def __missing__(self, key):
        if self.default_factory is None:
            raise KeyError(key)
        else:
            ret = self[key] = self.default_factory(name=key)
            return ret
def _cost_gp_withGradients(self,x):
        """
        Predicts the time cost and its gradient of evaluating the function at x.
        """
        m, _, dmdx, _= self.cost_model.predict_withGradients(x)
        return np.exp(m), np.exp(m)*dmdx