Initial program 13.5
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
Taylor expanded around 0 13.5
\[\leadsto \color{blue}{\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}\]
- Using strategy
rm Applied add-exp-log13.5
\[\leadsto \color{blue}{e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)\right)}}\]
- Using strategy
rm Applied add-log-exp13.5
\[\leadsto e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + \color{blue}{\log \left(e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)}\right)\right)\right)}\]
Applied add-log-exp13.5
\[\leadsto e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \left(\color{blue}{\log \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}}\right)} + \log \left(e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)\right)}\]
Applied sum-log13.5
\[\leadsto e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \color{blue}{\log \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)}\right)\right)}\]
Applied add-log-exp13.5
\[\leadsto e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\color{blue}{\log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}}\right)} + \log \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)}\]
Applied sum-log13.5
\[\leadsto e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \color{blue}{\log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)}\right)}\]
Applied add-log-exp13.5
\[\leadsto e^{\log \left(\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + \color{blue}{\log \left(e^{1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}}\right)}\right)\right) - \log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)}\]
Applied add-log-exp13.5
\[\leadsto e^{\log \left(\left(1 + \left(\color{blue}{\log \left(e^{0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}}\right)} + \log \left(e^{1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}}\right)\right)\right) - \log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)}\]
Applied sum-log13.6
\[\leadsto e^{\log \left(\left(1 + \color{blue}{\log \left(e^{0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}} \cdot e^{1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}}\right)}\right) - \log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)}\]
Applied add-log-exp13.6
\[\leadsto e^{\log \left(\left(\color{blue}{\log \left(e^{1}\right)} + \log \left(e^{0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}} \cdot e^{1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}}\right)\right) - \log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)}\]
Applied sum-log13.6
\[\leadsto e^{\log \left(\color{blue}{\log \left(e^{1} \cdot \left(e^{0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}} \cdot e^{1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}}\right)\right)} - \log \left(e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)\right)\right)}\]
Applied diff-log13.5
\[\leadsto e^{\log \color{blue}{\left(\log \left(\frac{e^{1} \cdot \left(e^{0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}} \cdot e^{1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}}\right)}{e^{1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}} \cdot \left(e^{1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}} \cdot e^{0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}}\right)}\right)\right)}}\]
Simplified13.5
\[\leadsto e^{\log \left(\log \color{blue}{\left(e^{\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}\right)}\right)}\]
Final simplification13.5
\[\leadsto e^{\log \left(\log \left(e^{\left(1 + \left(0.284496735999999972 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 1.45315202700000001 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.0614054289999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.42141374100000006 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.25482959199999999 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}\right)\right)}\]