3
np.array([-0.9, -0.7, -0.5, -0.3, -0.1,  0.1,  0.3,  0.5,  0.7,  0.9])
np.array([-3.88093371, -3.4272122 , -4.74537668, -5.5386266 , -4.43341161, -3.42710558, -2.7893164 , -1.92058122, -1.66543928,  0.34305472])
np.array([ 0.83356462,  0.63918248,  0.91485574,  0.78738578,  0.72548445,  0.59345372,  0.96006267,  0.50620061,  0.89174579,  0.9964046 ])
np.array([-0.9       , -0.88181818, -0.86363636, -0.84545455, -0.82727273, -0.80909091, -0.79090909, -0.77272727, -0.75454545, -0.73636364, -0.71818182, -0.7       , -0.68181818, -0.66363636, -0.64545455, -0.62727273, -0.60909091, -0.59090909, -0.57272727, -0.55454545, -0.53636364, -0.51818182, -0.5       , -0.48181818, -0.46363636, -0.44545455, -0.42727273, -0.40909091, -0.39090909, -0.37272727, -0.35454545, -0.33636364, -0.31818182, -0.3       , -0.28181818, -0.26363636, -0.24545455, -0.22727273, -0.20909091, -0.19090909, -0.17272727, -0.15454545, -0.13636364, -0.11818182, -0.1       , -0.08181818, -0.06363636, -0.04545455, -0.02727273, -0.00909091,  0.00909091,  0.02727273,  0.04545455,  0.06363636,  0.08181818,  0.1       ,  0.11818182,  0.13636364,  0.15454545,  0.17272727,  0.19090909,  0.20909091,  0.22727273,  0.24545455,  0.26363636,  0.28181818,  0.3       ,  0.31818182,  0.33636364,  0.35454545,  0.37272727,  0.39090909,  0.40909091,  0.42727273,  0.44545455,  0.46363636,  0.48181818,  0.5       ,  0.51818182,  0.53636364,  0.55454545,  0.57272727,  0.59090909,  0.60909091,  0.62727273,  0.64545455,  0.66363636,  0.68181818,  0.7       ,  0.71818182,  0.73636364,  0.75454545,  0.77272727,  0.79090909,  0.80909091,  0.82727273,  0.84545455,  0.86363636,  0.88181818,  0.9       ])
np.array([-3.58702012, -3.64463644, -3.70024986, -3.75386037, -3.80546799, -3.8550727 , -3.90267451, -3.94827342, -3.99186943, -4.03346253, -4.07305274, -4.11064004, -4.14622444, -4.17980594, -4.21138453, -4.24096023, -4.26853302, -4.29410291, -4.3176699 , -4.33923399, -4.35879517, -4.37635345, -4.39190884, -4.40546132, -4.4170109 , -4.42655757, -4.43410135, -4.43964222, -4.44318019, -4.44471526, -4.44424743, -4.44177669, -4.43730306, -4.43082652, -4.42234708, -4.41186474, -4.39937949, -4.38489135, -4.3684003 , -4.34990635, -4.3294095 , -4.30690975, -4.2824071 , -4.25590154, -4.22739308, -4.19688172, -4.16436746, -4.1298503 , -4.09333023, -4.05480727, -4.0142814 , -3.97175263, -3.92722096, -3.88068638, -3.83214891, -3.78160853, -3.72906525, -3.67451907, -3.61796999, -3.559418  , -3.49886312, -3.43630533, -3.37174464, -3.30518105, -3.23661455, -3.16604516, -3.09347286, -3.01889766, -2.94231956, -2.86373856, -2.78315465, -2.70056785, -2.61597814, -2.52938553, -2.44079002, -2.3501916 , -2.25759029, -2.16298607, -2.06637895, -1.96776893, -1.86715601, -1.76454018, -1.65992146, -1.55329983, -1.4446753 , -1.33404787, -1.22141754, -1.1067843 , -0.99014816, -0.87150913, -0.75086719, -0.62822234, -0.5035746 , -0.37692395, -0.24827041, -0.11761396,  0.0150454 ,  0.14970765,  0.2863728 ,  0.42504086])
np.array([-3.66633582, -3.703097  , -3.73844318, -3.77237438, -3.80489058, -3.83599179, -3.86567801, -3.89394925, -3.92080549, -3.94624673, -3.97027299, -3.99288426, -4.01408054, -4.03386182, -4.05222812, -4.06917942, -4.08471574, -4.09883706, -4.11154339, -4.12283474, -4.13271109, -4.14117245, -4.14821882, -4.15385019, -4.15806658, -4.16086798, -4.16225439, -4.1622258 , -4.16078223, -4.15792366, -4.1536501 , -4.14796156, -4.14085802, -4.13233949, -4.12240597, -4.11105746, -4.09829396, -4.08411546, -4.06852198, -4.05151351, -4.03309004, -4.01325159, -3.99199814, -3.96932971, -3.94524628, -3.91974786, -3.89283445, -3.86450605, -3.83476266, -3.80360428, -3.77103091, -3.73704254, -3.70163919, -3.66482085, -3.62658751, -3.58693918, -3.54587587, -3.50339756, -3.45950426, -3.41419597, -3.36747269, -3.31933442, -3.26978116, -3.21881291, -3.16642967, -3.11263143, -3.05741821, -3.00078999, -2.94274679, -2.88328859, -2.8224154 , -2.76012722, -2.69642405, -2.63130589, -2.56477274, -2.4968246 , -2.42746147, -2.35668335, -2.28449023, -2.21088213, -2.13585903, -2.05942095, -1.98156787, -1.9022998 , -1.82161675, -1.7395187 , -1.65600566, -1.57107763, -1.48473461, -1.39697659, -1.30780359, -1.2172156 , -1.12521261, -1.03179464, -0.93696167, -0.84071371, -0.74305077, -0.64397283, -0.5434799 , -0.44157198])
np.array([-3.50770442, -3.58617588, -3.66205653, -3.73534637, -3.8060454 , -3.87415361, -3.93967101, -4.00259759, -4.06293337, -4.12067833, -4.17583248, -4.22839581, -4.27836834, -4.32575005, -4.37054094, -4.41274103, -4.4523503 , -4.48936876, -4.5237964 , -4.55563324, -4.58487926, -4.61153446, -4.63559886, -4.65707244, -4.67595521, -4.69224716, -4.70594831, -4.71705864, -4.72557815, -4.73150686, -4.73484475, -4.73559183, -4.7337481 , -4.72931355, -4.72228819, -4.71267202, -4.70046503, -4.68566723, -4.66827862, -4.6482992 , -4.62572896, -4.60056791, -4.57281605, -4.54247338, -4.50953989, -4.47401559, -4.43590047, -4.39519455, -4.35189781, -4.30601026, -4.25753189, -4.20646271, -4.15280272, -4.09655192, -4.0377103 , -3.97627788, -3.91225463, -3.84564058, -3.77643571, -3.70464003, -3.63025354, -3.55327623, -3.47370811, -3.39154918, -3.30679944, -3.21945888, -3.12952751, -3.03700533, -2.94189233, -2.84418852, -2.7438939 , -2.64100847, -2.53553222, -2.42746516, -2.31680729, -2.2035586 , -2.0877191 , -1.96928879, -1.84826767, -1.72465573, -1.59845298, -1.46965942, -1.33827504, -1.20429986, -1.06773386, -0.92857704, -0.78682941, -0.64249098, -0.49556172, -0.34604166, -0.19393078, -0.03922909,  0.11806341,  0.27794673,  0.44042086,  0.6054858 ,  0.77314156,  0.94338813,  1.11622551,  1.2916537 ])
ax^2+bx+c
np.array([-0.9, -0.7, -0.5, -0.3, -0.1,  0.1,  0.3,  0.5,  0.7,  0.9])
np.array([-5.17911123, -2.66281751, -0.87513249, -4.03926097,  1.52517255, -0.40161262,  0.55630353,  3.87005147,  3.50629056,  3.12079303])
np.array([ 1.45252184,  1.10895492,  1.36574455,  0.81220066,  0.89172029,  1.45946836,  1.44593781,  0.89619412,  1.0078098 ,  0.92634995])
np.array([-0.9       , -0.88181818, -0.86363636, -0.84545455, -0.82727273, -0.80909091, -0.79090909, -0.77272727, -0.75454545, -0.73636364, -0.71818182, -0.7       , -0.68181818, -0.66363636, -0.64545455, -0.62727273, -0.60909091, -0.59090909, -0.57272727, -0.55454545, -0.53636364, -0.51818182, -0.5       , -0.48181818, -0.46363636, -0.44545455, -0.42727273, -0.40909091, -0.39090909, -0.37272727, -0.35454545, -0.33636364, -0.31818182, -0.3       , -0.28181818, -0.26363636, -0.24545455, -0.22727273, -0.20909091, -0.19090909, -0.17272727, -0.15454545, -0.13636364, -0.11818182, -0.1       , -0.08181818, -0.06363636, -0.04545455, -0.02727273, -0.00909091,  0.00909091,  0.02727273,  0.04545455,  0.06363636,  0.08181818,  0.1       ,  0.11818182,  0.13636364,  0.15454545,  0.17272727,  0.19090909,  0.20909091,  0.22727273,  0.24545455,  0.26363636,  0.28181818,  0.3       ,  0.31818182,  0.33636364,  0.35454545,  0.37272727,  0.39090909,  0.40909091,  0.42727273,  0.44545455,  0.46363636,  0.48181818,  0.5       ,  0.51818182,  0.53636364,  0.55454545,  0.57272727,  0.59090909,  0.60909091,  0.62727273,  0.64545455,  0.66363636,  0.68181818,  0.7       ,  0.71818182,  0.73636364,  0.75454545,  0.77272727,  0.79090909,  0.80909091,  0.82727273,  0.84545455,  0.86363636,  0.88181818,  0.9       ])
np.array([-4.44614539, -4.35798626, -4.26982714, -4.18166801, -4.09350888, -4.00534975, -3.91719063, -3.8290315 , -3.74087237, -3.65271324, -3.56455411, -3.47639499, -3.38823586, -3.30007673, -3.2119176 , -3.12375848, -3.03559935, -2.94744022, -2.85928109, -2.77112197, -2.68296284, -2.59480371, -2.50664458, -2.41848546, -2.33032633, -2.2421672 , -2.15400807, -2.06584894, -1.97768982, -1.88953069, -1.80137156, -1.71321243, -1.62505331, -1.53689418, -1.44873505, -1.36057592, -1.2724168 , -1.18425767, -1.09609854, -1.00793941, -0.91978029, -0.83162116, -0.74346203, -0.6553029 , -0.56714377, -0.47898465, -0.39082552, -0.30266639, -0.21450726, -0.12634814, -0.03818901,  0.04997012,  0.13812925,  0.22628837,  0.3144475 ,  0.40260663,  0.49076576,  0.57892489,  0.66708401,  0.75524314,  0.84340227,  0.9315614 ,  1.01972052,  1.10787965,  1.19603878,  1.28419791,  1.37235703,  1.46051616,  1.54867529,  1.63683442,  1.72499354,  1.81315267,  1.9013118 ,  1.98947093,  2.07763006,  2.16578918,  2.25394831,  2.34210744,  2.43026657,  2.51842569,  2.60658482,  2.69474395,  2.78290308,  2.8710622 ,  2.95922133,  3.04738046,  3.13553959,  3.22369871,  3.31185784,  3.40001697,  3.4881761 ,  3.57633523,  3.66449435,  3.75265348,  3.84081261,  3.92897174,  4.01713086,  4.10528999,  4.19344912,  4.28160825])
np.array([-4.24558819, -4.16830466, -4.09102112, -4.01373758, -3.93645405, -3.85917051, -3.78188698, -3.70460344, -3.6273199 , -3.55003637, -3.47275283, -3.39546929, -3.31818576, -3.24090222, -3.16361868, -3.08633515, -3.00905161, -2.93176808, -2.85448454, -2.777201  , -2.69991747, -2.62263393, -2.54535039, -2.46806686, -2.39078332, -2.31349979, -2.23621625, -2.15893271, -2.08164918, -2.00436564, -1.9270821 , -1.84979857, -1.77251503, -1.69523149, -1.61794796, -1.54066442, -1.46338089, -1.38609735, -1.30881381, -1.23153028, -1.15424674, -1.0769632 , -0.99967967, -0.92239613, -0.8451126 , -0.76782906, -0.69054552, -0.61326199, -0.53597845, -0.45869491, -0.38141138, -0.30412784, -0.2268443 , -0.14956077, -0.07227723,  0.0050063 ,  0.08228984,  0.15957338,  0.23685691,  0.31414045,  0.39142399,  0.46870752,  0.54599106,  0.62327459,  0.70055813,  0.77784167,  0.8551252 ,  0.93240874,  1.00969228,  1.08697581,  1.16425935,  1.24154289,  1.31882642,  1.39610996,  1.47339349,  1.55067703,  1.62796057,  1.7052441 ,  1.78252764,  1.85981118,  1.93709471,  2.01437825,  2.09166178,  2.16894532,  2.24622886,  2.32351239,  2.40079593,  2.47807947,  2.555363  ,  2.63264654,  2.70993008,  2.78721361,  2.86449715,  2.94178068,  3.01906422,  3.09634776,  3.17363129,  3.25091483,  3.32819837,  3.4054819 ])
np.array([-4.64670259, -4.54766787, -4.44863315, -4.34959843, -4.25056371, -4.15152899, -4.05249428, -3.95345956, -3.85442484, -3.75539012, -3.6563554 , -3.55732068, -3.45828596, -3.35925124, -3.26021652, -3.1611818 , -3.06214709, -2.96311237, -2.86407765, -2.76504293, -2.66600821, -2.56697349, -2.46793877, -2.36890405, -2.26986933, -2.17083461, -2.0717999 , -1.97276518, -1.87373046, -1.77469574, -1.67566102, -1.5766263 , -1.47759158, -1.37855686, -1.27952214, -1.18048742, -1.08145271, -0.98241799, -0.88338327, -0.78434855, -0.68531383, -0.58627911, -0.48724439, -0.38820967, -0.28917495, -0.19014023, -0.09110552,  0.0079292 ,  0.10696392,  0.20599864,  0.30503336,  0.40406808,  0.5031028 ,  0.60213752,  0.70117224,  0.80020696,  0.89924167,  0.99827639,  1.09731111,  1.19634583,  1.29538055,  1.39441527,  1.49344999,  1.59248471,  1.69151943,  1.79055415,  1.88958886,  1.98862358,  2.0876583 ,  2.18669302,  2.28572774,  2.38476246,  2.48379718,  2.5828319 ,  2.68186662,  2.78090134,  2.87993605,  2.97897077,  3.07800549,  3.17704021,  3.27607493,  3.37510965,  3.47414437,  3.57317909,  3.67221381,  3.77124853,  3.87028324,  3.96931796,  4.06835268,  4.1673874 ,  4.26642212,  4.36545684,  4.46449156,  4.56352628,  4.662561  ,  4.76159572,  4.86063043,  4.95966515,  5.05869987,  5.15773459])
ax
np.array([-4.        , -3.21428571, -2.42857143, -1.64285714, -0.85714286, -0.07142857,  0.71428571,  1.5       ,  2.28571429,  3.07142857,  3.85714286,  4.64285714,  5.42857143,  6.21428571,  7.        ])
np.array([-1.24447428, -0.0504509 , -0.91776988, -1.45218331,  4.9606289 ,  6.5542723 ,  3.55413179,  3.9211066 ,  2.52742598,  3.77098829,  1.35342239, -0.56606255,  2.33607342, -0.27247962, -0.83293   ])
np.array([ 0.75951818,  1.2851599 ,  0.82250217,  1.47605096,  1.32198021,  0.83954194,  0.89507305,  1.02378572,  0.81692811,  1.10501955,  1.43124289,  1.20360327,  1.24123581,  1.05969424,  1.22648757])
np.array([-4.        , -3.88888889, -3.77777778, -3.66666667, -3.55555556, -3.44444444, -3.33333333, -3.22222222, -3.11111111, -3.        , -2.88888889, -2.77777778, -2.66666667, -2.55555556, -2.44444444, -2.33333333, -2.22222222, -2.11111111, -2.        , -1.88888889, -1.77777778, -1.66666667, -1.55555556, -1.44444444, -1.33333333, -1.22222222, -1.11111111, -1.        , -0.88888889, -0.77777778, -0.66666667, -0.55555556, -0.44444444, -0.33333333, -0.22222222, -0.11111111,  0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,  0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ,  1.11111111,  1.22222222,  1.33333333,  1.44444444,  1.55555556,  1.66666667,  1.77777778,  1.88888889,  2.        ,  2.11111111,  2.22222222,  2.33333333,  2.44444444,  2.55555556,  2.66666667,  2.77777778,  2.88888889,  3.        ,  3.11111111,  3.22222222,  3.33333333,  3.44444444,  3.55555556,  3.66666667,  3.77777778,  3.88888889,  4.        ,  4.11111111,  4.22222222,  4.33333333,  4.44444444,  4.55555556,  4.66666667,  4.77777778,  4.88888889,  5.        ,  5.11111111,  5.22222222,  5.33333333,  5.44444444,  5.55555556,  5.66666667,  5.77777778,  5.88888889,  6.        ,  6.11111111,  6.22222222,  6.33333333,  6.44444444,  6.55555556,  6.66666667,  6.77777778,  6.88888889,  7.        ])
np.array([  7.19159069e-07,   1.72704501e-06,   4.04669622e-06,   9.25137885e-06,   2.06354645e-05,   4.49074808e-05,   9.53489283e-05,   1.97516144e-04,   3.99187335e-04,   7.87112029e-04,   1.51419111e-03,   2.84189633e-03,   5.20377499e-03,   9.29632088e-03,   1.62026413e-02,   2.75513349e-02,   4.57069026e-02,   7.39781856e-02,   1.16817783e-01,   1.79969367e-01,   2.70504104e-01,   3.96676523e-01,   5.67529969e-01,   7.92198072e-01,   1.07888566e+00,   1.43357026e+00,   1.85853806e+00,   2.35094349e+00,   2.90164138e+00,   3.49456488e+00,   4.10689410e+00,   4.71017239e+00,   5.27238525e+00,   5.76084321e+00,   6.14553948e+00,   6.40252461e+00,   6.51678922e+00,   6.48419097e+00,   6.31210103e+00,   6.01865207e+00,   5.63070238e+00,   5.18083849e+00,   4.70387979e+00,   4.23339604e+00,   3.79870064e+00,   3.42265673e+00,   3.12046478e+00,   2.89942822e+00,   2.75955189e+00,   2.69473851e+00,   2.69431740e+00,   2.74465951e+00,   2.83068748e+00,   2.93715856e+00,   3.04966552e+00,   3.15535324e+00,   3.24338223e+00,   3.30518531e+00,   3.33456418e+00,   3.32766481e+00,   3.28286055e+00,   3.20056204e+00,   3.08296787e+00,   2.93376711e+00,   2.75780608e+00,   2.56073376e+00,   2.34864272e+00,   2.12772364e+00,   1.90395125e+00,   1.68281706e+00,   1.46912062e+00,   1.26682588e+00,   1.07898409e+00,   9.07719464e-01,   7.54269716e-01,   6.19070446e-01,   5.01870687e-01,   4.01866623e-01,   3.17841344e-01,   2.48300264e-01,   1.91594181e-01,   1.46024521e-01,   1.09927817e-01,   8.17387056e-02,   6.00324751e-02,   4.35494909e-02,   3.12045738e-02,   2.20847134e-02,   1.54384473e-02,   1.06599167e-02,   7.27013279e-03,   4.89744102e-03,   3.25862530e-03,   2.14159812e-03,   1.39020827e-03,   8.91374277e-04,   5.64519135e-04,   3.53130783e-04,   2.18187982e-04,   1.33157127e-04])
np.array([  6.38531203e-07,   1.53348168e-06,   3.59326799e-06,   8.21498291e-06,   1.83241311e-05,   3.98781492e-05,   8.46716160e-05,   1.75399845e-04,   3.54492439e-04,   6.98987788e-04,   1.34467045e-03,   2.52374187e-03,   4.62121528e-03,   8.25561219e-03,   1.43887808e-02,   2.44669783e-02,   4.05899479e-02,   6.56959877e-02,   1.03738986e-01,   1.59819148e-01,   2.40215188e-01,   3.52256107e-01,   5.03970483e-01,   7.03465693e-01,   9.58022304e-01,   1.27294016e+00,   1.65023729e+00,   2.08736959e+00,   2.57619247e+00,   3.10240691e+00,   3.64570777e+00,   4.18077370e+00,   4.67911187e+00,   5.11161720e+00,   5.45155350e+00,   5.67755041e+00,   5.77616444e+00,   5.74359226e+00,   5.58624828e+00,   5.32010175e+00,   4.96887531e+00,   4.56139136e+00,   4.12847740e+00,   3.69988395e+00,   3.30162521e+00,   2.95404130e+00,   2.67073058e+00,   2.45834831e+00,   2.31714133e+00,   2.24200968e+00,   2.22385824e+00,   2.25102001e+00,   2.31058103e+00,   2.38949940e+00,   2.47547057e+00,   2.55753846e+00,   2.62648197e+00,   2.67501986e+00,   2.69787717e+00,   2.69174963e+00,   2.65519253e+00,   2.58845201e+00,   2.49325072e+00,   2.37253753e+00,   2.23021080e+00,   2.07082660e+00,   1.89930498e+00,   1.72064842e+00,   1.53968652e+00,   1.36085909e+00,   1.18804692e+00,   1.02445528e+00,   8.72551542e-01,   7.34053447e-01,   6.09961886e-01,   5.00629106e-01,   4.05852152e-01,   3.24980991e-01,   2.57031535e-01,   2.00795143e-01,   1.54938139e-01,   1.18086924e-01,   8.88962873e-02,   6.61003527e-02,   4.85469858e-02,   3.52175470e-02,   2.52344751e-02,   1.78594380e-02,   1.24847440e-02,   8.62044792e-03,   5.87920175e-03,   3.96045639e-03,   2.63518097e-03,   1.73186485e-03,   1.12423186e-03,   7.20835419e-04,   4.56514617e-04,   2.85569353e-04,   1.76443981e-04,   1.07681336e-04])
np.array([  7.99786935e-07,   1.92060834e-06,   4.50012446e-06,   1.02877748e-05,   2.29467979e-05,   4.99368124e-05,   1.06026241e-04,   2.19632444e-04,   4.43882232e-04,   8.75236270e-04,   1.68371176e-03,   3.16005079e-03,   5.78633469e-03,   1.03370296e-02,   1.80165019e-02,   3.06356914e-02,   5.08238573e-02,   8.22603836e-02,   1.29896580e-01,   2.00119586e-01,   3.00793019e-01,   4.41096940e-01,   6.31089455e-01,   8.80930451e-01,   1.19974902e+00,   1.59420037e+00,   2.06683884e+00,   2.61451739e+00,   3.22709029e+00,   3.88672286e+00,   4.56808042e+00,   5.23957109e+00,   5.86565863e+00,   6.41006921e+00,   6.83952546e+00,   7.12749881e+00,   7.25741400e+00,   7.22478969e+00,   7.03795378e+00,   6.71720240e+00,   6.29252944e+00,   5.80028562e+00,   5.27928217e+00,   4.76690812e+00,   4.29577607e+00,   3.89127216e+00,   3.57019897e+00,   3.34050812e+00,   3.20196244e+00,   3.14746734e+00,   3.16477656e+00,   3.23829901e+00,   3.35079392e+00,   3.48481771e+00,   3.62386047e+00,   3.75316803e+00,   3.86028248e+00,   3.93535076e+00,   3.97125118e+00,   3.96357999e+00,   3.91052856e+00,   3.81267207e+00,   3.67268502e+00,   3.49499669e+00,   3.28540136e+00,   3.05064092e+00,   2.79798046e+00,   2.53479887e+00,   2.26821598e+00,   2.00477502e+00,   1.75019431e+00,   1.50919648e+00,   1.28541664e+00,   1.08138548e+00,   8.98577546e-01,   7.37511786e-01,   5.97889222e-01,   4.78752255e-01,   3.78651153e-01,   2.95805386e-01,   2.28250223e-01,   1.73962117e-01,   1.30959346e-01,   9.73770585e-02,   7.15179644e-02,   5.18814348e-02,   3.71746724e-02,   2.63099888e-02,   1.83921506e-02,   1.26993855e-02,   8.66106382e-03,   5.83442565e-03,   3.88206963e-03,   2.55133139e-03,   1.65618468e-03,   1.06191313e-03,   6.72523652e-04,   4.20692212e-04,   2.59931984e-04,   1.58632917e-04])
a \exp\left(-\frac{(x-2.5)^2}{2}\right) + b \exp\left(-x^2\right)