Jmat.Real.dawson

Average Error: 29.6 → 0.0

Time: 33.4s

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 -17675.05046616965410066768527030944824219 \lor \neg \left(x \le 786.2107275504624794848496094346046447754\right):\\ \;\;\;\;\left(\frac{0.2514179000665373031608851306373253464699}{{x}^{3}} + \frac{0.1529819634592937127592904289485886693001}{{x}^{5}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{{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 \left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) \cdot \left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) - \left(\left(0.04240606040000000076517494562722276896238 + \left({x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4} + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6}\right)\right) \cdot \left(0.04240606040000000076517494562722276896238 + \left({x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4} + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6}\right)\right)\right) \cdot {x}^{8}\right)}{\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)}\\ \end{array}\]

C

double f(double x) {
        double r253521 = 1.0;
        double r253522 = 0.1049934947;
        double r253523 = x;
        double r253524 = r253523 * r253523;
        double r253525 = r253522 * r253524;
        double r253526 = r253521 + r253525;
        double r253527 = 0.0424060604;
        double r253528 = r253524 * r253524;
        double r253529 = r253527 * r253528;
        double r253530 = r253526 + r253529;
        double r253531 = 0.0072644182;
        double r253532 = r253528 * r253524;
        double r253533 = r253531 * r253532;
        double r253534 = r253530 + r253533;
        double r253535 = 0.0005064034;
        double r253536 = r253532 * r253524;
        double r253537 = r253535 * r253536;
        double r253538 = r253534 + r253537;
        double r253539 = 0.0001789971;
        double r253540 = r253536 * r253524;
        double r253541 = r253539 * r253540;
        double r253542 = r253538 + r253541;
        double r253543 = 0.7715471019;
        double r253544 = r253543 * r253524;
        double r253545 = r253521 + r253544;
        double r253546 = 0.2909738639;
        double r253547 = r253546 * r253528;
        double r253548 = r253545 + r253547;
        double r253549 = 0.0694555761;
        double r253550 = r253549 * r253532;
        double r253551 = r253548 + r253550;
        double r253552 = 0.0140005442;
        double r253553 = r253552 * r253536;
        double r253554 = r253551 + r253553;
        double r253555 = 0.0008327945;
        double r253556 = r253555 * r253540;
        double r253557 = r253554 + r253556;
        double r253558 = 2.0;
        double r253559 = r253558 * r253539;
        double r253560 = r253540 * r253524;
        double r253561 = r253559 * r253560;
        double r253562 = r253557 + r253561;
        double r253563 = r253542 / r253562;
        double r253564 = r253563 * r253523;
        return r253564;
}

↓

double f(double x) {
        double r253565 = x;
        double r253566 = -17675.050466169654;
        bool r253567 = r253565 <= r253566;
        double r253568 = 786.2107275504625;
        bool r253569 = r253565 <= r253568;
        double r253570 = !r253569;
        bool r253571 = r253567 || r253570;
        double r253572 = 0.2514179000665373;
        double r253573 = 3.0;
        double r253574 = pow(r253565, r253573);
        double r253575 = r253572 / r253574;
        double r253576 = 0.1529819634592937;
        double r253577 = 5.0;
        double r253578 = pow(r253565, r253577);
        double r253579 = r253576 / r253578;
        double r253580 = r253575 + r253579;
        double r253581 = 0.5;
        double r253582 = r253581 / r253565;
        double r253583 = r253580 + r253582;
        double r253584 = 6.0;
        double r253585 = pow(r253565, r253584);
        double r253586 = 2.0;
        double r253587 = 0.0001789971;
        double r253588 = r253586 * r253587;
        double r253589 = r253585 * r253588;
        double r253590 = 0.0694555761;
        double r253591 = r253589 + r253590;
        double r253592 = r253585 * r253591;
        double r253593 = 1.0;
        double r253594 = 0.7715471019;
        double r253595 = r253565 * r253565;
        double r253596 = r253594 * r253595;
        double r253597 = r253593 + r253596;
        double r253598 = 4.0;
        double r253599 = pow(r253565, r253598);
        double r253600 = 0.2909738639;
        double r253601 = 0.0008327945;
        double r253602 = r253585 * r253601;
        double r253603 = 0.0140005442;
        double r253604 = r253599 * r253603;
        double r253605 = r253602 + r253604;
        double r253606 = r253600 + r253605;
        double r253607 = r253599 * r253606;
        double r253608 = r253597 + r253607;
        double r253609 = r253592 + r253608;
        double r253610 = r253565 / r253609;
        double r253611 = 0.1049934947;
        double r253612 = r253611 * r253595;
        double r253613 = r253593 + r253612;
        double r253614 = 0.0072644182;
        double r253615 = r253585 * r253614;
        double r253616 = r253613 + r253615;
        double r253617 = r253616 * r253616;
        double r253618 = 0.0424060604;
        double r253619 = 0.0005064034;
        double r253620 = r253599 * r253619;
        double r253621 = r253587 * r253585;
        double r253622 = r253620 + r253621;
        double r253623 = r253618 + r253622;
        double r253624 = r253623 * r253623;
        double r253625 = 8.0;
        double r253626 = pow(r253565, r253625);
        double r253627 = r253624 * r253626;
        double r253628 = r253617 - r253627;
        double r253629 = r253610 * r253628;
        double r253630 = r253599 * r253623;
        double r253631 = r253616 - r253630;
        double r253632 = r253629 / r253631;
        double r253633 = r253571 ? r253583 : r253632;
        return r253633;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -17675.050466169654 or 786.2107275504625 < x

   1. Initial program 59.1

      \[\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 59.1

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

   4. Applied div-inv 59.1

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

   5. Applied associate-*l* 59.1

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

   6. Simplified 59.1

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

   8. Applied flip-+ 61.3

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

   9. Applied associate-*l/ 61.3

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

   10. Simplified 61.3

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

   11. Taylor expanded around inf 0.0

       \[\leadsto \color{blue}{0.2514179000665373031608851306373253464699 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592937127592904289485886693001 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

   12. Simplified 0.0

       \[\leadsto \color{blue}{\left(\frac{0.2514179000665373031608851306373253464699}{{x}^{3}} + \frac{0.1529819634592937127592904289485886693001}{{x}^{5}}\right) + \frac{0.5}{x}}\]

   if -17675.050466169654 < x < 786.2107275504625

   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 div-inv 0.0

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

   5. Applied associate-*l* 0.0

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

   6. Simplified 0.0

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

   8. Applied flip-+ 0.0

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

   9. Applied associate-*l/ 0.0

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

   10. Simplified 0.0

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

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -17675.05046616965410066768527030944824219 \lor \neg \left(x \le 786.2107275504624794848496094346046447754\right):\\ \;\;\;\;\left(\frac{0.2514179000665373031608851306373253464699}{{x}^{3}} + \frac{0.1529819634592937127592904289485886693001}{{x}^{5}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{{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 \left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) \cdot \left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) - \left(\left(0.04240606040000000076517494562722276896238 + \left({x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4} + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6}\right)\right) \cdot \left(0.04240606040000000076517494562722276896238 + \left({x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4} + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6}\right)\right)\right) \cdot {x}^{8}\right)}{\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)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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))