Average Error: 3.6 → 0.3
Time: 2.0m
Precision: 64
\[\left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
\[\begin{array}{l} \mathbf{if}\;double \le 2.3013792011211497 \cdot 10^{-308}:\\ \;\;\;\;\left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right) \cdot \left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}}\right)\\ \mathbf{elif}\;double \le 8.639190386689441 \cdot 10^{-295}:\\ \;\;\;\;\left(\left(e^{-24.935284482002924} \cdot 1.178869188132815 \cdot 10^{-10}\right) \cdot \left(\left(double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right) \cdot \left(double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)\right) + \left(\left(\left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot \left(\left(\log double \cdot e^{-24.935284482002924}\right) \cdot \left(double \cdot double\right)\right)\right) \cdot 2.35773837626563 \cdot 10^{-10} - \left(e^{-24.935284482002924} \cdot \left(double \cdot \log double + double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)\right) \cdot 7.073215113787779 \cdot 10^{-10}\right) + \left(e^{-24.935284482002924} + \left(\left(\left(double \cdot \log double\right) \cdot \left(double \cdot \log double\right)\right) \cdot e^{-24.935284482002924}\right) \cdot 1.178869188132815 \cdot 10^{-10}\right)\right)\right) \cdot \left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right)\\ \end{array}\]
\left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}
\begin{array}{l}
\mathbf{if}\;double \le 2.3013792011211497 \cdot 10^{-308}:\\
\;\;\;\;\left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right) \cdot \left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}}\right)\\

\mathbf{elif}\;double \le 8.639190386689441 \cdot 10^{-295}:\\
\;\;\;\;\left(\left(e^{-24.935284482002924} \cdot 1.178869188132815 \cdot 10^{-10}\right) \cdot \left(\left(double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right) \cdot \left(double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)\right) + \left(\left(\left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot \left(\left(\log double \cdot e^{-24.935284482002924}\right) \cdot \left(double \cdot double\right)\right)\right) \cdot 2.35773837626563 \cdot 10^{-10} - \left(e^{-24.935284482002924} \cdot \left(double \cdot \log double + double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)\right) \cdot 7.073215113787779 \cdot 10^{-10}\right) + \left(e^{-24.935284482002924} + \left(\left(\left(double \cdot \log double\right) \cdot \left(double \cdot \log double\right)\right) \cdot e^{-24.935284482002924}\right) \cdot 1.178869188132815 \cdot 10^{-10}\right)\right)\right) \cdot \left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right)\\

\end{array}
double f(double double, double i) {
        double r30947089 = double;
        double r30947090 = 48.0;
        double r30947091 = atan2(1.0, 0.0);
        double r30947092 = r30947090 * r30947091;
        double r30947093 = r30947092 * r30947091;
        double r30947094 = 1.205e-29;
        double r30947095 = r30947093 / r30947094;
        double r30947096 = r30947095 / r30947094;
        double r30947097 = r30947089 * r30947096;
        double r30947098 = 1.0;
        double r30947099 = 3.0;
        double r30947100 = r30947098 / r30947099;
        double r30947101 = r30947089 * r30947100;
        double r30947102 = pow(r30947097, r30947101);
        double r30947103 = 1e-06;
        double r30947104 = 1.1;
        double r30947105 = -r30947104;
        double r30947106 = 8.625e-05;
        double r30947107 = 823.0;
        double r30947108 = r30947106 * r30947107;
        double r30947109 = r30947105 / r30947108;
        double r30947110 = exp(r30947109);
        double r30947111 = r30947103 * r30947110;
        double r30947112 = r30947102 * r30947111;
        double r30947113 = i;
        double r30947114 = r30947113 + r30947098;
        double r30947115 = r30947089 * r30947114;
        double r30947116 = pow(r30947115, r30947101);
        double r30947117 = r30947112 * r30947116;
        double r30947118 = 1.77;
        double r30947119 = 2.0;
        double r30947120 = 6.25e+18;
        double r30947121 = r30947119 * r30947120;
        double r30947122 = r30947121 * r30947094;
        double r30947123 = r30947099 * r30947114;
        double r30947124 = r30947123 * r30947094;
        double r30947125 = 4.0;
        double r30947126 = r30947125 * r30947091;
        double r30947127 = r30947124 / r30947126;
        double r30947128 = r30947089 * r30947127;
        double r30947129 = pow(r30947128, r30947101);
        double r30947130 = r30947122 / r30947129;
        double r30947131 = r30947118 - r30947130;
        double r30947132 = -r30947131;
        double r30947133 = r30947132 / r30947108;
        double r30947134 = exp(r30947133);
        double r30947135 = r30947117 * r30947134;
        return r30947135;
}

double f(double double, double i) {
        double r30947136 = double;
        double r30947137 = 2.3013792011211497e-308;
        bool r30947138 = r30947136 <= r30947137;
        double r30947139 = atan2(1.0, 0.0);
        double r30947140 = 48.0;
        double r30947141 = r30947140 * r30947139;
        double r30947142 = r30947139 * r30947141;
        double r30947143 = 1.205e-29;
        double r30947144 = r30947142 / r30947143;
        double r30947145 = r30947144 / r30947143;
        double r30947146 = r30947136 * r30947145;
        double r30947147 = 0.3333333333333333;
        double r30947148 = r30947147 * r30947136;
        double r30947149 = pow(r30947146, r30947148);
        double r30947150 = 1e-06;
        double r30947151 = 1.1;
        double r30947152 = -r30947151;
        double r30947153 = 8.625e-05;
        double r30947154 = 823.0;
        double r30947155 = r30947153 * r30947154;
        double r30947156 = r30947152 / r30947155;
        double r30947157 = exp(r30947156);
        double r30947158 = r30947150 * r30947157;
        double r30947159 = r30947149 * r30947158;
        double r30947160 = i;
        double r30947161 = 1.0;
        double r30947162 = r30947160 + r30947161;
        double r30947163 = r30947162 * r30947136;
        double r30947164 = pow(r30947163, r30947148);
        double r30947165 = r30947159 * r30947164;
        double r30947166 = 1.77;
        double r30947167 = 6.25e+18;
        double r30947168 = 2.0;
        double r30947169 = r30947167 * r30947168;
        double r30947170 = r30947143 * r30947169;
        double r30947171 = 3.0;
        double r30947172 = r30947171 * r30947162;
        double r30947173 = r30947172 * r30947143;
        double r30947174 = 4.0;
        double r30947175 = r30947174 * r30947139;
        double r30947176 = r30947173 / r30947175;
        double r30947177 = r30947176 * r30947136;
        double r30947178 = pow(r30947177, r30947148);
        double r30947179 = r30947170 / r30947178;
        double r30947180 = r30947166 - r30947179;
        double r30947181 = -r30947180;
        double r30947182 = r30947181 / r30947155;
        double r30947183 = exp(r30947182);
        double r30947184 = cbrt(r30947183);
        double r30947185 = r30947184 * r30947184;
        double r30947186 = r30947185 * r30947184;
        double r30947187 = cbrt(r30947186);
        double r30947188 = r30947185 * r30947187;
        double r30947189 = r30947165 * r30947188;
        double r30947190 = 8.639190386689441e-295;
        bool r30947191 = r30947136 <= r30947190;
        double r30947192 = -24.935284482002924;
        double r30947193 = exp(r30947192);
        double r30947194 = 1.178869188132815e-10;
        double r30947195 = r30947193 * r30947194;
        double r30947196 = 9.0375e-30;
        double r30947197 = r30947196 / r30947139;
        double r30947198 = log(r30947197);
        double r30947199 = r30947136 * r30947198;
        double r30947200 = r30947199 * r30947199;
        double r30947201 = r30947195 * r30947200;
        double r30947202 = log(r30947136);
        double r30947203 = r30947202 * r30947193;
        double r30947204 = r30947136 * r30947136;
        double r30947205 = r30947203 * r30947204;
        double r30947206 = r30947198 * r30947205;
        double r30947207 = 2.35773837626563e-10;
        double r30947208 = r30947206 * r30947207;
        double r30947209 = r30947136 * r30947202;
        double r30947210 = r30947209 + r30947199;
        double r30947211 = r30947193 * r30947210;
        double r30947212 = 7.073215113787779e-10;
        double r30947213 = r30947211 * r30947212;
        double r30947214 = r30947208 - r30947213;
        double r30947215 = r30947209 * r30947209;
        double r30947216 = r30947215 * r30947193;
        double r30947217 = r30947216 * r30947194;
        double r30947218 = r30947193 + r30947217;
        double r30947219 = r30947214 + r30947218;
        double r30947220 = r30947201 + r30947219;
        double r30947221 = r30947220 * r30947165;
        double r30947222 = r30947186 * r30947165;
        double r30947223 = r30947191 ? r30947221 : r30947222;
        double r30947224 = r30947138 ? r30947189 : r30947223;
        return r30947224;
}

Error

Bits error versus double

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if double < 2.3013792011211497e-308

    1. Initial program 3.2

      \[\left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
    2. Using strategy rm
    3. Applied add-cube-cbrt3.1

      \[\leadsto \left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right)}\]
    4. Using strategy rm
    5. Applied add-cube-cbrt3.1

      \[\leadsto \left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot \left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}}}\right)\]

    if 2.3013792011211497e-308 < double < 8.639190386689441e-295

    1. Initial program 40.3

      \[\left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
    2. Taylor expanded around 0 2.0

      \[\leadsto \left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot \color{blue}{\left(\left(1.178869188132815 \cdot 10^{-10} \cdot \left({double}^{2} \cdot \left({\left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)}^{2} \cdot e^{-24.935284482002924}\right)\right) + \left(2.35773837626563 \cdot 10^{-10} \cdot \left({double}^{2} \cdot \left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot \left(\log double \cdot e^{-24.935284482002924}\right)\right)\right) + \left(1.178869188132815 \cdot 10^{-10} \cdot \left({double}^{2} \cdot \left({\left(\log double\right)}^{2} \cdot e^{-24.935284482002924}\right)\right) + e^{-24.935284482002924}\right)\right)\right) - \left(7.073215113787779 \cdot 10^{-10} \cdot \left(double \cdot \left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot e^{-24.935284482002924}\right)\right) + 7.073215113787779 \cdot 10^{-10} \cdot \left(double \cdot \left(\log double \cdot e^{-24.935284482002924}\right)\right)\right)\right)}\]
    3. Simplified2.0

      \[\leadsto \left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot \color{blue}{\left(\left(\left(e^{-24.935284482002924} + \left(e^{-24.935284482002924} \cdot \left(\left(double \cdot \log double\right) \cdot \left(double \cdot \log double\right)\right)\right) \cdot 1.178869188132815 \cdot 10^{-10}\right) + \left(\left(\left(\left(double \cdot double\right) \cdot \left(e^{-24.935284482002924} \cdot \log double\right)\right) \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right) \cdot 2.35773837626563 \cdot 10^{-10} - 7.073215113787779 \cdot 10^{-10} \cdot \left(e^{-24.935284482002924} \cdot \left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot double + double \cdot \log double\right)\right)\right)\right) + \left(\left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot double\right) \cdot \left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot double\right)\right) \cdot \left(e^{-24.935284482002924} \cdot 1.178869188132815 \cdot 10^{-10}\right)\right)}\]

    if 8.639190386689441e-295 < double

    1. Initial program 2.0

      \[\left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
    2. Using strategy rm
    3. Applied add-cube-cbrt0.1

      \[\leadsto \left(\left({\left(double \cdot \frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(double \cdot \frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(double \cdot \left(i + 1\right)\right)}^{\left(double \cdot \frac{1}{3}\right)}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(double \cdot \frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(double \cdot \frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right)}\]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;double \le 2.3013792011211497 \cdot 10^{-308}:\\ \;\;\;\;\left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right) \cdot \left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}}\right)\\ \mathbf{elif}\;double \le 8.639190386689441 \cdot 10^{-295}:\\ \;\;\;\;\left(\left(e^{-24.935284482002924} \cdot 1.178869188132815 \cdot 10^{-10}\right) \cdot \left(\left(double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right) \cdot \left(double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)\right) + \left(\left(\left(\log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right) \cdot \left(\left(\log double \cdot e^{-24.935284482002924}\right) \cdot \left(double \cdot double\right)\right)\right) \cdot 2.35773837626563 \cdot 10^{-10} - \left(e^{-24.935284482002924} \cdot \left(double \cdot \log double + double \cdot \log \left(\frac{9.0375 \cdot 10^{-30}}{\pi}\right)\right)\right) \cdot 7.073215113787779 \cdot 10^{-10}\right) + \left(e^{-24.935284482002924} + \left(\left(\left(double \cdot \log double\right) \cdot \left(double \cdot \log double\right)\right) \cdot e^{-24.935284482002924}\right) \cdot 1.178869188132815 \cdot 10^{-10}\right)\right)\right) \cdot \left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(1.77 - \frac{1.205 \cdot 10^{-29} \cdot \left(6.25 \cdot 10^{+18} \cdot 2\right)}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi} \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \left(\left({\left(double \cdot \frac{\frac{\pi \cdot \left(48 \cdot \pi\right)}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3} \cdot double\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(\left(i + 1\right) \cdot double\right)}^{\left(\frac{1}{3} \cdot double\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 1 
(FPCore (double i)
  :name "(pow((double)(48*PI*PI/1.205e-29/1.205e-29),(double)1/3)*( 1.0e-6*exp(-1.1/(8.625e-5 * 823))))*pow((double)(i+1),(double)1/3)*exp(-(1.77-2* 6.25e18 *1.205e-29/(pow((double)(3*(i+1)*1.205e-29/(4*PI)),(double)1/3)))/( 8.625e-5 * 823))"
  (* (* (* (pow (* double (/ (/ (* (* 48 PI) PI) 1.205e-29) 1.205e-29)) (* double (/ 1 3))) (* 1e-06 (exp (/ (- 1.1) (* 8.625e-05 823))))) (pow (* double (+ i 1)) (* double (/ 1 3)))) (exp (/ (- (- 1.77 (/ (* (* 2 6.25e+18) 1.205e-29) (pow (* double (/ (* (* 3 (+ i 1)) 1.205e-29) (* 4 PI))) (* double (/ 1 3)))))) (* 8.625e-05 823)))))