sine function from 0 to pi

        x          f(x)     interpolation
    0.157080     0.156434     0.156351
    0.471239     0.453990     0.453981
    0.785398     0.707107     0.707088
    1.099557     0.891007     0.890984
    1.413717     0.987688     0.987663
    1.727876     0.987688     0.987663
    2.042035     0.891007     0.890983
    2.356194     0.707107     0.707089
    2.670354     0.453991     0.453978
    2.984513     0.156434     0.156433

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exponential function from 0 to 1

        x          f(x)     interpolation
    0.050000     1.051271     1.051268
    0.150000     1.161834     1.161834
    0.250000     1.284025     1.284025
    0.350000     1.419068     1.419067
    0.450000     1.568312     1.568312
    0.550000     1.733253     1.733253
    0.650000     1.915541     1.915540
    0.750000     2.117000     2.116999
    0.850000     2.339647     2.339646
    0.950000     2.585710     2.585709

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