least_square_fit.c
fit exp(x)*sin(x) 100 points 0.0 to Pi, 3 degree polynomial
C[0]=1.03481 
C[1]=-4.74761 
C[2]=7.91925 
C[3]=-2.03683 
check_pn k=100, xmin=0.0314, xmax=3.14, ymin=0.0323963, ymax=7.46048 
max=1.11264 at 100, xbad=3.14, ybad=0.0367964
rms_err=0.369805, avg_err=0.317624, max_err=1.11264 

fit exp(x)*sin(x) 100 points 0.0 to Pi, 4 degree polynomial
C[0]=-0.181694 
C[1]=2.59571 
C[2]=-2.37989 
C[3]=2.99796 
C[4]=-0.79378 
check_pn k=100, xmin=0.0314, xmax=3.14, ymin=0.0323963, ymax=7.46048 
max=0.13484 at 1, xbad=0.0314, ybad=0.0323963
rms_err=0.0462658, avg_err=0.0401402, max_err=0.13484 

fit exp(x)*sin(x) 100 points 0.0 to Pi, 5 degree polynomial
C[0]=-0.00389295 
C[1]=1.02343 
C[2]=1.0217 
C[3]=0.15938 
C[4]=0.210597 
C[5]=-0.126679 
check_pn k=100, xmin=0.0314, xmax=3.14, ymin=0.0323963, ymax=7.46048 
max=0.0149835 at 100, xbad=3.14, ybad=0.0367964
rms_err=0.00343216, avg_err=0.00270314, max_err=0.0149835 

fit exp(x)*sin(x) 100 points 0.0 to Pi, 6 degree polynomial
C[0]=0.00842522 
C[1]=0.875111 
C[2]=1.47548 
C[3]=-0.405692 
C[4]=0.542791 
C[5]=-0.218666 
C[6]=0.00966836 
check_pn k=100, xmin=0.0314, xmax=3.14, ymin=0.0323963, ymax=7.46048 
max=0.0068923 at 100, xbad=3.14, ybad=0.0367964
rms_err=0.00202802, avg_err=0.00172947, max_err=0.0068923 

fit exp(x)*sin(x) 100 points 0.0 to Pi, 7 degree polynomial
C[0]=-0.00182356 
C[1]=1.03452 
C[2]=0.824861 
C[3]=0.712647 
C[4]=-0.41787 
C[5]=0.215548 
C[6]=-0.0890414 
C[7]=0.00889285 
check_pn k=100, xmin=0.0314, xmax=3.14, ymin=0.0323963, ymax=7.46048 
max=0.00104117 at 100, xbad=3.14, ybad=0.0367964
rms_err=0.000339239, avg_err=0.000293251, max_err=0.00104117