```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor fused_norm_residual_mul(
    torch::Tensor x,
    torch::Tensor y,
    double eps);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/AccumulateType.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda.h>
#include <cuda_runtime.h>

template <typename T>
__device__ __forceinline__ T block_sum(T value, T* scratch) {
    const int lane = threadIdx.x & 31;
    const int warp = threadIdx.x >> 5;

    #pragma unroll
    for (int offset = 16; offset > 0; offset >>= 1)
        value += __shfl_down_sync(0xffffffff, value, offset);

    if (lane == 0)
        scratch[warp] = value;
    __syncthreads();

    if (warp == 0) {
        value = lane < 8 ? scratch[lane] : T(0);
        #pragma unroll
        for (int offset = 16; offset > 0; offset >>= 1)
            value += __shfl_down_sync(0xffffffff, value, offset);
        if (lane == 0)
            scratch[0] = value;
    }
    __syncthreads();

    T result = scratch[0];
    __syncthreads();
    return result;
}

template <typename scalar_t, bool Cache>
__global__ void norm_residual_mul_kernel(
    const scalar_t* __restrict__ x,
    const scalar_t* __restrict__ y,
    scalar_t* __restrict__ out,
    int64_t width,
    double eps)
{
    using acc_t = at::acc_type<scalar_t, true>;

    __shared__ acc_t scratch[8];
    acc_t values[Cache ? 32 : 1];

    const int64_t base = int64_t(blockIdx.x) * width;
    acc_t sum = acc_t(0);

    int item = 0;
    for (int64_t col = threadIdx.x; col < width; col += 256, ++item) {
        acc_t value = static_cast<acc_t>(x[base + col]);
        if constexpr (Cache)
            values[item] = value;
        sum += value;
    }

    const acc_t mean = block_sum(sum, scratch) / acc_t(width);

    acc_t squared_deviations = acc_t(0);
    item = 0;
    for (int64_t col = threadIdx.x; col < width; col += 256, ++item) {
        acc_t value;
        if constexpr (Cache)
            value = values[item];
        else
            value = static_cast<acc_t>(x[base + col]);

        const acc_t centered = value - mean;
        squared_deviations += centered * centered;
    }

    const acc_t variance =
        block_sum(squared_deviations, scratch) / acc_t(width);
    const acc_t inv_std = acc_t(1) / sqrt(variance + acc_t(eps));

    item = 0;
    for (int64_t col = threadIdx.x; col < width; col += 256, ++item) {
        acc_t value;
        if constexpr (Cache)
            value = values[item];
        else
            value = static_cast<acc_t>(x[base + col]);

        const acc_t residual = static_cast<acc_t>(y[base + col]);

        // Preserve rounding at the original operator boundaries.
        const scalar_t normalized =
            static_cast<scalar_t>((value - mean) * inv_std);
        const scalar_t added =
            static_cast<scalar_t>(static_cast<acc_t>(normalized) + residual);
        out[base + col] =
            static_cast<scalar_t>(static_cast<acc_t>(added) * residual);
    }
}

torch::Tensor fused_norm_residual_mul(
    torch::Tensor x,
    torch::Tensor y,
    double eps)
{
    TORCH_CHECK(x.is_cuda() && y.is_cuda(), "Expected CUDA tensors");
    TORCH_CHECK(x.device() == y.device(), "Devices must match");
    TORCH_CHECK(x.scalar_type() == y.scalar_type(), "Dtypes must match");
    TORCH_CHECK(x.dim() == 2 && x.sizes() == y.sizes(),
                "Expected matching two-dimensional tensors");
    TORCH_CHECK(x.is_contiguous(), "x must be contiguous");
    TORCH_CHECK(x.size(1) > 1, "Normalization requires more than one value");

    const c10::cuda::CUDAGuard device_guard(x.device());
    auto residual = y.contiguous();
    auto out = torch::empty_like(x);

    if (x.size(0) == 0)
        return out;

    const int64_t width = x.size(1);
    const auto stream = at::cuda::getCurrentCUDAStream();

    AT_DISPATCH_FLOATING_TYPES_AND2(
        at::ScalarType::Half,
        at::ScalarType::BFloat16,
        x.scalar_type(),
        "fused_norm_residual_mul",
        [&] {
            if (width <= 8192) {
                norm_residual_mul_kernel<scalar_t, true>
                    <<<x.size(0), 256, 0, stream>>>(
                        x.data_ptr<scalar_t>(),
                        residual.data_ptr<scalar_t>(),
                        out.data_ptr<scalar_t>(),
                        width, eps);
            } else {
                norm_residual_mul_kernel<scalar_t, false>
                    <<<x.size(0), 256, 0, stream>>>(
                        x.data_ptr<scalar_t>(),
                        residual.data_ptr<scalar_t>(),
                        out.data_ptr<scalar_t>(),
                        width, eps);
            }
        });

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return out;
}
"""

_fused_ops = load_inline(
    name="fused_instance_norm_residual_mul_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_norm_residual_mul"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3", "--fmad=false"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_features, out_features, eps=1e-5, momentum=0.1):
        super().__init__()
        self.bmm = nn.Linear(in_features, out_features)
        self.instance_norm = nn.InstanceNorm2d(
            out_features, eps=eps, momentum=momentum
        )

    def forward(self, x, y):
        x = self.bmm(x)

        if (
            x.is_cuda
            and y.is_cuda
            and x.device == y.device
            and x.dtype == y.dtype
            and x.ndim == 2
            and x.shape == y.shape
            and x.shape[1] > 1
        ):
            return _fused_ops.fused_norm_residual_mul(
                x.contiguous(), y, self.instance_norm.eps
            )

        x = self.instance_norm(
            x.unsqueeze(1).unsqueeze(1)
        ).squeeze(1).squeeze(1)
        return (x + y) * y
```