Jmat.Real.dawson

Average Error: 29.5 → 0.0

Time: 15.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -519755.088550737302 \lor \neg \left(x \le 683.88112364834728\right):\\ \;\;\;\;\frac{0.5}{x} + \left(\frac{0.1529819634592933}{{x}^{5}} + \frac{0.25141790006653753}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{\sqrt{\left(\left({x}^{6} \cdot 0.069455576099999999 + 1\right) + {\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right)}^{3}\right) + \left({\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(1.789971 \cdot 10^{-4} \cdot 2\right) \cdot {x}^{12}\right)}}}{\sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)}}\\ \end{array}\]

C

double f(double x) {
        double r238703 = 1.0;
        double r238704 = 0.1049934947;
        double r238705 = x;
        double r238706 = r238705 * r238705;
        double r238707 = r238704 * r238706;
        double r238708 = r238703 + r238707;
        double r238709 = 0.0424060604;
        double r238710 = r238706 * r238706;
        double r238711 = r238709 * r238710;
        double r238712 = r238708 + r238711;
        double r238713 = 0.0072644182;
        double r238714 = r238710 * r238706;
        double r238715 = r238713 * r238714;
        double r238716 = r238712 + r238715;
        double r238717 = 0.0005064034;
        double r238718 = r238714 * r238706;
        double r238719 = r238717 * r238718;
        double r238720 = r238716 + r238719;
        double r238721 = 0.0001789971;
        double r238722 = r238718 * r238706;
        double r238723 = r238721 * r238722;
        double r238724 = r238720 + r238723;
        double r238725 = 0.7715471019;
        double r238726 = r238725 * r238706;
        double r238727 = r238703 + r238726;
        double r238728 = 0.2909738639;
        double r238729 = r238728 * r238710;
        double r238730 = r238727 + r238729;
        double r238731 = 0.0694555761;
        double r238732 = r238731 * r238714;
        double r238733 = r238730 + r238732;
        double r238734 = 0.0140005442;
        double r238735 = r238734 * r238718;
        double r238736 = r238733 + r238735;
        double r238737 = 0.0008327945;
        double r238738 = r238737 * r238722;
        double r238739 = r238736 + r238738;
        double r238740 = 2.0;
        double r238741 = r238740 * r238721;
        double r238742 = r238722 * r238706;
        double r238743 = r238741 * r238742;
        double r238744 = r238739 + r238743;
        double r238745 = r238724 / r238744;
        double r238746 = r238745 * r238705;
        return r238746;
}

↓

double f(double x) {
        double r238747 = x;
        double r238748 = -519755.0885507373;
        bool r238749 = r238747 <= r238748;
        double r238750 = 683.8811236483473;
        bool r238751 = r238747 <= r238750;
        double r238752 = !r238751;
        bool r238753 = r238749 || r238752;
        double r238754 = 0.5;
        double r238755 = r238754 / r238747;
        double r238756 = 0.15298196345929327;
        double r238757 = 5.0;
        double r238758 = pow(r238747, r238757);
        double r238759 = r238756 / r238758;
        double r238760 = 0.2514179000665375;
        double r238761 = 3.0;
        double r238762 = pow(r238747, r238761);
        double r238763 = r238760 / r238762;
        double r238764 = r238759 + r238763;
        double r238765 = r238755 + r238764;
        double r238766 = r238747 * r238747;
        double r238767 = 4.0;
        double r238768 = pow(r238766, r238767);
        double r238769 = 0.0005064034;
        double r238770 = 0.0001789971;
        double r238771 = r238766 * r238770;
        double r238772 = r238769 + r238771;
        double r238773 = r238768 * r238772;
        double r238774 = 6.0;
        double r238775 = pow(r238747, r238774);
        double r238776 = 0.0072644182;
        double r238777 = r238775 * r238776;
        double r238778 = 1.0;
        double r238779 = 0.1049934947;
        double r238780 = 0.0424060604;
        double r238781 = r238780 * r238766;
        double r238782 = r238779 + r238781;
        double r238783 = r238766 * r238782;
        double r238784 = r238778 + r238783;
        double r238785 = r238777 + r238784;
        double r238786 = r238773 + r238785;
        double r238787 = r238786 * r238747;
        double r238788 = 0.0694555761;
        double r238789 = r238775 * r238788;
        double r238790 = r238789 + r238778;
        double r238791 = 0.7715471019;
        double r238792 = 0.2909738639;
        double r238793 = r238792 * r238766;
        double r238794 = r238791 + r238793;
        double r238795 = r238766 * r238794;
        double r238796 = cbrt(r238795);
        double r238797 = pow(r238796, r238761);
        double r238798 = r238790 + r238797;
        double r238799 = 0.0140005442;
        double r238800 = 0.0008327945;
        double r238801 = r238766 * r238800;
        double r238802 = r238799 + r238801;
        double r238803 = r238768 * r238802;
        double r238804 = 2.0;
        double r238805 = r238770 * r238804;
        double r238806 = 12.0;
        double r238807 = pow(r238747, r238806);
        double r238808 = r238805 * r238807;
        double r238809 = r238803 + r238808;
        double r238810 = r238798 + r238809;
        double r238811 = sqrt(r238810);
        double r238812 = r238787 / r238811;
        double r238813 = pow(r238766, r238774);
        double r238814 = r238804 * r238813;
        double r238815 = r238814 * r238770;
        double r238816 = r238796 * r238796;
        double r238817 = r238816 * r238796;
        double r238818 = r238817 + r238778;
        double r238819 = r238789 + r238818;
        double r238820 = r238815 + r238819;
        double r238821 = r238803 + r238820;
        double r238822 = sqrt(r238821);
        double r238823 = r238812 / r238822;
        double r238824 = r238753 ? r238765 : r238823;
        return r238824;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -519755.0885507373 or 683.8811236483473 < x

   1. Initial program 59.6

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

   2. Simplified 59.6

      \[\leadsto \color{blue}{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right)\right)}}\]

   3. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{0.25141790006653753 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592933 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

   4. Simplified 0.0

      \[\leadsto \color{blue}{\frac{0.5}{x} + \left(\frac{0.1529819634592933}{{x}^{5}} + \frac{0.25141790006653753}{{x}^{3}}\right)}\]

   if -519755.0885507373 < x < 683.8811236483473

   1. Initial program 0.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

   2. Simplified 0.0

      \[\leadsto \color{blue}{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right)\right)}}\]
   3. Using strategy rm

   4. Applied add-cube-cbrt 0.0

      \[\leadsto \frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\color{blue}{\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}} + 1\right)\right)\right)}\]
   5. Using strategy rm

   6. Applied add-sqr-sqrt 0.0

      \[\leadsto \frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{\color{blue}{\sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)} \cdot \sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)}}}\]

   7. Applied associate-/r* 0.0

      \[\leadsto \color{blue}{\frac{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{\sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)}}}{\sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)}}}\]

   8. Simplified 0.0

      \[\leadsto \frac{\color{blue}{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{\sqrt{\left(\left({x}^{6} \cdot 0.069455576099999999 + 1\right) + {\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right)}^{3}\right) + \left({\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(1.789971 \cdot 10^{-4} \cdot 2\right) \cdot {x}^{12}\right)}}}}{\sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -519755.088550737302 \lor \neg \left(x \le 683.88112364834728\right):\\ \;\;\;\;\frac{0.5}{x} + \left(\frac{0.1529819634592933}{{x}^{5}} + \frac{0.25141790006653753}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \left(x \cdot x\right) \cdot 1.789971 \cdot 10^{-4}\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{\sqrt{\left(\left({x}^{6} \cdot 0.069455576099999999 + 1\right) + {\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right)}^{3}\right) + \left({\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(1.789971 \cdot 10^{-4} \cdot 2\right) \cdot {x}^{12}\right)}}}{\sqrt{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(\sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)}\right) \cdot \sqrt[3]{\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right)} + 1\right)\right)\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))