612343788146973\right):\\ \;\;\;\;\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \left(\frac{0.5}{x} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{\mathsf{fma}\left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}, {\left(x \cdot x\right)}^{6}, \mathsf{fma}\left({\left(x \cdot x\right)}^{4}, \mathsf{fma}\left(8.327945000000000442749725770852364803432 \cdot 10^{-4}, x \cdot x, 0.01400054419999999938406531896362139377743\right), \mathsf{fma}\left(0.06945557609999999937322456844412954524159, {x}^{6}, \mathsf{fma}\left(0.2909738639000000182122107617033179849386, {x}^{4}, \mathsf{fma}\left(x \cdot x, 0.7715471018999999763821051601553335785866, 1\right)\right)\right)\right)\right)}{\mathsf{fma}\left(0.007264418199999999985194687468492702464573, {x}^{6}, \mathsf{fma}\left(\mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, {x}^{2}, 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right), {\left(x \cdot x\right)}^{4}, \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)\right)}}{\mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, \mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, {x}^{2}, 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) \cdot {\left(x \cdot x\right)}^{4}\right) - \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)} \cdot \left(\mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, {\left(x \cdot x\right)}^{4} \cdot \left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot \left(x \cdot x\right) + 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right)\right) - \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(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))