ok 1 - machine epsilon is same as ULP(1)
# eps              =>  2.22044604925031308e-16
# ulp(1)           =>  2.22044604925031308e-16
ok 2 - machine epsilon is not same as ULP(2)
# ulp(2)           =>  4.44089209850062616e-16
ok 3 - machine epsilon scaled by 2 is actually the same as ULP(2)
# 2*eps            =>  4.44089209850062616e-16
ok 4 - machine epsilon is _not_ scaled by 2.1 to give the same as ULP(2)
# 2.1*eps          =>  4.66293670342565767e-16
# ulp(2.1)         =>  4.44089209850062616e-16
ok 5 - machine epsilon is not the same as ULP(1/10)
# ulp(1/10)        =>  1.38777878078144568e-17
# using machine epsilon does not give the results you seem to think
ok 6 - 1 million single steps is not the same as removing one million times the step-value
# x                => -1.33288113454699264e-06
# diff             =>  0.00000000000000000e+00
ok 7
# sectokia         => -1.33288113410290343e-06
# stringify sectokia = -1.3328811341029e-06
# in case you don't believe mine is equivalent:
# loop    0:
# 	x        =  8.00000000000000044e-01 = '0.8',
# 	sectokia =  8.00000000000000488e-01 = '0.8',
# 	diff     =  8.00000000000000044e-01 = '0.8'
# loop    1:
# 	x        =  7.90000000000000036e-01 = '0.79',
# 	sectokia =  7.90000000000000480e-01 = '0.79',
# 	diff     =  7.90000000000000036e-01 = '0.79'
# loop    2:
# 	x        =  7.80000000000000027e-01 = '0.78',
# 	sectokia =  7.80000000000000471e-01 = '0.78',
# 	diff     =  7.80000000000000027e-01 = '0.78'
# loop    3:
# 	x        =  7.70000000000000018e-01 = '0.77',
# 	sectokia =  7.70000000000000462e-01 = '0.77',
# 	diff     =  7.70000000000000018e-01 = '0.77'
# loop    4:
# 	x        =  7.60000000000000009e-01 = '0.76',
# 	sectokia =  7.60000000000000453e-01 = '0.76',
# 	diff     =  7.60000000000000009e-01 = '0.76'
# loop    5:
# 	x        =  7.50000000000000000e-01 = '0.75',
# 	sectokia =  7.50000000000000444e-01 = '0.75',
# 	diff     =  7.50000000000000000e-01 = '0.75'
# loop    6:
# 	x        =  7.39999999999999991e-01 = '0.74',
# 	sectokia =  7.40000000000000435e-01 = '0.74',
# 	diff     =  7.39999999999999991e-01 = '0.74'
# loop    7:
# 	x        =  7.29999999999999982e-01 = '0.73',
# 	sectokia =  7.30000000000000426e-01 = '0.73',
# 	diff     =  7.29999999999999982e-01 = '0.73'
# loop    8:
# 	x        =  7.19999999999999973e-01 = '0.72',
# 	sectokia =  7.20000000000000417e-01 = '0.72',
# 	diff     =  7.20000000000000084e-01 = '0.72'
# loop    9:
# 	x        =  7.09999999999999964e-01 = '0.71',
# 	sectokia =  7.10000000000000409e-01 = '0.71',
# 	diff     =  7.10000000000000075e-01 = '0.71'
# loop   70:
# 	x        =  9.99999999999994643e-02 = '0.0999999999999995',
# 	sectokia =  9.99999999999999084e-02 = '0.0999999999999999',
# 	diff     =  9.99999999999999778e-02 = '0.1'
# mismatch ends loop at 70
# 
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