code: def test_custom_root_scalar(self, solve_method):
      def scalar_solve(f, y):
          return y / f(1.0)
  
      def sqrt_cubed(x, tangent_solve=scalar_solve):
          f = lambda y: y**2 - x**3
          # Note: Nonzero derivative at x0 required for newton_raphson
          return lax.custom_root(f, 1.0, solve_method, tangent_solve)
  
      value, grad = jax.value_and_grad(sqrt_cubed)(5.0)
      self.assertAllClose(
          value, 5**1.5, check_dtypes=False, rtol=1e-6
      )
      rtol = 5e-6 if jtu.test_device_matches(["tpu"]) else 1e-7
      self.assertAllClose(
          grad, jax.grad(pow)(5.0, 1.5), check_dtypes=False, rtol=rtol
      )
      jtu.check_grads(
          sqrt_cubed,
          (5.0,),
          order=2,
          rtol={jnp.float32: 1e-2, jnp.float64: 1e-3},
      )
  
      inputs = jnp.array([4.0, 5.0])
      results = jax.vmap(sqrt_cubed)(inputs)
      self.assertAllClose(
          results,
          inputs**1.5,
          check_dtypes=False,
          atol={jnp.float32: 1e-3, jnp.float64: 1e-6},
          rtol={jnp.float32: 1e-3, jnp.float64: 1e-6},
      )
  
      results = jax.jit(sqrt_cubed)(5.0)
      self.assertAllClose(
          results,
          5.0**1.5,
          check_dtypes=False,
          rtol={np.float64: 1e-7},
      )
  
imports: import re
  from absl.testing import absltest
  from absl.testing import parameterized
  import numpy
  import jax
  from jax import lax
  from jax._src import test_util
  from jax import tree_util
  import jax.numpy
  import jax.scipy
  from jax import config
label_desc: Use image node_id 1 for calling the CustomRootTest obj's underlying member method code with example usage: obj.test_custom_root_scalar(solve_method) and returns: unknown, lax