Jmat.Real.dawson

Average Error: 29.0 → 0.0

Time: 14.4s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -857599.9443123471 \lor \neg \left(x \le 572.145439533324748\right):\\ \;\;\;\;\left(\left(\left(\frac{1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}}{{x}^{3}} \cdot 6498.0921714254673 + 94126.4510442121682 \cdot \frac{1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}}{{x}^{5}}\right) + \frac{1.4145575542843991}{{x}^{3}}\right) + \frac{17.0013437336652409}{{x}^{5}}\right) - \frac{2793.34134463630971 \cdot \left(1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \sqrt[3]{{\left(x \cdot \sqrt{1.789971 \cdot 10^{-4}}\right)}^{3}} \cdot \left(x \cdot \sqrt{1.789971 \cdot 10^{-4}}\right)\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right)\right)}\\ \end{array}\]

C

double f(double x) {
        double r287002 = 1.0;
        double r287003 = 0.1049934947;
        double r287004 = x;
        double r287005 = r287004 * r287004;
        double r287006 = r287003 * r287005;
        double r287007 = r287002 + r287006;
        double r287008 = 0.0424060604;
        double r287009 = r287005 * r287005;
        double r287010 = r287008 * r287009;
        double r287011 = r287007 + r287010;
        double r287012 = 0.0072644182;
        double r287013 = r287009 * r287005;
        double r287014 = r287012 * r287013;
        double r287015 = r287011 + r287014;
        double r287016 = 0.0005064034;
        double r287017 = r287013 * r287005;
        double r287018 = r287016 * r287017;
        double r287019 = r287015 + r287018;
        double r287020 = 0.0001789971;
        double r287021 = r287017 * r287005;
        double r287022 = r287020 * r287021;
        double r287023 = r287019 + r287022;
        double r287024 = 0.7715471019;
        double r287025 = r287024 * r287005;
        double r287026 = r287002 + r287025;
        double r287027 = 0.2909738639;
        double r287028 = r287027 * r287009;
        double r287029 = r287026 + r287028;
        double r287030 = 0.0694555761;
        double r287031 = r287030 * r287013;
        double r287032 = r287029 + r287031;
        double r287033 = 0.0140005442;
        double r287034 = r287033 * r287017;
        double r287035 = r287032 + r287034;
        double r287036 = 0.0008327945;
        double r287037 = r287036 * r287021;
        double r287038 = r287035 + r287037;
        double r287039 = 2.0;
        double r287040 = r287039 * r287020;
        double r287041 = r287021 * r287005;
        double r287042 = r287040 * r287041;
        double r287043 = r287038 + r287042;
        double r287044 = r287023 / r287043;
        double r287045 = r287044 * r287004;
        return r287045;
}

↓

double f(double x) {
        double r287046 = x;
        double r287047 = -857599.9443123471;
        bool r287048 = r287046 <= r287047;
        double r287049 = 572.1454395333247;
        bool r287050 = r287046 <= r287049;
        double r287051 = !r287050;
        bool r287052 = r287048 || r287051;
        double r287053 = 0.0001789971;
        double r287054 = -1.0;
        double r287055 = cbrt(r287054);
        double r287056 = r287053 * r287055;
        double r287057 = 3.0;
        double r287058 = pow(r287046, r287057);
        double r287059 = r287056 / r287058;
        double r287060 = 6498.092171425467;
        double r287061 = r287059 * r287060;
        double r287062 = 94126.45104421217;
        double r287063 = 5.0;
        double r287064 = pow(r287046, r287063);
        double r287065 = r287056 / r287064;
        double r287066 = r287062 * r287065;
        double r287067 = r287061 + r287066;
        double r287068 = 1.414557554284399;
        double r287069 = r287068 / r287058;
        double r287070 = r287067 + r287069;
        double r287071 = 17.00134373366524;
        double r287072 = r287071 / r287064;
        double r287073 = r287070 + r287072;
        double r287074 = 2793.3413446363097;
        double r287075 = r287074 * r287056;
        double r287076 = r287075 / r287046;
        double r287077 = r287073 - r287076;
        double r287078 = r287046 * r287046;
        double r287079 = 4.0;
        double r287080 = pow(r287078, r287079);
        double r287081 = 0.0005064034;
        double r287082 = sqrt(r287053);
        double r287083 = r287046 * r287082;
        double r287084 = pow(r287083, r287057);
        double r287085 = cbrt(r287084);
        double r287086 = r287085 * r287083;
        double r287087 = r287081 + r287086;
        double r287088 = r287080 * r287087;
        double r287089 = 6.0;
        double r287090 = pow(r287046, r287089);
        double r287091 = 0.0072644182;
        double r287092 = r287090 * r287091;
        double r287093 = 1.0;
        double r287094 = 0.1049934947;
        double r287095 = 0.0424060604;
        double r287096 = r287095 * r287078;
        double r287097 = r287094 + r287096;
        double r287098 = r287078 * r287097;
        double r287099 = r287093 + r287098;
        double r287100 = r287092 + r287099;
        double r287101 = r287088 + r287100;
        double r287102 = r287101 * r287046;
        double r287103 = 0.0140005442;
        double r287104 = 0.0008327945;
        double r287105 = r287078 * r287104;
        double r287106 = r287103 + r287105;
        double r287107 = r287080 * r287106;
        double r287108 = 2.0;
        double r287109 = pow(r287078, r287089);
        double r287110 = r287108 * r287109;
        double r287111 = r287110 * r287053;
        double r287112 = 0.0694555761;
        double r287113 = r287090 * r287112;
        double r287114 = 0.7715471019;
        double r287115 = 0.2909738639;
        double r287116 = r287115 * r287078;
        double r287117 = r287114 + r287116;
        double r287118 = r287078 * r287117;
        double r287119 = r287118 + r287093;
        double r287120 = r287113 + r287119;
        double r287121 = r287111 + r287120;
        double r287122 = r287107 + r287121;
        double r287123 = r287102 / r287122;
        double r287124 = r287052 ? r287077 : r287123;
        return r287124;
}

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < -857599.9443123471 or 572.1454395333247 < x

   1. Initial program 58.8

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

   2. Simplified 58.8

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

   4. Applied add-sqr-sqrt 58.9

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

   5. Applied unswap-sqr 58.9

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

   7. Applied add-cbrt-cube 58.9

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

   8. Applied add-cbrt-cube 58.9

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

   9. Applied cbrt-unprod 58.9

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

   10. Simplified 58.9

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

   11. Taylor expanded around -inf 1.0

       \[\leadsto \color{blue}{\left(6498.0921714254673 \cdot \frac{\sqrt[3]{-1} \cdot {\left(\sqrt{1.789971 \cdot 10^{-4}}\right)}^{2}}{{x}^{3}} + \left(94126.4510442121682 \cdot \frac{\sqrt[3]{-1} \cdot {\left(\sqrt{1.789971 \cdot 10^{-4}}\right)}^{2}}{{x}^{5}} + \left(17.0013437336652409 \cdot \frac{1}{{x}^{5}} + 1.4145575542843991 \cdot \frac{1}{{x}^{3}}\right)\right)\right) - 2793.34134463630971 \cdot \frac{\sqrt[3]{-1} \cdot {\left(\sqrt{1.789971 \cdot 10^{-4}}\right)}^{2}}{x}}\]

   12. Simplified 0.0

       \[\leadsto \color{blue}{\left(\left(\left(\frac{1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}}{{x}^{3}} \cdot 6498.0921714254673 + 94126.4510442121682 \cdot \frac{1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}}{{x}^{5}}\right) + \frac{1.4145575542843991}{{x}^{3}}\right) + \frac{17.0013437336652409}{{x}^{5}}\right) - \frac{2793.34134463630971 \cdot \left(1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}\right)}{x}}\]

   if -857599.9443123471 < x < 572.1454395333247

   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-sqr-sqrt 0.0

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

   5. Applied unswap-sqr 0.0

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

   7. Applied add-cbrt-cube 0.0

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

   8. Applied add-cbrt-cube 0.0

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

   9. Applied cbrt-unprod 0.0

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

   10. Simplified 0.0

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

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -857599.9443123471 \lor \neg \left(x \le 572.145439533324748\right):\\ \;\;\;\;\left(\left(\left(\frac{1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}}{{x}^{3}} \cdot 6498.0921714254673 + 94126.4510442121682 \cdot \frac{1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}}{{x}^{5}}\right) + \frac{1.4145575542843991}{{x}^{3}}\right) + \frac{17.0013437336652409}{{x}^{5}}\right) - \frac{2793.34134463630971 \cdot \left(1.789971 \cdot 10^{-4} \cdot \sqrt[3]{-1}\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({\left(x \cdot x\right)}^{4} \cdot \left(5.0640340000000002 \cdot 10^{-4} + \sqrt[3]{{\left(x \cdot \sqrt{1.789971 \cdot 10^{-4}}\right)}^{3}} \cdot \left(x \cdot \sqrt{1.789971 \cdot 10^{-4}}\right)\right) + \left({x}^{6} \cdot 0.00726441819999999999 + \left(1 + \left(x \cdot x\right) \cdot \left(0.1049934947 + 0.042406060400000001 \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot x}{{\left(x \cdot x\right)}^{4} \cdot \left(0.014000544199999999 + \left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4}\right) + \left(\left(2 \cdot {\left(x \cdot x\right)}^{6}\right) \cdot 1.789971 \cdot 10^{-4} + \left({x}^{6} \cdot 0.069455576099999999 + \left(\left(x \cdot x\right) \cdot \left(0.77154710189999998 + 0.29097386390000002 \cdot \left(x \cdot x\right)\right) + 1\right)\right)\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))