import time
start_time = time.time()
_eq_map_cache = {}
#
def get_eq_map(vals):
    # Given a list of floating point values, returns a map from result values
    # to an equation string returning that result.
    global _eq_map_cache
    if tuple(vals) not in _eq_map_cache:
        eq_map = {}
        if len(vals) == 1:
            eq_map[vals[0]] = str(vals[0])
        else:
            for i in range(1, len(vals)):
                head_eq_map = get_eq_map(vals[:i])
                tail_eq_map = get_eq_map(vals[i:])
                for h,heq in head_eq_map.iteritems():
                    heq2 = "(" + heq
                    for t,teq in tail_eq_map.iteritems():
                        teq2 = teq + ")"
                        eq_map[h + t] = heq2 + "+" + teq2
                        eq_map[h - t] = heq2 + "-" + teq2
                        eq_map[h * t] = heq2 + "*" + teq2
                        if t != 0:
                            eq_map[h / t] = heq2 + "/" + teq2
        _eq_map_cache[tuple(vals)] = eq_map
    return _eq_map_cache[tuple(vals)]
#
all_vals = get_eq_map([float(x) for x in range(1, 10)])
print 'Time:', time.time() - start_time
print 'Total number of values', len(all_vals)
for i in (float(x) for x in range(1900, 2100)):
    if i in all_vals:
        print i, all_vals[i]
    else:
        print i, 'None'