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 r91755 = 1.0;
        double r91756 = 0.1049934947;
        double r91757 = x;
        double r91758 = r91757 * r91757;
        double r91759 = r91756 * r91758;
        double r91760 = r91755 + r91759;
        double r91761 = 0.0424060604;
        double r91762 = r91758 * r91758;
        double r91763 = r91761 * r91762;
        double r91764 = r91760 + r91763;
        double r91765 = 0.0072644182;
        double r91766 = r91762 * r91758;
        double r91767 = r91765 * r91766;
        double r91768 = r91764 + r91767;
        double r91769 = 0.0005064034;
        double r91770 = r91766 * r91758;
        double r91771 = r91769 * r91770;
        double r91772 = r91768 + r91771;
        double r91773 = 0.0001789971;
        double r91774 = r91770 * r91758;
        double r91775 = r91773 * r91774;
        double r91776 = r91772 + r91775;
        double r91777 = 0.7715471019;
        double r91778 = r91777 * r91758;
        double r91779 = r91755 + r91778;
        double r91780 = 0.2909738639;
        double r91781 = r91780 * r91762;
        double r91782 = r91779 + r91781;
        double r91783 = 0.0694555761;
        double r91784 = r91783 * r91766;
        double r91785 = r91782 + r91784;
        double r91786 = 0.0140005442;
        double r91787 = r91786 * r91770;
        double r91788 = r91785 + r91787;
        double r91789 = 0.0008327945;
        double r91790 = r91789 * r91774;
        double r91791 = r91788 + r91790;
        double r91792 = 2.0;
        double r91793 = r91792 * r91773;
        double r91794 = r91774 * r91758;
        double r91795 = r91793 * r91794;
        double r91796 = r91791 + r91795;
        double r91797 = r91776 / r91796;
        double r91798 = r91797 * r91757;
        return r91798;
}
↓
double f(double x) {
        double r91799 = x;
        double r91800 = -3928786.6725021615;
        bool r91801 = r91799 <= r91800;
        double r91802 = 949.5942511062235;
        bool r91803 = r91799 <= r91802;
        double r91804 = !r91803;
        bool r91805 = r91801 || r91804;
        double r91806 = 0.2514179000665375;
        double r91807 = 3.0;
        double r91808 = pow(r91799, r91807);
        double r91809 = r91806 / r91808;
        double r91810 = 0.15298196345929327;
        double r91811 = 5.0;
        double r91812 = pow(r91799, r91811);
        double r91813 = r91810 / r91812;
        double r91814 = r91809 + r91813;
        double r91815 = 0.5;
        double r91816 = r91815 / r91799;
        double r91817 = r91814 + r91816;
        double r91818 = 1.0;
        double r91819 = 12.0;
        double r91820 = pow(r91799, r91819);
        double r91821 = 2.0;
        double r91822 = 0.0001789971;
        double r91823 = r91821 * r91822;
        double r91824 = 9.0;
        double r91825 = pow(r91799, r91824);
        double r91826 = r91799 * r91825;
        double r91827 = 0.0008327945;
        double r91828 = 8.0;
        double r91829 = pow(r91799, r91828);
        double r91830 = 0.0140005442;
        double r91831 = 0.0694555761;
        double r91832 = 6.0;
        double r91833 = pow(r91799, r91832);
        double r91834 = 0.2909738639;
        double r91835 = 4.0;
        double r91836 = pow(r91799, r91835);
        double r91837 = 0.7715471019;
        double r91838 = r91837 * r91799;
        double r91839 = 1.0;
        double r91840 = fma(r91838, r91799, r91839);
        double r91841 = fma(r91834, r91836, r91840);
        double r91842 = fma(r91831, r91833, r91841);
        double r91843 = fma(r91829, r91830, r91842);
        double r91844 = fma(r91826, r91827, r91843);
        double r91845 = fma(r91820, r91823, r91844);
        double r91846 = 0.0005064034;
        double r91847 = 0.0072644182;
        double r91848 = 0.0424060604;
        double r91849 = r91799 * r91799;
        double r91850 = 0.1049934947;
        double r91851 = fma(r91849, r91850, r91839);
        double r91852 = fma(r91836, r91848, r91851);
        double r91853 = fma(r91833, r91847, r91852);
        double r91854 = fma(r91846, r91829, r91853);
        double r91855 = fma(r91822, r91826, r91854);
        double r91856 = r91845 / r91855;
        double r91857 = r91818 / r91856;
        double r91858 = r91857 * r91799;
        double r91859 = r91805 ? r91817 : r91858;
        return r91859;
}

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))