[bug] Fix optimization of exp with negative exponent (#8398)

Issue: fixes #8269 

### Brief Summary

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### <samp>🤖 Generated by Copilot at 7a8b410</samp>

Fix the return type of exponent statements that are simplified by
`alg_simp` and add a test case for this optimization. This improves the
correctness and performance of code generation for exponent operations.

### Walkthrough

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copilot:walkthrough
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### <samp>🤖 Generated by Copilot at 7a8b410</samp>

* Simplify negative exponents by using reciprocal function
([link](https://github.com/taichi-dev/taichi/pull/8398/files?diff=unified&w=0#diff-77d8ca8e4dc6081988bd6dddb74bb9a5485af28ce3e0b43bc06d123256695513R282),
[link](https://github.com/taichi-dev/taichi/pull/8398/files?diff=unified&w=0#diff-77d8ca8e4dc6081988bd6dddb74bb9a5485af28ce3e0b43bc06d123256695513R288))
- Set return type of new exponent statement to match original right-hand
side
([link](https://github.com/taichi-dev/taichi/pull/8398/files?diff=unified&w=0#diff-77d8ca8e4dc6081988bd6dddb74bb9a5485af28ce3e0b43bc06d123256695513R282))
- Set return type of result statement to match original exponent
statement
([link](https://github.com/taichi-dev/taichi/pull/8398/files?diff=unified&w=0#diff-77d8ca8e4dc6081988bd6dddb74bb9a5485af28ce3e0b43bc06d123256695513R288))
* Add test case for negative exponent simplification in
`test_optimization.py`
([link](https://github.com/taichi-dev/taichi/pull/8398/files?diff=unified&w=0#diff-b8b031f0789413acece482512df4af5b8419a2a2dea3624b26114bbb9b57d334L156-R169))

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

taichi/transforms/alg_simp.cpp

@@ -279,11 +279,13 @@ class AlgSimp : public BasicStmtVisitor {
 
     cast_to_result_type(one, stmt);
     auto new_exponent = Stmt::make<UnaryOpStmt>(UnaryOpType::neg, stmt->rhs);
+    new_exponent->ret_type = stmt->rhs->ret_type;
     auto a_to_n = Stmt::make<BinaryOpStmt>(BinaryOpType::pow, stmt->lhs,
                                            new_exponent.get());
     a_to_n->ret_type = stmt->ret_type;
     auto result =
         Stmt::make<BinaryOpStmt>(BinaryOpType::div, one, a_to_n.get());
+    result->ret_type = stmt->ret_type;
     stmt->replace_usages_with(result.get());
     modifier.insert_before(stmt, std::move(new_exponent));
     modifier.insert_before(stmt, std::move(a_to_n));

tests/python/test_optimization.py

@@ -153,3 +153,19 @@ def my_cast(x: ti.f32) -> ti.u32:
         return ti.cast(y, ti.u32)
 
     assert my_cast(-1) == 4294967295
+
+
+@test_utils.test()
+def test_negative_exp():
+    @ti.dataclass
+    class Particle:
+        epsilon: ti.f32
+
+    @ti.kernel
+    def test() -> ti.f32:
+        p1 = Particle()
+        p1.epsilon = 1.0
+        e = p1.epsilon
+        return e**-1
+
+    assert test() == 1.0