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%%time
# apply, but pre-select columns e and f instead of complete rows: iteration misdemeanor

def myfunc4(b, c):
    x = (b + c)**2
    y = (b - c)**2
    z = (b - c)**2
    return x, y,z

dfY = pd.DataFrame()

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%%time
# apply row-wise: iteration crime

def myfunc3(row):
    return pd.Series(myfunc2(row))

dfY = pd.DataFrame()
dfY[["x", "y", "z"]] = dfS.apply(myfunc3, axis=1)
display(dfY.tail())

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%%time
# convert df to dictionary before iterating

dictS = dfS.to_dict(orient="records")
for row in dictS:
    res = myfunc2a(row)

dfY = pd.DataFrame.from_dict(dictY).T
dfY.columns = ["x", "y", "z"]
display(dfY.tail())

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def myfunc2a(row):
    x = (row["B"] + row["C"])**2
    y = (row["B"] - row["C"])**2
    z = (row["B"] - row["C"])**2
    return [x, y,z]

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%%time
# itertuples: iteration misdemeanor

dictY = dict()
for row in dfS.itertuples(): 
    res = myfunc2(row)
    dictY[row] = list(res)
    
dfY = pd.DataFrame.from_dict(dictY).T
dfY.columns = ["x", "y", "z"]

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%%time
# iterrows: iteration felony

dictY = dict()
for i, row in dfS.iterrows():   
    res = myfunc2(row)
    dictY[row.name] = list(res)
    
dfY = pd.DataFrame.from_dict(dictY).T
dfY.columns = ["x", "y", "z"]

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def myfunc2(row):
    x = (row.B + row.C)**2
    y = (row.B - row.C)**2
    z = (row.B - row.C)**2
    return [x, y,z]

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%%time
# conventional loop using iloc - iteration crime
dfY = pd.DataFrame()
for i in range(dfS.shape[0]):
    res = myfunc1(dfS["B"].iloc[i], dfS["C"].iloc[i])
    dfY = pd.concat([dfY, pd.DataFrame([res])], ignore_index=True)
dfY.rename(columns={0:"x", 1:"y", 2:"z"}, inplace=True)
display(dfY.tail())

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def myfunc1(b, c):
    x = (b + c)**2
    y = (b - c)**2
    z = (b - c)**2
    return [x,y,z]

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def myfunc0(b, c):
    r = np.sqrt(np.mean((b - c)**2))
    return r


def variants(df, dftype):
    dfX = df.copy()
    print(dftype)
    %timeit  dfX["r1"] = (((dfX["B"] - dfX["C"])**2).mean())**0.5
    %timeit  dfX["r2"] = np.sqrt( np.mean((dfX["B"] - dfX["C"])**2))