LegendreFit.java running
Legendre coefficients for exp(x)
a[0]=2.350403134460353
a[1]=0.7357606105797231
a[2]=0.14312943062344857
a[3]=0.020135645144729136
a[4]=0.002225030722350368
a[5]=2.1211336479808485E-4
for 2 power: avgerr=0.022937574054669646
            maxerr=0.0762858556098509
            rmserr=0.026818001015715416
for 3 power: avgerr=0.002859405962157746
            maxerr=0.009986903202082065
            rmserr=0.0033331473109269347
for 4 power: avgerr=2.873724638302416E-4
            maxerr=9.531751236155905E-4
            rmserr=3.32271483675132E-4
for 5 power: avgerr=3.4346991557190345E-5
            maxerr=9.998558234725063E-5
            rmserr=3.8613995181327256E-5