testing LeastSquareFit 20th order fit of 20 points at given points: x[i], y[i], P(x[i]) 0.0, 0.0, 7.251829821772732E-10 0.1, 0.09983341664682815, 0.0998334103986217 0.2, 0.19866933079506122, 0.1986693516560063 0.3, 0.29552020666133955, 0.29552017480110054 0.4, 0.3894183423086505, 0.3894183560026707 0.5, 0.479425538604203, 0.47942555939668124 0.6, 0.5646424733950354, 0.5646424541026575 0.7, 0.644217687237691, 0.6442176711238111 0.8, 0.7173560908995228, 0.7173561108907732 0.9, 0.7833269096274834, 0.7833269236186415 1.0, 0.8414709848078965, 0.84147096396827 1.1, 0.8912073600614354, 0.8912073495539083 1.2, 0.9320390859672263, 0.9320391096666125 1.3, 0.963558185417193, 0.9635581858482939 1.4, 0.9854497299884601, 0.9854497049469896 1.5, 0.9974949866040544, 0.9974950123596787 1.6, 0.9995736030415051, 0.9995735895102106 1.7, 0.9916648104524686, 0.9916648146193424 1.8, 0.9738476308781951, 0.9738476301632083 1.9, 0.9463000876874145, 0.9463000877460729 norm2 of error = 7.703813668444514E-8 at mid points: x[i], y[i], P(x[i]) 0.05, 0.04997916927067833, 0.0499790337346202 0.15000000000000002, 0.14943813247359924, 0.14943818071459472 0.25, 0.24740395925452294, 0.24740393916348194 0.35, 0.34289780745545134, 0.3428977941313003 0.45, 0.43496553411123023, 0.43496556175593165 0.55, 0.5226872289306592, 0.5226872292259386 0.65, 0.6051864057360395, 0.6051863799289786 0.75, 0.6816387600233341, 0.6816387631379555 0.8500000000000001, 0.7512804051402927, 0.7512804295999658 0.9500000000000001, 0.8134155047893737, 0.8134154997812976 1.05, 0.867423225594017, 0.8674232022115426 1.1500000000000001, 0.9127639402605211, 0.912763950078556 1.25, 0.9489846193555862, 0.9489846396271937 1.35, 0.9757233578266591, 0.9757233366430029 1.45, 0.9927129910375885, 0.9927129874611477 1.55, 0.999783764189357, 0.9997837921065563 1.6500000000000001, 0.9968650284539189, 0.9968649757625024 1.75, 0.9839859468739369, 0.9839860901582649 1.85, 0.9612752029752999, 0.9612743391644092 norm2 of error = 8.916909781997061E-7 integral = 1.4053559550196792 Repeat using order 10 approximating polynomial at given points: x[i], y[i], P(x[i]) 0.0, 0.0, -1.2414555221617548E-10 0.1, 0.09983341664682815, 0.09983341716221275 0.2, 0.19866933079506122, 0.19866933019964964 0.3, 0.29552020666133955, 0.29552020652092165 0.4, 0.3894183423086505, 0.38941834272123993 0.5, 0.479425538604203, 0.47942553888599476 0.6, 0.5646424733950354, 0.564642473223084 0.7, 0.644217687237691, 0.6442176868772911 0.8, 0.7173560908995228, 0.7173560907692423 0.9, 0.7833269096274834, 0.7833269098434843 1.0, 0.8414709848078965, 0.8414709851113948 1.1, 0.8912073600614354, 0.8912073601171727 1.2, 0.9320390859672263, 0.9320390857212796 1.3, 0.963558185417193, 0.963558185167638 1.4, 0.9854497299884601, 0.9854497300608379 1.5, 0.9974949866040544, 0.9974949869098022 1.6, 0.9995736030415051, 0.9995736030770119 1.7, 0.9916648104524686, 0.991664810089714 1.8, 0.9738476308781951, 0.9738476311037629 1.9, 0.9463000876874145, 0.9463000876440754 norm2 of error = 1.2768332762994582E-9 at mid points: x[i], y[i], P(x[i]) 0.05, 0.04997916927067833, 0.04997917042681341 0.15000000000000002, 0.14943813247359924, 0.1494381322105442 0.25, 0.24740395925452294, 0.24740395877148466 0.35, 0.34289780745545134, 0.3428978076625457 0.45, 0.43496553411123023, 0.4349655345384351 0.55, 0.5226872289306592, 0.5226872289836109 0.65, 0.6051864057360395, 0.6051864054137409 0.75, 0.6816387600233341, 0.6816387597374299 0.8500000000000001, 0.7512804051402927, 0.7512804051957429 0.9500000000000001, 0.8134155047893737, 0.8134155050958688 1.05, 0.867423225594017, 0.8674232258043459 1.1500000000000001, 0.9127639402605211, 0.9127639401468189 1.25, 0.9489846193555862, 0.9489846190575539 1.35, 0.9757233578266591, 0.9757233577150973 1.45, 0.9927129910375885, 0.9927129912727602 1.55, 0.999783764189357, 0.999783764426262 1.6500000000000001, 0.9968650284539189, 0.9968650282380649 1.75, 0.9839859468739369, 0.9839859466409449 1.85, 0.9612752029752999, 0.9612752036543288 norm2 of error = 1.7273395967024474E-9 integral = 1.3232323665517618 Repeat using order 5 approximating polynomial at given points: x[i], y[i], P(x[i]) 0.0, 0.0, 2.226078326445722E-5 0.1, 0.09983341664682815, 0.09980715222810704 0.2, 0.19866933079506122, 0.19864736593397458 0.3, 0.29552020666133955, 0.29551927561472113 0.4, 0.3894183423086505, 0.3894350271472141 0.5, 0.479425538604203, 0.47944814311814377 0.6, 0.5646424733950354, 0.5646591273708335 0.7, 0.644217687237691, 0.6442210695520488 0.8, 0.7173560908995228, 0.7173452496588083 0.9, 0.7833269096274834, 0.7833067425851921 1.0, 0.8414709848078965, 0.8414500226691526 1.1, 0.8912073600614354, 0.8911945682393241 1.2, 0.9320390859672263, 0.9320404661618322 1.3, 0.963558185417193, 0.9635740163871038 1.4, 0.9854497299884601, 0.9854733364966773 1.5, 0.9974949866040544, 0.9975139662500113 1.6, 0.9995736030415051, 0.9995744721312956 1.7, 0.9916648104524686, 0.9916420518962601 1.8, 0.9738476308781951, 0.9738181391189857 1.9, 0.9463000876874145, 0.9463240077387121 norm2 of error = 8.369450220559833E-5 at mid points: x[i], y[i], P(x[i]) 0.05, 0.04997916927067833, 0.04996757047938262 0.15000000000000002, 0.14943813247359924, 0.1494100931730845 0.25, 0.24740395925452294, 0.24739200374853731 0.35, 0.34289780745545134, 0.34290686143275056 0.45, 0.43496553411123023, 0.4349867998891519 0.55, 0.5226872289306592, 0.522708131764397 0.65, 0.6051864057360395, 0.6051969532351787 0.75, 0.6816387600233341, 0.6816347485550384 0.8500000000000001, 0.7512804051402927, 0.7512639946011738 0.9500000000000001, 0.8134155047893737, 0.8133937654212502 1.05, 0.867423225594017, 0.8674053367802096 1.1500000000000001, 0.9127639402605211, 0.9127577907070806 1.25, 0.9489846193555862, 0.9489936200417887 1.35, 0.9757233578266591, 0.9757443329819648 1.45, 0.9927129910375885, 0.9927360576297561 1.55, 0.999783764189357, 0.9997951465386363 1.6500000000000001, 0.9968650284539189, 0.9968537812602133 1.75, 0.9839859468739369, 0.9839555768910417 1.85, 0.9612752029752999, 0.9612611866194303 norm2 of error = 7.913239721121714E-5 integral = 1.3562444982975046 exact=1.3232895668635034