from diofant import *

cases = [oo, -oo, I*oo, -I*oo, oo - I*oo, oo + I*oo,
         -oo - I*oo, -oo + I*oo]

bad = 0
for f in [asin, acos, asec, acsc, asinh, acosh, atan, acot, atanh, acoth]:
    for a in cases:
        if f(a, evaluate=False).evalf() != f(a, evaluate=True).evalf():
            bad += 1
            print(f, a)
print(f"Bad cases: {bad}")

from diofant import *

x = symbols('x')

funcs = [cos, sin, tan, cot, csc, sec, acos, asin, atan, acot, acsc, asec,
         cosh, sinh, tanh, coth, csch, sech, acosh, asinh, atanh, acoth]
#        acsch, asech]

points = [oo, -oo, I*oo, -I*oo]

bad = 0
total = 0
for f1 in funcs:
    for f2 in funcs:
        total += 1
        expr1 = f1(x)
        expr2 = expr1.rewrite(f2)
        fine = True
        for p in points:
            val1 = expr1.subs({x: p}).evalf()
            try:
                val2 = expr2.subs({x: p}).evalf()
                test = val1 != val2
            except:
                test = True
            if test:
                if expr1.limit(x, p).evalf() == expr2.limit(x, p).evalf():
                    continue
                print()
                pprint((f1, f2, p))
                pprint((expr1, ' --> ', expr2))
                fine = False
        if not fine:
            bad += 1

print(bad, 'bad rewrites out of', total)

import numpy as np
from diofant import *

x = symbols('x')

funcs = [cos, sin, tan, cot , csc , sec , acos, asin, atan, acot , acsc , asec,
         cosh, sinh, tanh, coth, csch, sech, acosh, asinh, atanh, acoth]

numtests = 10
std = 10
normal = np.random.randn
points_real = std*normal(numtests)
points_complex = std*(normal(numtests) + normal(numtests)*1j)
points = ([Float(_, dps=60) for _ in points_real] +
          [Float(_.real, dps=60) + I*Float(_.imag, dps=60) for _ in points_complex])

def isclose(n1, n2):
    try:
        return bool(abs(n1 - n2)/(abs(n1) + abs(n2)) < 1e-5)
    except TypeError:
        return False

bad = 0
total = 0
for f1 in funcs:
    for f2 in funcs:
        total += 1
        expr1 = f1(x)
        expr2 = expr1.rewrite(f2)
        fine = True
        for p in points:
            val1 = expr1.subs({x:p}).evalf(strict=False)
            val2 = expr2.subs({x:p}).evalf(strict=False)
            if not isclose(val1, val2):
                print()
                print(f1, f2, p)
                print(expr1, ' --> ', expr2)
                print(val1, val2)
                fine = False
        if not fine:
            bad += 1

print(bad, 'bad rewrites out of', total)