Jmat.Real.dawson

Average Error: 29.6 → 0.0

Time: 40.7s

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 -598.9087026034708287625107914209365844727 \lor \neg \left(x \le 605.8743541032351913599995896220207214355\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}:\\ \;\;\;\;\frac{1}{\sqrt{\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)}} \cdot \frac{x}{e^{\log \left(\frac{\sqrt{\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)}\right)}}\\ \end{array}\]

C

double f(double x) {
        double r243415 = 1.0;
        double r243416 = 0.1049934947;
        double r243417 = x;
        double r243418 = r243417 * r243417;
        double r243419 = r243416 * r243418;
        double r243420 = r243415 + r243419;
        double r243421 = 0.0424060604;
        double r243422 = r243418 * r243418;
        double r243423 = r243421 * r243422;
        double r243424 = r243420 + r243423;
        double r243425 = 0.0072644182;
        double r243426 = r243422 * r243418;
        double r243427 = r243425 * r243426;
        double r243428 = r243424 + r243427;
        double r243429 = 0.0005064034;
        double r243430 = r243426 * r243418;
        double r243431 = r243429 * r243430;
        double r243432 = r243428 + r243431;
        double r243433 = 0.0001789971;
        double r243434 = r243430 * r243418;
        double r243435 = r243433 * r243434;
        double r243436 = r243432 + r243435;
        double r243437 = 0.7715471019;
        double r243438 = r243437 * r243418;
        double r243439 = r243415 + r243438;
        double r243440 = 0.2909738639;
        double r243441 = r243440 * r243422;
        double r243442 = r243439 + r243441;
        double r243443 = 0.0694555761;
        double r243444 = r243443 * r243426;
        double r243445 = r243442 + r243444;
        double r243446 = 0.0140005442;
        double r243447 = r243446 * r243430;
        double r243448 = r243445 + r243447;
        double r243449 = 0.0008327945;
        double r243450 = r243449 * r243434;
        double r243451 = r243448 + r243450;
        double r243452 = 2.0;
        double r243453 = r243452 * r243433;
        double r243454 = r243434 * r243418;
        double r243455 = r243453 * r243454;
        double r243456 = r243451 + r243455;
        double r243457 = r243436 / r243456;
        double r243458 = r243457 * r243417;
        return r243458;
}

↓

double f(double x) {
        double r243459 = x;
        double r243460 = -598.9087026034708;
        bool r243461 = r243459 <= r243460;
        double r243462 = 605.8743541032352;
        bool r243463 = r243459 <= r243462;
        double r243464 = !r243463;
        bool r243465 = r243461 || r243464;
        double r243466 = 0.2514179000665375;
        double r243467 = 1.0;
        double r243468 = 3.0;
        double r243469 = pow(r243459, r243468);
        double r243470 = r243467 / r243469;
        double r243471 = r243466 * r243470;
        double r243472 = 0.15298196345929327;
        double r243473 = 5.0;
        double r243474 = pow(r243459, r243473);
        double r243475 = r243467 / r243474;
        double r243476 = r243472 * r243475;
        double r243477 = 0.5;
        double r243478 = r243467 / r243459;
        double r243479 = r243477 * r243478;
        double r243480 = r243476 + r243479;
        double r243481 = r243471 + r243480;
        double r243482 = r243459 * r243459;
        double r243483 = pow(r243482, r243468);
        double r243484 = r243483 * r243469;
        double r243485 = r243459 * r243484;
        double r243486 = 0.0008327945;
        double r243487 = 2.0;
        double r243488 = 0.0001789971;
        double r243489 = r243487 * r243488;
        double r243490 = r243482 * r243489;
        double r243491 = r243486 + r243490;
        double r243492 = r243485 * r243491;
        double r243493 = 0.7715471019;
        double r243494 = 0.2909738639;
        double r243495 = r243494 * r243482;
        double r243496 = r243493 + r243495;
        double r243497 = r243482 * r243496;
        double r243498 = 1.0;
        double r243499 = r243497 + r243498;
        double r243500 = r243492 + r243499;
        double r243501 = 6.0;
        double r243502 = pow(r243459, r243501);
        double r243503 = 0.0694555761;
        double r243504 = 0.0140005442;
        double r243505 = r243482 * r243504;
        double r243506 = r243503 + r243505;
        double r243507 = r243502 * r243506;
        double r243508 = r243500 + r243507;
        double r243509 = sqrt(r243508);
        double r243510 = r243467 / r243509;
        double r243511 = 4.0;
        double r243512 = pow(r243482, r243511);
        double r243513 = 0.0005064034;
        double r243514 = r243482 * r243488;
        double r243515 = r243513 + r243514;
        double r243516 = r243512 * r243515;
        double r243517 = 0.1049934947;
        double r243518 = r243517 * r243482;
        double r243519 = r243498 + r243518;
        double r243520 = r243516 + r243519;
        double r243521 = pow(r243459, r243511);
        double r243522 = 0.0424060604;
        double r243523 = 0.0072644182;
        double r243524 = r243482 * r243523;
        double r243525 = r243522 + r243524;
        double r243526 = r243521 * r243525;
        double r243527 = r243520 + r243526;
        double r243528 = r243509 / r243527;
        double r243529 = log(r243528);
        double r243530 = exp(r243529);
        double r243531 = r243459 / r243530;
        double r243532 = r243510 * r243531;
        double r243533 = r243465 ? r243481 : r243532;
        return r243533;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -598.9087026034708 or 605.8743541032352 < x

   1. Initial program 59.5

      \[\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 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 -598.9087026034708 < x < 605.8743541032352

   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 *-un-lft-identity 0.0

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

   5. Applied add-sqr-sqrt 0.0

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

   6. Applied times-frac 0.0

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

   7. Applied *-un-lft-identity 0.0

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

   8. Applied times-frac 0.0

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

   9. Simplified 0.0

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

   11. Applied add-exp-log 0.0

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

   12. Applied add-exp-log 0.0

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

   13. Applied div-exp 0.0

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

   14. Simplified 0.0

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

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -598.9087026034708287625107914209365844727 \lor \neg \left(x \le 605.8743541032351913599995896220207214355\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}:\\ \;\;\;\;\frac{1}{\sqrt{\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)}} \cdot \frac{x}{e^{\log \left(\frac{\sqrt{\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)}\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))