Average Error: 29.2 → 0.0
Time: 1.1m
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\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3928786.6725021614693105220794677734375 \lor \neg \left(x \le 949.594251106223509850678965449333190918\right):\\ \;\;\;\;\left(\frac{0.2514179000665375252054900556686334311962}{{x}^{3}} + \frac{0.1529819634592932686700805788859724998474}{{x}^{5}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left({x}^{12}, 2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}, \mathsf{fma}\left(x \cdot {x}^{9}, 8.327945000000000442749725770852364803432 \cdot 10^{-4}, \mathsf{fma}\left({x}^{8}, 0.01400054419999999938406531896362139377743, \mathsf{fma}\left(0.06945557609999999937322456844412954524159, {x}^{6}, \mathsf{fma}\left(0.2909738639000000182122107617033179849386, {x}^{4}, \mathsf{fma}\left(0.7715471018999999763821051601553335785866 \cdot x, x, 1\right)\right)\right)\right)\right)\right)}{\mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, x \cdot {x}^{9}, \mathsf{fma}\left(5.064034000000000243502107366566633572802 \cdot 10^{-4}, {x}^{8}, \mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)\right)\right)}} \cdot x\\ \end{array}\]
\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 -3928786.6725021614693105220794677734375 \lor \neg \left(x \le 949.594251106223509850678965449333190918\right):\\
\;\;\;\;\left(\frac{0.2514179000665375252054900556686334311962}{{x}^{3}} + \frac{0.1529819634592932686700805788859724998474}{{x}^{5}}\right) + \frac{0.5}{x}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\mathsf{fma}\left({x}^{12}, 2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}, \mathsf{fma}\left(x \cdot {x}^{9}, 8.327945000000000442749725770852364803432 \cdot 10^{-4}, \mathsf{fma}\left({x}^{8}, 0.01400054419999999938406531896362139377743, \mathsf{fma}\left(0.06945557609999999937322456844412954524159, {x}^{6}, \mathsf{fma}\left(0.2909738639000000182122107617033179849386, {x}^{4}, \mathsf{fma}\left(0.7715471018999999763821051601553335785866 \cdot x, x, 1\right)\right)\right)\right)\right)\right)}{\mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, x \cdot {x}^{9}, \mathsf{fma}\left(5.064034000000000243502107366566633572802 \cdot 10^{-4}, {x}^{8}, \mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)\right)\right)}} \cdot x\\

\end{array}
double f(double x) {
        double r117363 = 1.0;
        double r117364 = 0.1049934947;
        double r117365 = x;
        double r117366 = r117365 * r117365;
        double r117367 = r117364 * r117366;
        double r117368 = r117363 + r117367;
        double r117369 = 0.0424060604;
        double r117370 = r117366 * r117366;
        double r117371 = r117369 * r117370;
        double r117372 = r117368 + r117371;
        double r117373 = 0.0072644182;
        double r117374 = r117370 * r117366;
        double r117375 = r117373 * r117374;
        double r117376 = r117372 + r117375;
        double r117377 = 0.0005064034;
        double r117378 = r117374 * r117366;
        double r117379 = r117377 * r117378;
        double r117380 = r117376 + r117379;
        double r117381 = 0.0001789971;
        double r117382 = r117378 * r117366;
        double r117383 = r117381 * r117382;
        double r117384 = r117380 + r117383;
        double r117385 = 0.7715471019;
        double r117386 = r117385 * r117366;
        double r117387 = r117363 + r117386;
        double r117388 = 0.2909738639;
        double r117389 = r117388 * r117370;
        double r117390 = r117387 + r117389;
        double r117391 = 0.0694555761;
        double r117392 = r117391 * r117374;
        double r117393 = r117390 + r117392;
        double r117394 = 0.0140005442;
        double r117395 = r117394 * r117378;
        double r117396 = r117393 + r117395;
        double r117397 = 0.0008327945;
        double r117398 = r117397 * r117382;
        double r117399 = r117396 + r117398;
        double r117400 = 2.0;
        double r117401 = r117400 * r117381;
        double r117402 = r117382 * r117366;
        double r117403 = r117401 * r117402;
        double r117404 = r117399 + r117403;
        double r117405 = r117384 / r117404;
        double r117406 = r117405 * r117365;
        return r117406;
}
↓
double f(double x) {
        double r117407 = x;
        double r117408 = -3928786.6725021615;
        bool r117409 = r117407 <= r117408;
        double r117410 = 949.5942511062235;
        bool r117411 = r117407 <= r117410;
        double r117412 = !r117411;
        bool r117413 = r117409 || r117412;
        double r117414 = 0.2514179000665375;
        double r117415 = 3.0;
        double r117416 = pow(r117407, r117415);
        double r117417 = r117414 / r117416;
        double r117418 = 0.15298196345929327;
        double r117419 = 5.0;
        double r117420 = pow(r117407, r117419);
        double r117421 = r117418 / r117420;
        double r117422 = r117417 + r117421;
        double r117423 = 0.5;
        double r117424 = r117423 / r117407;
        double r117425 = r117422 + r117424;
        double r117426 = 1.0;
        double r117427 = 12.0;
        double r117428 = pow(r117407, r117427);
        double r117429 = 2.0;
        double r117430 = 0.0001789971;
        double r117431 = r117429 * r117430;
        double r117432 = 9.0;
        double r117433 = pow(r117407, r117432);
        double r117434 = r117407 * r117433;
        double r117435 = 0.0008327945;
        double r117436 = 8.0;
        double r117437 = pow(r117407, r117436);
        double r117438 = 0.0140005442;
        double r117439 = 0.0694555761;
        double r117440 = 6.0;
        double r117441 = pow(r117407, r117440);
        double r117442 = 0.2909738639;
        double r117443 = 4.0;
        double r117444 = pow(r117407, r117443);
        double r117445 = 0.7715471019;
        double r117446 = r117445 * r117407;
        double r117447 = 1.0;
        double r117448 = fma(r117446, r117407, r117447);
        double r117449 = fma(r117442, r117444, r117448);
        double r117450 = fma(r117439, r117441, r117449);
        double r117451 = fma(r117437, r117438, r117450);
        double r117452 = fma(r117434, r117435, r117451);
        double r117453 = fma(r117428, r117431, r117452);
        double r117454 = 0.0005064034;
        double r117455 = 0.0072644182;
        double r117456 = 0.0424060604;
        double r117457 = r117407 * r117407;
        double r117458 = 0.1049934947;
        double r117459 = fma(r117457, r117458, r117447);
        double r117460 = fma(r117444, r117456, r117459);
        double r117461 = fma(r117441, r117455, r117460);
        double r117462 = fma(r117454, r117437, r117461);
        double r117463 = fma(r117430, r117434, r117462);
        double r117464 = r117453 / r117463;
        double r117465 = r117426 / r117464;
        double r117466 = r117465 * r117407;
        double r117467 = r117413 ? r117425 : r117466;
        return r117467;
}

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes

  2. if x < -3928786.6725021615 or 949.5942511062235 < x

    1. Initial program 59.5

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

    2. 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

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

    if -3928786.6725021615 < x < 949.5942511062235

    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 clear-num0.0

      \[\leadsto \color{blue}{\frac{1}{\frac{\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)}{\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)}}} \cdot x\]

    4. Simplified0.0

      \[\leadsto \frac{1}{\color{blue}{\frac{\mathsf{fma}\left({x}^{12}, 2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}, \mathsf{fma}\left(x \cdot {x}^{9}, 8.327945000000000442749725770852364803432 \cdot 10^{-4}, \mathsf{fma}\left({x}^{8}, 0.01400054419999999938406531896362139377743, \mathsf{fma}\left(0.06945557609999999937322456844412954524159, {x}^{6}, \mathsf{fma}\left(0.2909738639000000182122107617033179849386, {x}^{4}, \mathsf{fma}\left(0.7715471018999999763821051601553335785866 \cdot x, x, 1\right)\right)\right)\right)\right)\right)}{\mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, x \cdot {x}^{9}, \mathsf{fma}\left(5.064034000000000243502107366566633572802 \cdot 10^{-4}, {x}^{8}, \mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)\right)\right)}}} \cdot x\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3928786.6725021614693105220794677734375 \lor \neg \left(x \le 949.594251106223509850678965449333190918\right):\\ \;\;\;\;\left(\frac{0.2514179000665375252054900556686334311962}{{x}^{3}} + \frac{0.1529819634592932686700805788859724998474}{{x}^{5}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left({x}^{12}, 2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}, \mathsf{fma}\left(x \cdot {x}^{9}, 8.327945000000000442749725770852364803432 \cdot 10^{-4}, \mathsf{fma}\left({x}^{8}, 0.01400054419999999938406531896362139377743, \mathsf{fma}\left(0.06945557609999999937322456844412954524159, {x}^{6}, \mathsf{fma}\left(0.2909738639000000182122107617033179849386, {x}^{4}, \mathsf{fma}\left(0.7715471018999999763821051601553335785866 \cdot x, x, 1\right)\right)\right)\right)\right)\right)}{\mathsf{fma}\left(1.789971000000000009994005623070734145585 \cdot 10^{-4}, x \cdot {x}^{9}, \mathsf{fma}\left(5.064034000000000243502107366566633572802 \cdot 10^{-4}, {x}^{8}, \mathsf{fma}\left({x}^{6}, 0.007264418199999999985194687468492702464573, \mathsf{fma}\left({x}^{4}, 0.04240606040000000076517494562722276896238, \mathsf{fma}\left(x \cdot x, 0.1049934946999999951788851149103720672429, 1\right)\right)\right)\right)\right)}} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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))