Average Error: 29.7 → 0.0
Time: 1.8m
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 -244114386.9095483124256134033203125 \lor \neg \left(x \le 750.4504576576831595957628451287746429443\right):\\ \;\;\;\;0.2514179000665368590716752805747091770172 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634593110322384745813906192779541 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\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\\ \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 -244114386.9095483124256134033203125 \lor \neg \left(x \le 750.4504576576831595957628451287746429443\right):\\
\;\;\;\;0.2514179000665368590716752805747091770172 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634593110322384745813906192779541 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\

\mathbf{else}:\\
\;\;\;\;\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\\

\end{array}
double f(double x) {
        double r222498 = 1.0;
        double r222499 = 0.1049934947;
        double r222500 = x;
        double r222501 = r222500 * r222500;
        double r222502 = r222499 * r222501;
        double r222503 = r222498 + r222502;
        double r222504 = 0.0424060604;
        double r222505 = r222501 * r222501;
        double r222506 = r222504 * r222505;
        double r222507 = r222503 + r222506;
        double r222508 = 0.0072644182;
        double r222509 = r222505 * r222501;
        double r222510 = r222508 * r222509;
        double r222511 = r222507 + r222510;
        double r222512 = 0.0005064034;
        double r222513 = r222509 * r222501;
        double r222514 = r222512 * r222513;
        double r222515 = r222511 + r222514;
        double r222516 = 0.0001789971;
        double r222517 = r222513 * r222501;
        double r222518 = r222516 * r222517;
        double r222519 = r222515 + r222518;
        double r222520 = 0.7715471019;
        double r222521 = r222520 * r222501;
        double r222522 = r222498 + r222521;
        double r222523 = 0.2909738639;
        double r222524 = r222523 * r222505;
        double r222525 = r222522 + r222524;
        double r222526 = 0.0694555761;
        double r222527 = r222526 * r222509;
        double r222528 = r222525 + r222527;
        double r222529 = 0.0140005442;
        double r222530 = r222529 * r222513;
        double r222531 = r222528 + r222530;
        double r222532 = 0.0008327945;
        double r222533 = r222532 * r222517;
        double r222534 = r222531 + r222533;
        double r222535 = 2.0;
        double r222536 = r222535 * r222516;
        double r222537 = r222517 * r222501;
        double r222538 = r222536 * r222537;
        double r222539 = r222534 + r222538;
        double r222540 = r222519 / r222539;
        double r222541 = r222540 * r222500;
        return r222541;
}
↓
double f(double x) {
        double r222542 = x;
        double r222543 = -244114386.9095483;
        bool r222544 = r222542 <= r222543;
        double r222545 = 750.4504576576832;
        bool r222546 = r222542 <= r222545;
        double r222547 = !r222546;
        bool r222548 = r222544 || r222547;
        double r222549 = 0.25141790006653686;
        double r222550 = 1.0;
        double r222551 = 3.0;
        double r222552 = pow(r222542, r222551);
        double r222553 = r222550 / r222552;
        double r222554 = r222549 * r222553;
        double r222555 = 0.15298196345931103;
        double r222556 = 5.0;
        double r222557 = pow(r222542, r222556);
        double r222558 = r222550 / r222557;
        double r222559 = r222555 * r222558;
        double r222560 = 0.5;
        double r222561 = r222550 / r222542;
        double r222562 = r222560 * r222561;
        double r222563 = r222559 + r222562;
        double r222564 = r222554 + r222563;
        double r222565 = 1.0;
        double r222566 = 0.1049934947;
        double r222567 = r222542 * r222542;
        double r222568 = r222566 * r222567;
        double r222569 = r222565 + r222568;
        double r222570 = 0.0424060604;
        double r222571 = r222567 * r222567;
        double r222572 = r222570 * r222571;
        double r222573 = r222569 + r222572;
        double r222574 = 0.0072644182;
        double r222575 = r222571 * r222567;
        double r222576 = r222574 * r222575;
        double r222577 = r222573 + r222576;
        double r222578 = 0.0005064034;
        double r222579 = r222575 * r222567;
        double r222580 = r222578 * r222579;
        double r222581 = r222577 + r222580;
        double r222582 = 0.0001789971;
        double r222583 = r222579 * r222567;
        double r222584 = r222582 * r222583;
        double r222585 = r222581 + r222584;
        double r222586 = 0.7715471019;
        double r222587 = r222586 * r222567;
        double r222588 = r222565 + r222587;
        double r222589 = 0.2909738639;
        double r222590 = r222589 * r222571;
        double r222591 = r222588 + r222590;
        double r222592 = 0.0694555761;
        double r222593 = r222592 * r222575;
        double r222594 = r222591 + r222593;
        double r222595 = 0.0140005442;
        double r222596 = r222595 * r222579;
        double r222597 = r222594 + r222596;
        double r222598 = 0.0008327945;
        double r222599 = r222598 * r222583;
        double r222600 = r222597 + r222599;
        double r222601 = 2.0;
        double r222602 = r222601 * r222582;
        double r222603 = r222583 * r222567;
        double r222604 = r222602 * r222603;
        double r222605 = r222600 + r222604;
        double r222606 = r222585 / r222605;
        double r222607 = r222606 * r222542;
        double r222608 = r222548 ? r222564 : r222607;
        return r222608;
}

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 < -244114386.9095483 or 750.4504576576832 < x

    1. Initial program 59.7

      \[\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. Simplified59.6

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

    4. Applied flip3-+63.0

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

    5. Applied associate-*r/63.2

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

    6. Applied flip-+63.2

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

    7. Applied frac-add63.4

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

    8. Applied associate-/r/63.4

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

    9. Simplified63.4

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

    10. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{0.2514179000665368590716752805747091770172 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634593110322384745813906192779541 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

    if -244114386.9095483 < x < 750.4504576576832

    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\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -244114386.9095483124256134033203125 \lor \neg \left(x \le 750.4504576576831595957628451287746429443\right):\\ \;\;\;\;0.2514179000665368590716752805747091770172 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634593110322384745813906192779541 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\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\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))