Jmat.Real.dawson

Average Error: 29.1 → 0.0

Time: 31.3s

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\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -4052405089.347076416015625 \lor \neg \left(x \le 673.5332051604526668597827665507793426514\right):\\ \;\;\;\;\left(\frac{0.2514179000665375252054900556686334311962}{{x}^{3}} + \frac{0.1529819634592932686700805788859724998474}{{x}^{5}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left({x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4} + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6}\right)\right)}{\sqrt{{x}^{6} \cdot \left({x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + 0.06945557609999999937322456844412954524159\right) + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot \left(0.2909738639000000182122107617033179849386 + \left({x}^{6} \cdot 8.327945000000000442749725770852364803432 \cdot 10^{-4} + {x}^{4} \cdot 0.01400054419999999938406531896362139377743\right)\right)\right)}}}{\sqrt{{x}^{6} \cdot \left({x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + 0.06945557609999999937322456844412954524159\right) + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot \left(0.2909738639000000182122107617033179849386 + \left({x}^{6} \cdot 8.327945000000000442749725770852364803432 \cdot 10^{-4} + {x}^{4} \cdot 0.01400054419999999938406531896362139377743\right)\right)\right)}} \cdot x\\ \end{array}\]

C

double f(double x) {
        double r149435 = 1.0;
        double r149436 = 0.1049934947;
        double r149437 = x;
        double r149438 = r149437 * r149437;
        double r149439 = r149436 * r149438;
        double r149440 = r149435 + r149439;
        double r149441 = 0.0424060604;
        double r149442 = r149438 * r149438;
        double r149443 = r149441 * r149442;
        double r149444 = r149440 + r149443;
        double r149445 = 0.0072644182;
        double r149446 = r149442 * r149438;
        double r149447 = r149445 * r149446;
        double r149448 = r149444 + r149447;
        double r149449 = 0.0005064034;
        double r149450 = r149446 * r149438;
        double r149451 = r149449 * r149450;
        double r149452 = r149448 + r149451;
        double r149453 = 0.0001789971;
        double r149454 = r149450 * r149438;
        double r149455 = r149453 * r149454;
        double r149456 = r149452 + r149455;
        double r149457 = 0.7715471019;
        double r149458 = r149457 * r149438;
        double r149459 = r149435 + r149458;
        double r149460 = 0.2909738639;
        double r149461 = r149460 * r149442;
        double r149462 = r149459 + r149461;
        double r149463 = 0.0694555761;
        double r149464 = r149463 * r149446;
        double r149465 = r149462 + r149464;
        double r149466 = 0.0140005442;
        double r149467 = r149466 * r149450;
        double r149468 = r149465 + r149467;
        double r149469 = 0.0008327945;
        double r149470 = r149469 * r149454;
        double r149471 = r149468 + r149470;
        double r149472 = 2.0;
        double r149473 = r149472 * r149453;
        double r149474 = r149454 * r149438;
        double r149475 = r149473 * r149474;
        double r149476 = r149471 + r149475;
        double r149477 = r149456 / r149476;
        double r149478 = r149477 * r149437;
        return r149478;
}

↓

double f(double x) {
        double r149479 = x;
        double r149480 = -4052405089.3470764;
        bool r149481 = r149479 <= r149480;
        double r149482 = 673.5332051604527;
        bool r149483 = r149479 <= r149482;
        double r149484 = !r149483;
        bool r149485 = r149481 || r149484;
        double r149486 = 0.2514179000665375;
        double r149487 = 3.0;
        double r149488 = pow(r149479, r149487);
        double r149489 = r149486 / r149488;
        double r149490 = 0.15298196345929327;
        double r149491 = 5.0;
        double r149492 = pow(r149479, r149491);
        double r149493 = r149490 / r149492;
        double r149494 = r149489 + r149493;
        double r149495 = 0.5;
        double r149496 = r149495 / r149479;
        double r149497 = r149494 + r149496;
        double r149498 = 1.0;
        double r149499 = 0.1049934947;
        double r149500 = r149479 * r149479;
        double r149501 = r149499 * r149500;
        double r149502 = r149498 + r149501;
        double r149503 = 6.0;
        double r149504 = pow(r149479, r149503);
        double r149505 = 0.0072644182;
        double r149506 = r149504 * r149505;
        double r149507 = r149502 + r149506;
        double r149508 = 4.0;
        double r149509 = pow(r149479, r149508);
        double r149510 = 0.0424060604;
        double r149511 = 0.0005064034;
        double r149512 = r149509 * r149511;
        double r149513 = 0.0001789971;
        double r149514 = r149513 * r149504;
        double r149515 = r149512 + r149514;
        double r149516 = r149510 + r149515;
        double r149517 = r149509 * r149516;
        double r149518 = r149507 + r149517;
        double r149519 = 2.0;
        double r149520 = r149519 * r149513;
        double r149521 = r149504 * r149520;
        double r149522 = 0.0694555761;
        double r149523 = r149521 + r149522;
        double r149524 = r149504 * r149523;
        double r149525 = 0.7715471019;
        double r149526 = r149525 * r149500;
        double r149527 = r149498 + r149526;
        double r149528 = 0.2909738639;
        double r149529 = 0.0008327945;
        double r149530 = r149504 * r149529;
        double r149531 = 0.0140005442;
        double r149532 = r149509 * r149531;
        double r149533 = r149530 + r149532;
        double r149534 = r149528 + r149533;
        double r149535 = r149509 * r149534;
        double r149536 = r149527 + r149535;
        double r149537 = r149524 + r149536;
        double r149538 = sqrt(r149537);
        double r149539 = r149518 / r149538;
        double r149540 = r149539 / r149538;
        double r149541 = r149540 * r149479;
        double r149542 = r149485 ? r149497 : r149541;
        return r149542;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -4052405089.3470764 or 673.5332051604527 < x

   1. Initial program 59.9

      \[\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. Simplified 59.8

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

   4. Applied add-sqr-sqrt 59.8

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

   5. Applied associate-/r* 59.8

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

   6. Taylor expanded around inf 0.0

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

   7. Simplified 0.0

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

   if -4052405089.3470764 < x < 673.5332051604527

   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

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

   4. Applied add-sqr-sqrt 0.0

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

   5. Applied associate-/r* 0.0

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

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4052405089.347076416015625 \lor \neg \left(x \le 673.5332051604526668597827665507793426514\right):\\ \;\;\;\;\left(\frac{0.2514179000665375252054900556686334311962}{{x}^{3}} + \frac{0.1529819634592932686700805788859724998474}{{x}^{5}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + {x}^{4} \cdot \left(0.04240606040000000076517494562722276896238 + \left({x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4} + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6}\right)\right)}{\sqrt{{x}^{6} \cdot \left({x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + 0.06945557609999999937322456844412954524159\right) + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot \left(0.2909738639000000182122107617033179849386 + \left({x}^{6} \cdot 8.327945000000000442749725770852364803432 \cdot 10^{-4} + {x}^{4} \cdot 0.01400054419999999938406531896362139377743\right)\right)\right)}}}{\sqrt{{x}^{6} \cdot \left({x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + 0.06945557609999999937322456844412954524159\right) + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot \left(0.2909738639000000182122107617033179849386 + \left({x}^{6} \cdot 8.327945000000000442749725770852364803432 \cdot 10^{-4} + {x}^{4} \cdot 0.01400054419999999938406531896362139377743\right)\right)\right)}} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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))