scipy: BUG: unclear error for invalid bracketing

Describe your issue.

I have enclosed a minimum reproducible example with data and I am trying to use two methods in the scipy optimize package - https://docs.scipy.org/doc/scipy/reference/optimize.html

One is minimize_scalar and the other is Brent’s method. But both the outputs have large differences. Can anybody explain why ?

Also I get a runtime error while running Brent-

test.py:29: RuntimeWarning: invalid value encountered in power ls = np.sum((x1[1:] - x1[:-1]*np.sign(a)*a**dt)**2)

Additionally the Brent one has another one if I specify a triple interval ala - dum = brent(func,brack=(-1,0,1),tol=3.0e-8) ValueError : Not a bracketing interval.

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brent.html But docs say that I can specify a triplet in the bracketing interval.

Reproducing Code Example

`import numpy as np
from scipy.optimize import brent,minimize_scalar
import math

def main():

    data = np.loadtxt("x.dat",skiprows=0)
    t = data[:,0] 
    x = data[:,1]
    dum = minls(t,x)
    
def minls(t,x):
    a = 1/math.e
    dt = np.diff(t)
    def func(a):
        try:
            ls = np.sum((x[1:] - x[:-1]*a**dt)**2)
        except Warning:
            print(traceback.format_exc())
        return ls

    dum = brent(func,brack=(-1,0,1),tol=3.0e-8)
    dum1 = minimize_scalar(func, bounds=[0, 1], method='bounded').x
    print(dum,dum1)
    return dum

main()
`

Error message

I encounter an error and a warning wi this

Test.py:29: RuntimeWarning: invalid value encountered in power 


ValueError  : Not a bracketing interval.

SciPy/NumPy/Python version information

Scipy 1.7.1 /Numpy 1.19.1/Python3.8