def log_b(x): """ helper for hadamard decomp. """ return 2 * jnp.log(top_b(x) / bottom(x))
def second_log_a(x): """ helper for hadamard decomp. """ return jnp.log(back_log_in(x))
def first_log_a(x): """ helper for hadamard decomp. """ return 4 * jnp.log(top_a(x) / bottom(x))
def log_b(x): return 2 * jnp.log(top_b(x) / bottom(x))
def second_log_a(x): return jnp.log(back_log_in(x))
def first_log_a(x): return 4 * jnp.log(top_a(x) / bottom(x))