Wrong values from scipy.special.erf (erf(x) != -erf(-x))

We are seeing incorrect values returned from scipy.special.erf

We have some equations that depend on the symmetry of the erf function, but scipy violates this assumption.

Mathematically, for reals, erf(x) == -erf(-x), but scipy.special.erf does not seem to honor this property.

The difference from expectation seems to be beyond a simple floating point representation problem.

Reproducing code example:

# succeeds
import math
difference = math.erf(5.905732037710919)+math.erf(-5.905732037710919)
assert abs(difference) == 0.0

# fails, difference should be 0.0, difference is actually -1.1102230246251565e-16
import scipy.special
difference = scipy.special.erf(5.905732037710919)+scipy.special.erf(-5.905732037710919)
assert abs(difference) == 0.0

Error message:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AssertionError

Scipy/Numpy/Python version information:

1.1.0 1.14.0 sys.version_info(major=3, minor=6, micro=3, releaselevel='final', serial=0)

(Older versions of scipy affected as well)

[person142]

cut-off of scipy (cdflib)

We use Cephes erf, not cdflib.

[ev-br]

(just had an open environment and a bit of time to spare) It seems easiest to throw gh-9351 over the wall and forget.