Average Error: 29.0 → 0.0
Time: 10.1s
Precision: 64
\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.042406060400000001 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.00726441819999999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.0640340000000002 \cdot 10^{-4} \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 1.789971 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.77154710189999998 \cdot \left(x \cdot x\right)\right) + 0.29097386390000002 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.069455576099999999 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.014000544199999999 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 8.32794500000000044 \cdot 10^{-4} \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 1.789971 \cdot 10^{-4}\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -106772652.369797722 \lor \neg \left(x \le 653.87127844365295\right):\\ \;\;\;\;\left(\frac{0.1529819634592933}{{x}^{5}} + \frac{0.25141790006653753}{{x}^{3}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{2} + 5.0640340000000002 \cdot 10^{-4}, {\left(x \cdot x\right)}^{4}, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left({x}^{4}, 0.042406060400000001, \mathsf{fma}\left(x \cdot x, 0.1049934947, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(1.789971 \cdot 10^{-4}, 2 \cdot {\left(x \cdot x\right)}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right) + \mathsf{fma}\left({x}^{6}, 0.069455576099999999, {\left(x \cdot x\right)}^{4} \cdot \left(\left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4} + 0.014000544199999999\right)\right)\right)}\\ \end{array}\]
\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 -106772652.369797722 \lor \neg \left(x \le 653.87127844365295\right):\\
\;\;\;\;\left(\frac{0.1529819634592933}{{x}^{5}} + \frac{0.25141790006653753}{{x}^{3}}\right) + \frac{0.5}{x}\\

\mathbf{else}:\\
\;\;\;\;\frac{\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{2} + 5.0640340000000002 \cdot 10^{-4}, {\left(x \cdot x\right)}^{4}, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left({x}^{4}, 0.042406060400000001, \mathsf{fma}\left(x \cdot x, 0.1049934947, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(1.789971 \cdot 10^{-4}, 2 \cdot {\left(x \cdot x\right)}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right) + \mathsf{fma}\left({x}^{6}, 0.069455576099999999, {\left(x \cdot x\right)}^{4} \cdot \left(\left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4} + 0.014000544199999999\right)\right)\right)}\\

\end{array}
double f(double x) {
        double r176077 = 1.0;
        double r176078 = 0.1049934947;
        double r176079 = x;
        double r176080 = r176079 * r176079;
        double r176081 = r176078 * r176080;
        double r176082 = r176077 + r176081;
        double r176083 = 0.0424060604;
        double r176084 = r176080 * r176080;
        double r176085 = r176083 * r176084;
        double r176086 = r176082 + r176085;
        double r176087 = 0.0072644182;
        double r176088 = r176084 * r176080;
        double r176089 = r176087 * r176088;
        double r176090 = r176086 + r176089;
        double r176091 = 0.0005064034;
        double r176092 = r176088 * r176080;
        double r176093 = r176091 * r176092;
        double r176094 = r176090 + r176093;
        double r176095 = 0.0001789971;
        double r176096 = r176092 * r176080;
        double r176097 = r176095 * r176096;
        double r176098 = r176094 + r176097;
        double r176099 = 0.7715471019;
        double r176100 = r176099 * r176080;
        double r176101 = r176077 + r176100;
        double r176102 = 0.2909738639;
        double r176103 = r176102 * r176084;
        double r176104 = r176101 + r176103;
        double r176105 = 0.0694555761;
        double r176106 = r176105 * r176088;
        double r176107 = r176104 + r176106;
        double r176108 = 0.0140005442;
        double r176109 = r176108 * r176092;
        double r176110 = r176107 + r176109;
        double r176111 = 0.0008327945;
        double r176112 = r176111 * r176096;
        double r176113 = r176110 + r176112;
        double r176114 = 2.0;
        double r176115 = r176114 * r176095;
        double r176116 = r176096 * r176080;
        double r176117 = r176115 * r176116;
        double r176118 = r176113 + r176117;
        double r176119 = r176098 / r176118;
        double r176120 = r176119 * r176079;
        return r176120;
}
↓
double f(double x) {
        double r176121 = x;
        double r176122 = -106772652.36979772;
        bool r176123 = r176121 <= r176122;
        double r176124 = 653.871278443653;
        bool r176125 = r176121 <= r176124;
        double r176126 = !r176125;
        bool r176127 = r176123 || r176126;
        double r176128 = 0.15298196345929327;
        double r176129 = 5.0;
        double r176130 = pow(r176121, r176129);
        double r176131 = r176128 / r176130;
        double r176132 = 0.2514179000665375;
        double r176133 = 3.0;
        double r176134 = pow(r176121, r176133);
        double r176135 = r176132 / r176134;
        double r176136 = r176131 + r176135;
        double r176137 = 0.5;
        double r176138 = r176137 / r176121;
        double r176139 = r176136 + r176138;
        double r176140 = 0.0001789971;
        double r176141 = 2.0;
        double r176142 = pow(r176121, r176141);
        double r176143 = r176140 * r176142;
        double r176144 = 0.0005064034;
        double r176145 = r176143 + r176144;
        double r176146 = r176121 * r176121;
        double r176147 = 4.0;
        double r176148 = pow(r176146, r176147);
        double r176149 = 0.0072644182;
        double r176150 = 6.0;
        double r176151 = pow(r176121, r176150);
        double r176152 = pow(r176121, r176147);
        double r176153 = 0.0424060604;
        double r176154 = 0.1049934947;
        double r176155 = 1.0;
        double r176156 = fma(r176146, r176154, r176155);
        double r176157 = fma(r176152, r176153, r176156);
        double r176158 = fma(r176149, r176151, r176157);
        double r176159 = fma(r176145, r176148, r176158);
        double r176160 = r176159 * r176121;
        double r176161 = 2.0;
        double r176162 = pow(r176146, r176150);
        double r176163 = r176161 * r176162;
        double r176164 = 0.2909738639;
        double r176165 = 0.7715471019;
        double r176166 = r176165 * r176121;
        double r176167 = fma(r176166, r176121, r176155);
        double r176168 = fma(r176164, r176152, r176167);
        double r176169 = 0.0694555761;
        double r176170 = 0.0008327945;
        double r176171 = r176146 * r176170;
        double r176172 = 0.0140005442;
        double r176173 = r176171 + r176172;
        double r176174 = r176148 * r176173;
        double r176175 = fma(r176151, r176169, r176174);
        double r176176 = r176168 + r176175;
        double r176177 = fma(r176140, r176163, r176176);
        double r176178 = r176160 / r176177;
        double r176179 = r176127 ? r176139 : r176178;
        return r176179;
}

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes

  2. if x < -106772652.36979772 or 653.871278443653 < x

    1. Initial program 59.0

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

    2. Simplified59.0

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

    4. Applied *-un-lft-identity59.0

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

    5. Applied associate-/r*59.0

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

    6. Simplified59.0

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

    8. Applied fma-udef59.0

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

    9. Simplified59.0

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

    10. Taylor expanded around inf 0.0

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

    11. Simplified0.0

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

    if -106772652.36979772 < x < 653.871278443653

    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. Simplified0.0

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

    4. Applied *-un-lft-identity0.0

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

    5. Applied associate-/r*0.0

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

    6. Simplified0.0

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

    8. Applied fma-udef0.0

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

    9. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -106772652.369797722 \lor \neg \left(x \le 653.87127844365295\right):\\ \;\;\;\;\left(\frac{0.1529819634592933}{{x}^{5}} + \frac{0.25141790006653753}{{x}^{3}}\right) + \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(1.789971 \cdot 10^{-4} \cdot {x}^{2} + 5.0640340000000002 \cdot 10^{-4}, {\left(x \cdot x\right)}^{4}, \mathsf{fma}\left(0.00726441819999999999, {x}^{6}, \mathsf{fma}\left({x}^{4}, 0.042406060400000001, \mathsf{fma}\left(x \cdot x, 0.1049934947, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(1.789971 \cdot 10^{-4}, 2 \cdot {\left(x \cdot x\right)}^{6}, \mathsf{fma}\left(0.29097386390000002, {x}^{4}, \mathsf{fma}\left(0.77154710189999998 \cdot x, x, 1\right)\right) + \mathsf{fma}\left({x}^{6}, 0.069455576099999999, {\left(x \cdot x\right)}^{4} \cdot \left(\left(x \cdot x\right) \cdot 8.32794500000000044 \cdot 10^{-4} + 0.014000544199999999\right)\right)\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))