auto x_1 = ConjugateHelper(scope, op.input(0));
  auto x_2 = ConjugateHelper(scope, op.input(1));
  // y = (x_1 - x_2)^2
  // dy/dx_1 = 2 * (x_1 - x_2)
  // dy/dx_2 = -2 * (x_1 - x_2)
  auto two = Cast(scope, Const(scope, 2), grad_inputs[0].type());
  auto gx_1 = Mul(scope, grad_inputs[0], Mul(scope, two, Sub(scope, x_1, x_2)));
  auto gx_2 = Neg(scope, gx_1);

  auto c_1 = ops::Const(root, {{2.0}, {3.0}});
  EXPECT_EQ(c_1.node()->name(), "Const_1");

  auto x = ops::Const(root.WithOpName("x"), 1);
  EXPECT_EQ(x.node()->name(), "x");
  auto x_1 = ops::Const(root.WithOpName("x"), 1);
  EXPECT_EQ(x_1.node()->name(), "x_1");

  Scope child = root.NewSubScope("c");
  auto c_y = ops::Const(child.WithOpName("y"), 1);
  EXPECT_EQ(c_y.node()->name(), "c/y");

	// as described in the Ed25519 paper
	//
	// Group even and odd coefficients
	// x*B     = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
	//         + x_1*16^1*B + x_3*16^3*B + ... + x_63*16^63*B
	// x*B     = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
	//    + 16*( x_1*16^0*B + x_3*16^2*B + ... + x_63*16^62*B)
	//
	// We use a lookup table for each i to get x_i*16^(2*i)*B
	// and do four doublings to multiply by 16.

}

TEST_F(NaryGradTest, Div) {
  TensorShape x_shape({3, 2, 5});
  auto x = Placeholder(scope_, DT_FLOAT, Placeholder::Shape(x_shape));
  // Test x / (1 + |x|) rather than x_1 / x_2 to avoid triggering large
  // division errors in the numeric estimator used by the gradient checker.
  auto y = Div(scope_, x, Add(scope_, Const<float>(scope_, 1), Abs(scope_, x)));
  RunTest({x}, {x_shape}, {y}, {x_shape});

	p := participle.MustBuild(
		&ObjectKey{},
		participle.Lexer(sqlLexer),
		participle.CaseInsensitive("Keyword"),
	)

	validCases := []string{
		"['abc']",
		"['ab''c']",
		"['a''b''c']",
		"['abc-x_1##@(*&(#*))/\\']",
	}
	for i, tc := range validCases {
		err := p.ParseString(tc, &k)
		if err != nil {
			t.Fatalf("%d: %v", i, err)
		}
		if string(*k.Lit) == "" {
			t.Fatalf("Incorrect parse %#v", k)

// every pair y_i in y and x_j in x.  Note that the Jacobian is defined directly
// over the elements of tensors y and x, and doesn't depend on their shapes.
//
// If x = (x_1, x_2, ..., x_m) and y = (y_1, y_2, .., y_n) the matrix evaluated
// is actually the Jacobian transpose, defined as this mxn matrix:
// dy_1/d_x1 dy_2/dx_1 ... dy_n/dx_1
// dy_1/dx_2 dy_2/dx_2 ... dy_n/dx_2
//     .

      For example, the code
        x.a()
        x.b()
        %c = y.c()
        x.d(%c)
      would be transformed into something like
        call @x_1()
        %c = call @y_1()
        call @x_2(%c)
      with @x_1, @x_2 and @y_1 filled in.
  }];
  let constructor = "TF::CreateGroupByDialectPass()";
}

def RemoveUnusedArgumentsPass : Pass<"tf-remove-unused-arguments", "ModuleOp"> {

"top" function is configurable.

For example, the code
  x.a()
  x.b()
  %c = y.c()
  x.d(%c)
would be transformed into something like
  call @x_1()
  %c = call @y_1()
  call @x_2(%c)
with @x_1, @x_2 and @y_1 filled in.
### `-tf-guarantee-all-funcs-one-use`

_Guarantee all FuncOp's have only a single use._

### `-tf-hoist-loop-invariant`

	for {
		if v_0.Op != OpTrunc32to16 {
			break
		}
		x := v_0.Args[0]
		if x.Op != OpRsh32x64 {
			break
		}
		_ = x.Args[1]
		x_1 := x.Args[1]
		if x_1.Op != OpConst64 {
			break
		}
		s := auxIntToInt64(x_1.AuxInt)
		if !(s >= 16) {
			break
		}
		v.copyOf(x)
		return true
	}
	return false
}

//    `ReduceWindowOp` with `AddOp` as body.
//
// Example:
// Let f : R^4 -> R^2 be an average pool function with window size 3, stride 2,
// and SAME padding with 0's. It is defined by
//    f(x) = [ (x_1 + x_2 + x_3) / 3 ]      ( x = (x_1, x_2, x_3, x_4) )
//           [ (x_3 + x_4 + 0)   / 2 ]      (the 0 results from right padding)
// Note that for SAME padding in `AvgPool` the padded entries are not counted