Jmat.Real.erf

Average Error: 13.9 → 13.0

Time: 20.2s

Precision: binary64

Math

\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

↓

\[\frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)}^{3}}{{1}^{6} + \left({\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left(1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)\right)}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

Error

Bits error versus x

Derivation

1. Initial program 13.9

   \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

2. Simplified 13.9

   \[\leadsto \color{blue}{1 - \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}}\]
3. Using strategy rm

4. Applied flip3-- 13.9

   \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right)}^{3}}{1 \cdot 1 + \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right) \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right) + 1 \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right)\right)}}\]

5. Simplified 13.9

   \[\leadsto \frac{\color{blue}{{1}^{3} - {\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{1 \cdot 1 + \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right) \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right) + 1 \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\right)\right)}\]

6. Simplified 13.9

   \[\leadsto \frac{{1}^{3} - {\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}{\color{blue}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}}\]
7. Using strategy rm

8. Applied add-sqr-sqrt 13.1

   \[\leadsto \frac{{1}^{3} - \color{blue}{\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

9. Taylor expanded around 0 14.2

   \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\color{blue}{1 \cdot \frac{{\left(\left(1.0614054289999999 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.42141374100000006 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right)\right) - \left(1.45315202700000001 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.284496735999999972 \cdot \frac{1}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}^{3}}{{\left(e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}}}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

10. Simplified 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\color{blue}{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]
11. Using strategy rm

12. Applied flip3-- 13.0

    \[\leadsto \frac{\color{blue}{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)}^{3}}{{1}^{3} \cdot {1}^{3} + \left(\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right) \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)\right)}}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

13. Simplified 13.0

    \[\leadsto \frac{\frac{\color{blue}{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)}^{3}}}{{1}^{3} \cdot {1}^{3} + \left(\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right) \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(\frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}} + \left(0.25482959199999999 + \left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right)\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)\right)}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

14. Simplified 13.0

    \[\leadsto \frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)}^{3}}{\color{blue}{{1}^{6} + \left({\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left(1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)\right)}}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

15. Final simplification 13.0

    \[\leadsto \frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)}^{3}}{{1}^{6} + \left({\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left(1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{1 \cdot \frac{{\left(0.25482959199999999 + \left(\left(\frac{1.42141374100000006}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} - \left(\frac{1.45315202700000001}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{3}} + \frac{0.284496735999999972}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)\right) + \frac{1.0614054289999999}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{4}}\right)\right)}^{3}}{{\left(\left(1 + 0.32759110000000002 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}\right)\right)}}{1 \cdot 1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \frac{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)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (neg (* (fabs x) (fabs x)))))))