Iteration and Vectorization return different results

Question

I am trying to vectorize the Brown function, which is evaluated over the range (-1,4). S (vectorized) and sigma (iterative) should therefore be equal, which they are for most input arrays I have tested, i.e. the commented a, but not for the uncommented a, where the difference is quite large (-40960). Since the function implementations are equivalent as far as I know, I cannot figure out why the results are different. Any help would be much appreciated!

import numpy as np
from decimal import Decimal
np.set_printoptions(precision=100)
D = 90
a = np.array([
    -0.8195813369795628  ,  2.1078160649038598  ,
    0.5728485376392076  ,  0.19214447077132535 ,
    2.01979863827681    ,  1.861016566323948   ,
    0.03570569401002843 ,  1.2179443346030103  ,
    -0.2023148152997174  ,  2.344402437732328   ,
    0.3992427517339374  , -0.580084584056455   ,
    2.8553419396152955  , -0.9053166646802753  ,
    2.4078276437008532  ,  1.769295277018315   ,
    0.05839942222762762 ,  0.1594092290921887  ,
    0.7285414841081187  , -0.62168457722208    ,
    1.1889002818073933  ,  0.6524303072620927  ,
    3.3633879172407637  ,  3.0769408543464998  ,
    -0.45519320493350635 ,  0.43102403540370915 ,
    -0.9252201822835948  ,  3.12911155641771    ,
    2.302579839847708   ,  3.16984716563936    ,
    1.3127842651843633  ,  0.20958492282551844 ,
    3.981729076545438   ,  1.0909855253127345  ,
    3.9449203415891487  ,  1.3493337542750858  ,
    0.045652220005763855,  3.9876425656088075  ,
    2.348089357316039   ,  3.556978916005656   ,
    1.7058246955468757  , -0.1903975039419017  ,
    -0.8527195886839736  ,  3.943660607246864   ,
    3.6468743314466314  ,  1.369093942433826   ,
    3.075116242479504   ,  2.334122427494658   ,
    3.2895527223960297  ,  0.14290418230167345 ,
    0.4959100263489993  ,  2.9460988192449147  ,
    1.8885423993409554  ,  3.003770472482533   ,
    0.8120286831579513  , -0.0938573811789214  ,
    3.316954973064636   ,  2.776219448028004   ,
    3.976149157953796   ,  3.836526854565294   ,
    2.5311757286425833  ,  0.7206181274066051  ,
    -0.5537806875062783  ,  0.3505280689662853  ,
    1.1798421347136443  , -0.8201745245328302  ,
    2.1829779508510687  ,  1.6780163409792823  ,
    1.3730944605318656  ,  1.70487098007274    ,
    -0.9772480011318625  ,  3.8936145630943297  ,
    2.208108667511484   ,  1.3737024114348877  ,
    3.607651563373506   ,  2.032977481458486   ,
    2.0759850609302424  , -0.39569125550256734 ,
    2.1840048431472256  , -0.7307503352781088  ,
    -0.2280889610541812  ,  0.31422245330372567 ,
    1.2536427131615615  ,  2.9155338041621053  ,
    -0.8296245906825948  ,  2.6033094690850427  ,
    1.628556602479812   , -0.6583839970597181  ,
    3.2178860860566343  , -0.4291117469753949
])

# a = np.array([
#     -0.24326079350064667,  1.9398461449036972 ,  1.1797471464017137 ,
#     2.785342560109509  ,  2.1256127620820333 ,  2.17932485196713   ,
#     -0.5056361946982487 , -0.6015891193965008 ,  1.3604221619244674 ,
#     1.5906269601677465 , -0.5838110012848782 , -0.7794260647387554 ,
#     3.7414065063184694 ,  3.908191088860524  ,  1.7398922245943935 ,
#     0.2594518014543459 ,  0.26853905876986417,  2.6513759153963536 ,
#     3.9300813391410507 , -0.22684113001034145, -0.9510375598056205 ,
#     -0.6861883509333768 , -0.18193551587912327,  2.2606226238298963 ,
#     3.8876765949132253 ,  0.35301727341430644,  3.2521698770948593 ,
#     -0.3758906340542608 , -0.25640107769661824, -0.15220637767735046,
#     2.7460929984988507 ,  0.33843737080084413,  1.8371601261136985 ,
#     0.12611175385637474, -0.650561948254508  , -0.4779901630615837 ,
#     2.0010286412998437 ,  3.884377947986377  ,  3.6300883926415874 ,
#     0.3356095899399807 ,  1.2882384696767533 ,  1.990009296808449  ,
#     2.5253383884760527 ,  1.135461522592501  ,  1.9495805928096308 ,
#     0.9083711321253394 , -0.23634761490005896,  1.7484076577378653 ,
#     3.6219200691205877 ,  3.078817955667887  ,  0.8501396510730472 ,
#     3.359302276017435  ,  0.7731124557398252 ,  1.8948667444885072 ,
#     2.6958910486918066 ,  2.9209091072651847 ,  3.4129582373243705 ,
#     1.5821807306506335 ,  0.6762606433965022 ,  3.8822452600542663 ,
#     3.818937414485327  , -0.20335236087550024,  1.823951066425706  ,
#     1.532365782386333  ,  3.3698354058360334 ,  3.5832883562938784 ,
#     -0.8018961048636466 ,  3.6581456199131264 ,  3.521788869215107  ,
#     -0.39667357751053645,  1.3733773721715767 , -0.07239496582275817,
#     3.905023791644104  ,  3.625188362904372  ,  3.7790115400299955 ,
#     3.020466900608116  ,  3.658497613816361  ,  2.9759327122014114 ,
#     -0.7121009035990102 ,  0.06379796314462038,  0.7256262413218697 ,
#     1.1444416096632541 ,  2.281575941092746  ,  2.4506770467922987 ,
#     1.5220049951348589 , -0.9653485342086856 ,  3.8988630900360306 ,
#     2.17529438453628   ,  3.723873897373978  , -0.49841970841454497
# ])

# Iterative calculation
z = a.copy()
sigma = 0
for i in range(D - 1):
    base = z[i] ** 2
    power = z[i + 1] ** 2 + 1
    sigma = sigma + base ** power

    base = z[i + 1] ** 2
    power = z[i] ** 2 + 1
    sigma = sigma + base ** power

print(f'Iterative sum: {Decimal(float(sigma))}')


# Vectorized calculation
z = a[np.newaxis,:]
S = 0
for d in range(D-1):
    t1 = z[:,d]**2
    t2 = z[:,d+1]**2
    t3 = t1**(t2+1)
    t4 = t2**(t1+1)
    S += t3 + t4

print(f'Vectorized sum: {Decimal(float(S))}')


# Difference
print(f'Difference: {Decimal(float(sigma - S))}')