Average Error: 28.9 → 0.0
Time: 2.1m
Precision: 64
\[\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\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1126932.864487643353641033172607421875 \lor \neg \left(x \le 641.7354232188947662507416680455207824707\right):\\ \;\;\;\;\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \left(\frac{0.5}{x} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3}} \cdot \left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)} \cdot x\right)\\ \end{array}\]
\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 -1126932.864487643353641033172607421875 \lor \neg \left(x \le 641.7354232188947662507416680455207824707\right):\\
\;\;\;\;\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \left(\frac{0.5}{x} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3}} \cdot \left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)} \cdot x\right)\\

\end{array}
double f(double x) {
        double r175415 = 1.0;
        double r175416 = 0.1049934947;
        double r175417 = x;
        double r175418 = r175417 * r175417;
        double r175419 = r175416 * r175418;
        double r175420 = r175415 + r175419;
        double r175421 = 0.0424060604;
        double r175422 = r175418 * r175418;
        double r175423 = r175421 * r175422;
        double r175424 = r175420 + r175423;
        double r175425 = 0.0072644182;
        double r175426 = r175422 * r175418;
        double r175427 = r175425 * r175426;
        double r175428 = r175424 + r175427;
        double r175429 = 0.0005064034;
        double r175430 = r175426 * r175418;
        double r175431 = r175429 * r175430;
        double r175432 = r175428 + r175431;
        double r175433 = 0.0001789971;
        double r175434 = r175430 * r175418;
        double r175435 = r175433 * r175434;
        double r175436 = r175432 + r175435;
        double r175437 = 0.7715471019;
        double r175438 = r175437 * r175418;
        double r175439 = r175415 + r175438;
        double r175440 = 0.2909738639;
        double r175441 = r175440 * r175422;
        double r175442 = r175439 + r175441;
        double r175443 = 0.0694555761;
        double r175444 = r175443 * r175426;
        double r175445 = r175442 + r175444;
        double r175446 = 0.0140005442;
        double r175447 = r175446 * r175430;
        double r175448 = r175445 + r175447;
        double r175449 = 0.0008327945;
        double r175450 = r175449 * r175434;
        double r175451 = r175448 + r175450;
        double r175452 = 2.0;
        double r175453 = r175452 * r175433;
        double r175454 = r175434 * r175418;
        double r175455 = r175453 * r175454;
        double r175456 = r175451 + r175455;
        double r175457 = r175436 / r175456;
        double r175458 = r175457 * r175417;
        return r175458;
}
↓
double f(double x) {
        double r175459 = x;
        double r175460 = -1126932.8644876434;
        bool r175461 = r175459 <= r175460;
        double r175462 = 641.7354232188948;
        bool r175463 = r175459 <= r175462;
        double r175464 = !r175463;
        bool r175465 = r175461 || r175464;
        double r175466 = 0.15298196345929327;
        double r175467 = 5.0;
        double r175468 = pow(r175459, r175467);
        double r175469 = r175466 / r175468;
        double r175470 = 0.5;
        double r175471 = r175470 / r175459;
        double r175472 = 0.2514179000665375;
        double r175473 = 3.0;
        double r175474 = pow(r175459, r175473);
        double r175475 = r175472 / r175474;
        double r175476 = r175471 + r175475;
        double r175477 = r175469 + r175476;
        double r175478 = 1.0;
        double r175479 = 0.1049934947;
        double r175480 = r175459 * r175459;
        double r175481 = r175479 * r175480;
        double r175482 = r175478 + r175481;
        double r175483 = 4.0;
        double r175484 = pow(r175459, r175483);
        double r175485 = 0.0424060604;
        double r175486 = r175484 * r175485;
        double r175487 = 6.0;
        double r175488 = pow(r175459, r175487);
        double r175489 = 0.0072644182;
        double r175490 = r175488 * r175489;
        double r175491 = r175486 + r175490;
        double r175492 = 0.0005064034;
        double r175493 = r175492 * r175488;
        double r175494 = 8.0;
        double r175495 = pow(r175459, r175494);
        double r175496 = 0.0001789971;
        double r175497 = r175495 * r175496;
        double r175498 = r175493 + r175497;
        double r175499 = r175480 * r175498;
        double r175500 = r175491 + r175499;
        double r175501 = r175482 + r175500;
        double r175502 = pow(r175501, r175473);
        double r175503 = cbrt(r175502);
        double r175504 = 1.0;
        double r175505 = 12.0;
        double r175506 = pow(r175459, r175505);
        double r175507 = 2.0;
        double r175508 = r175507 * r175496;
        double r175509 = r175506 * r175508;
        double r175510 = 0.0008327945;
        double r175511 = r175488 * r175484;
        double r175512 = r175510 * r175511;
        double r175513 = 0.0694555761;
        double r175514 = r175488 * r175513;
        double r175515 = 0.7715471019;
        double r175516 = r175515 * r175480;
        double r175517 = r175478 + r175516;
        double r175518 = 0.2909738639;
        double r175519 = r175484 * r175518;
        double r175520 = r175517 + r175519;
        double r175521 = r175514 + r175520;
        double r175522 = r175512 + r175521;
        double r175523 = 0.0140005442;
        double r175524 = r175523 * r175495;
        double r175525 = r175522 + r175524;
        double r175526 = r175509 + r175525;
        double r175527 = r175504 / r175526;
        double r175528 = r175527 * r175459;
        double r175529 = r175503 * r175528;
        double r175530 = r175465 ? r175477 : r175529;
        return r175530;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -1126932.8644876434 or 641.7354232188948 < x

    1. Initial program 59.0

      \[\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. Taylor expanded around inf 0.0

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

    3. Simplified0.0

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

    if -1126932.8644876434 < x < 641.7354232188948

    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. Using strategy rm

    3. Applied add-cbrt-cube0.0

      \[\leadsto \color{blue}{\sqrt[3]{\left(\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 \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)}\right) \cdot \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\]

    4. Simplified0.0

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)}\right)}^{3}}} \cdot x\]
    5. Using strategy rm

    6. Applied div-inv0.0

      \[\leadsto \sqrt[3]{{\color{blue}{\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right) \cdot \frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)}\right)}}^{3}} \cdot x\]

    7. Applied unpow-prod-down0.0

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3} \cdot {\left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)}\right)}^{3}}} \cdot x\]

    8. Applied cbrt-prod0.0

      \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)}\right)}^{3}}\right)} \cdot x\]

    9. Applied associate-*l*0.0

      \[\leadsto \color{blue}{\sqrt[3]{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3}} \cdot \left(\sqrt[3]{{\left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)}\right)}^{3}} \cdot x\right)}\]

    10. Simplified0.0

      \[\leadsto \sqrt[3]{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3}} \cdot \color{blue}{\left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)} \cdot x\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1126932.864487643353641033172607421875 \lor \neg \left(x \le 641.7354232188947662507416680455207824707\right):\\ \;\;\;\;\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \left(\frac{0.5}{x} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + \left(\left({x}^{4} \cdot 0.04240606040000000076517494562722276896238 + {x}^{6} \cdot 0.007264418199999999985194687468492702464573\right) + \left(x \cdot x\right) \cdot \left(5.064034000000000243502107366566633572802 \cdot 10^{-4} \cdot {x}^{6} + {x}^{8} \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)}^{3}} \cdot \left(\frac{1}{{x}^{12} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right) + \left(\left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot \left({x}^{6} \cdot {x}^{4}\right) + \left({x}^{6} \cdot 0.06945557609999999937322456844412954524159 + \left(\left(1 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right)\right)\right) + 0.01400054419999999938406531896362139377743 \cdot {x}^{8}\right)} \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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))