def _interp_evaluate(coefficients, t0, t1, t):
    """Evaluate polynomial interpolation at the given time point.
    Args:
        coefficients: list of Tensor coefficients as created by `interp_fit`.
        t0: scalar float64 Tensor giving the start of the interval.
        t1: scalar float64 Tensor giving the end of the interval.
        t: scalar float64 Tensor giving the desired interpolation point.
    Returns:
        Polynomial interpolation of the coefficients at time `t`.
    """
    assert (t0 <= t) & (t <= t1), 'invalid interpolation, fails `t0 <= t <= t1`: {}, {}, {}'.format(t0, t, t1)
    x = (t - t0) / (t1 - t0)

    total = coefficients[0] + x * coefficients[1]
    x_power = x
    for coefficient in coefficients[2:]:
        x_power = x_power * x
        total = total + x_power * coefficient

    return total