def transform(x):
    table = (-8, 6, 2, 7, -7, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -8}, {"input": 4, "output": 10}, {"input": 6, "output": 8}, {"input": 1, "output": 8}, {"input": 3, "output": -4}, {"input": 7, "output": 2}]

Current certified implementation:
```python
def transform(x):
    table = (-8, -8, 2, 7, -7, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 4, 5, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 2}, {"input": 3, "output": 24}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 4, 5, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (2, 8, 0, -3, -1, -8)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 2}, {"input": 4, "output": 12}, {"input": 6, "output": 6}, {"input": 1, "output": -2}, {"input": 3, "output": 2}, {"input": 7, "output": -1}]

Current certified implementation:
```python
def transform(x):
    table = (8, 8, 0, -3, -1, -8)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 2, 5, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 2}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 2, 5, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_009", "bit_rotate.protected.case_010", "bit_rotate.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    table = (8, 0, 5, 3, -8, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 8}, {"input": 4, "output": 4}, {"input": 6, "output": 11}, {"input": 1, "output": 4}, {"input": 3, "output": -5}, {"input": 7, "output": 8}]

Current certified implementation:
```python
def transform(x):
    table = (8, 0, 5, 2, -8, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_009", "parity_grid.protected.case_010", "parity_grid.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 4, 2, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 8}, {"input": 3, "output": 17}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 4, 3, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    table = (4, -6, -6, 0, -1, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 4}, {"input": 4, "output": -2}, {"input": 6, "output": 0}, {"input": 1, "output": 1}, {"input": 3, "output": 2}, {"input": 7, "output": 9}]

Current certified implementation:
```python
def transform(x):
    table = (4, 4, -6, 0, -1, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 3, 5, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 2}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 2, 5, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (3, -1, -6, 2, 5, 8)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 3}, {"input": 4, "output": 3}, {"input": 6, "output": 0}, {"input": 1, "output": 3}, {"input": 3, "output": 8}, {"input": 7, "output": 15}]

Current certified implementation:
```python
def transform(x):
    table = (3, -3, -6, 2, 5, 8)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 2, 5, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 2}, {"input": 3, "output": 17}]

Current certified implementation:
```python
def transform(x):
    shifts = (2, 2, 5, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (1, 8, 5, -2, -1, -2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 1}, {"input": 4, "output": 12}, {"input": 6, "output": 11}, {"input": 1, "output": -1}, {"input": 3, "output": 2}, {"input": 7, "output": 5}]

Current certified implementation:
```python
def transform(x):
    table = (1, 7, 5, -2, -1, -2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 2, 1, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 4}, {"input": 3, "output": 24}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 1, 1, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (4, 8, -1, 2, -7, 0)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 4}, {"input": 4, "output": 12}, {"input": 6, "output": 5}, {"input": 1, "output": 3}, {"input": 3, "output": -4}, {"input": 7, "output": 7}]

Current certified implementation:
```python
def transform(x):
    table = (4, 8, -1, 0, -7, 0)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_009", "parity_grid.protected.case_010", "parity_grid.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 2, 1, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 4}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (5, 3, 1, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (8, 7, 2, 5, 0, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 8}, {"input": 4, "output": 11}, {"input": 6, "output": 8}, {"input": 1, "output": 6}, {"input": 3, "output": 3}, {"input": 7, "output": 9}]

Current certified implementation:
```python
def transform(x):
    table = (8, 7, -5, 5, 0, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_006", "parity_grid.protected.case_007", "parity_grid.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 5, 2, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 8}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 5, 2, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (-5, -1, 2, 6, 3, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -5}, {"input": 4, "output": 3}, {"input": 6, "output": 8}, {"input": 1, "output": 7}, {"input": 3, "output": 6}, {"input": 7, "output": 3}]

Current certified implementation:
```python
def transform(x):
    table = (-5, -1, 2, 6, 3, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 3, 2, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 8}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (5, 3, 2, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (6, 0, 5, -1, 5, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 4, "output": 4}, {"input": 6, "output": 11}, {"input": 1, "output": 0}, {"input": 3, "output": 8}, {"input": 7, "output": 2}]

Current certified implementation:
```python
def transform(x):
    table = (0, 0, 5, -1, 5, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (2, 5, 3, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 16}, {"input": 3, "output": 17}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 5, 3, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (3, 4, 0, 4, 6, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 6}, {"input": 1, "output": 5}, {"input": 3, "output": 9}, {"input": 7, "output": 10}]

Current certified implementation:
```python
def transform(x):
    table = (3, -8, 0, 4, 6, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 2, 1, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 4}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 2, 1, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_009", "bit_rotate.protected.case_010", "bit_rotate.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    table = (7, 5, -6, 3, 2, 4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 7}, {"input": 4, "output": 9}, {"input": 6, "output": 0}, {"input": 1, "output": 4}, {"input": 3, "output": 5}, {"input": 7, "output": 11}]

Current certified implementation:
```python
def transform(x):
    table = (7, 5, -6, -8, 2, 4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_009", "parity_grid.protected.case_010", "parity_grid.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 1, 1, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 1, 1, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (7, -8, 7, -7, -1, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 7}, {"input": 4, "output": -4}, {"input": 6, "output": 13}, {"input": 1, "output": -6}, {"input": 3, "output": 2}, {"input": 7, "output": 10}]

Current certified implementation:
```python
def transform(x):
    table = (-6, -8, 7, -7, -1, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 1, 4, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 1}, {"input": 3, "output": 24}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 1, 4, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (6, -6, -3, 7, 8, 7)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 4, "output": -2}, {"input": 6, "output": 3}, {"input": 1, "output": 8}, {"input": 3, "output": 11}, {"input": 7, "output": 14}]

Current certified implementation:
```python
def transform(x):
    table = (6, -6, -7, 7, 8, 7)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_006", "parity_grid.protected.case_007", "parity_grid.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 2, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 16}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (5, 1, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (8, 5, 3, 4, -6, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 8}, {"input": 4, "output": 9}, {"input": 6, "output": 9}, {"input": 1, "output": 5}, {"input": 3, "output": -3}, {"input": 7, "output": 2}]

Current certified implementation:
```python
def transform(x):
    table = (8, 5, 3, 4, -6, 4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 5, 3, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 16}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 2, 3, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (3, -3, -1, 4, -6, -1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 3}, {"input": 4, "output": 1}, {"input": 6, "output": 5}, {"input": 1, "output": 5}, {"input": 3, "output": -3}, {"input": 7, "output": 6}]

Current certified implementation:
```python
def transform(x):
    table = (3, -8, -1, 4, -6, -1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 3, 3, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 16}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (5, 1, 3, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (-8, 2, 1, -7, 3, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -8}, {"input": 4, "output": 6}, {"input": 6, "output": 7}, {"input": 1, "output": -6}, {"input": 3, "output": 6}, {"input": 7, "output": 9}]

Current certified implementation:
```python
def transform(x):
    table = (-8, 2, 1, -7, -3, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_012", "parity_grid.protected.case_013", "parity_grid.protected.case_014"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 4, 5, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 2}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 3, 5, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (-6, 8, -8, -2, 1, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -6}, {"input": 4, "output": 12}, {"input": 6, "output": -2}, {"input": 1, "output": -1}, {"input": 3, "output": 4}, {"input": 7, "output": 3}]

Current certified implementation:
```python
def transform(x):
    table = (6, 8, -8, -2, 1, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 5, 3, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 16}, {"input": 3, "output": 24}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 5, 5, 3)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    table = (8, 1, 7, -6, 5, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 8}, {"input": 4, "output": 5}, {"input": 6, "output": 13}, {"input": 1, "output": -5}, {"input": 3, "output": 8}, {"input": 7, "output": 10}]

Current certified implementation:
```python
def transform(x):
    table = (-8, 1, 7, -6, 5, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 4, 4, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 1}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 3, 4, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (0, 3, 6, -2, -8, 8)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 4, "output": 7}, {"input": 6, "output": 12}, {"input": 1, "output": -1}, {"input": 3, "output": -5}, {"input": 7, "output": 15}]

Current certified implementation:
```python
def transform(x):
    table = (0, 3, 6, -2, -8, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 4, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 16}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 4, 1, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    table = (1, -4, -8, 0, 4, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 1}, {"input": 4, "output": 0}, {"input": 6, "output": -2}, {"input": 1, "output": 1}, {"input": 3, "output": 7}, {"input": 7, "output": 8}]

Current certified implementation:
```python
def transform(x):
    table = (5, -4, -8, 0, 4, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 5, 1, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 4}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 5, 1, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (6, 5, 6, -7, -3, 6)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 4, "output": 9}, {"input": 6, "output": 12}, {"input": 1, "output": -6}, {"input": 3, "output": 0}, {"input": 7, "output": 13}]

Current certified implementation:
```python
def transform(x):
    table = (6, 5, 6, -7, 5, 6)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_012", "parity_grid.protected.case_013", "parity_grid.protected.case_014"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 4, 5, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 2}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 4, 5, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_009", "bit_rotate.protected.case_010", "bit_rotate.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    table = (1, 1, -8, -3, -3, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 1}, {"input": 4, "output": 5}, {"input": 6, "output": -2}, {"input": 1, "output": -2}, {"input": 3, "output": 0}, {"input": 7, "output": 9}]

Current certified implementation:
```python
def transform(x):
    table = (1, 1, -8, -3, -2, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_012", "parity_grid.protected.case_013", "parity_grid.protected.case_014"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 1, 3, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 16}, {"input": 3, "output": 17}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 4, 3, 4)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (0, 0, 6, 6, -7, 5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 4, "output": 4}, {"input": 6, "output": 12}, {"input": 1, "output": 7}, {"input": 3, "output": -4}, {"input": 7, "output": 12}]

Current certified implementation:
```python
def transform(x):
    table = (0, 0, 6, 6, -7, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (2, 2, 5, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 2}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (2, 2, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    table = (5, -8, -3, 4, 1, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 5}, {"input": 4, "output": -4}, {"input": 6, "output": 3}, {"input": 1, "output": 5}, {"input": 3, "output": 4}, {"input": 7, "output": 8}]

Current certified implementation:
```python
def transform(x):
    table = (5, -8, -3, 4, -3, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_012", "parity_grid.protected.case_013", "parity_grid.protected.case_014"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 1, 1, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (5, 1, 1, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (-8, 0, -5, -3, 5, 8)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -8}, {"input": 4, "output": 4}, {"input": 6, "output": 1}, {"input": 1, "output": -2}, {"input": 3, "output": 8}, {"input": 7, "output": 15}]

Current certified implementation:
```python
def transform(x):
    table = (-8, 0, -5, -3, 5, -6)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 5, 4, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 1}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 5, 4, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (7, -1, -3, -5, -7, 4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 7}, {"input": 4, "output": 3}, {"input": 6, "output": 3}, {"input": 1, "output": -4}, {"input": 3, "output": -4}, {"input": 7, "output": 11}]

Current certified implementation:
```python
def transform(x):
    table = (7, -1, -3, -5, -7, -3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 1, 2, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 8}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 1, 2, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_009", "bit_rotate.protected.case_010", "bit_rotate.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    table = (-7, -1, -5, -4, -6, -5)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -7}, {"input": 4, "output": 3}, {"input": 6, "output": 1}, {"input": 1, "output": -3}, {"input": 3, "output": -3}, {"input": 7, "output": 2}]

Current certified implementation:
```python
def transform(x):
    table = (-7, -1, -5, -4, -6, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 2, 4, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 1}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 3, 4, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (-5, -3, -2, 7, -4, -6)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -5}, {"input": 4, "output": 1}, {"input": 6, "output": 4}, {"input": 1, "output": 8}, {"input": 3, "output": -1}, {"input": 7, "output": 1}]

Current certified implementation:
```python
def transform(x):
    table = (6, -3, -2, 7, -4, -6)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 2, 2, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 8}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 5, 2, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (2, -2, 6, 6, 0, 4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 2}, {"input": 4, "output": 2}, {"input": 6, "output": 12}, {"input": 1, "output": 7}, {"input": 3, "output": 3}, {"input": 7, "output": 11}]

Current certified implementation:
```python
def transform(x):
    table = (2, -2, 6, 6, 8, 4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_012", "parity_grid.protected.case_013", "parity_grid.protected.case_014"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 4, 4, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 1}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 3, 4, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (-2, 5, 6, 1, -5, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -2}, {"input": 4, "output": 9}, {"input": 6, "output": 12}, {"input": 1, "output": 2}, {"input": 3, "output": -2}, {"input": 7, "output": 3}]

Current certified implementation:
```python
def transform(x):
    table = (-2, 5, 6, 1, 5, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_012", "parity_grid.protected.case_013", "parity_grid.protected.case_014"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 4, 3, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 16}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 4, 2, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    table = (-7, 7, 5, -5, 8, -6)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -7}, {"input": 4, "output": 11}, {"input": 6, "output": 11}, {"input": 1, "output": -4}, {"input": 3, "output": 11}, {"input": 7, "output": 1}]

Current certified implementation:
```python
def transform(x):
    table = (-7, 7, 5, -5, 8, -3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 2, 4, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 1}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (4, 2, 4, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (4, 1, -8, 6, 5, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 4}, {"input": 4, "output": 5}, {"input": 6, "output": -2}, {"input": 1, "output": 7}, {"input": 3, "output": 8}, {"input": 7, "output": 10}]

Current certified implementation:
```python
def transform(x):
    table = (4, 1, -8, -4, 5, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_009", "parity_grid.protected.case_010", "parity_grid.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 4, 1, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 16}, {"input": 2, "output": 4}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 2, 1, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (-4, 1, 6, -3, -2, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -4}, {"input": 4, "output": 5}, {"input": 6, "output": 12}, {"input": 1, "output": -2}, {"input": 3, "output": 1}, {"input": 7, "output": 9}]

Current certified implementation:
```python
def transform(x):
    table = (-4, 2, 6, -3, -2, 2)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_003", "parity_grid.protected.case_004", "parity_grid.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 2, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 16}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 2, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (7, 7, -6, 7, -7, -3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 7}, {"input": 4, "output": 11}, {"input": 6, "output": 0}, {"input": 1, "output": 8}, {"input": 3, "output": -4}, {"input": 7, "output": 4}]

Current certified implementation:
```python
def transform(x):
    table = (-6, 7, -6, 7, -7, -3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (5, 2, 3, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 16}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (5, 2, 3, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_009", "bit_rotate.protected.case_010", "bit_rotate.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    table = (7, -8, 2, 7, -6, -1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 7}, {"input": 4, "output": -4}, {"input": 6, "output": 8}, {"input": 1, "output": 8}, {"input": 3, "output": -3}, {"input": 7, "output": 6}]

Current certified implementation:
```python
def transform(x):
    table = (7, -8, 2, 7, -6, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (2, 1, 1, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 12}]

Current certified implementation:
```python
def transform(x):
    shifts = (2, 4, 1, 2)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (-4, 6, 0, -3, 7, -3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -4}, {"input": 4, "output": 10}, {"input": 6, "output": 6}, {"input": 1, "output": -2}, {"input": 3, "output": 10}, {"input": 7, "output": 4}]

Current certified implementation:
```python
def transform(x):
    table = (-4, 6, 0, -3, 7, -1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_015", "parity_grid.protected.case_016", "parity_grid.protected.case_017"]

Produce the next complete implementation.


def transform(x):
    shifts = (1, 1, 1, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 3, 1, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_003", "bit_rotate.protected.case_004", "bit_rotate.protected.case_005"]

Produce the next complete implementation.


def transform(x):
    table = (7, -5, 8, -1, -7, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 7}, {"input": 4, "output": -1}, {"input": 6, "output": 14}, {"input": 1, "output": 0}, {"input": 3, "output": -4}, {"input": 7, "output": 10}]

Current certified implementation:
```python
def transform(x):
    table = (7, -5, 3, -1, -7, 3)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_006", "parity_grid.protected.case_007", "parity_grid.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    shifts = (4, 5, 2, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 1}, {"input": 2, "output": 8}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (1, 5, 2, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=10
failed_count=2
failed_obligation_ids=["bit_rotate.protected.case_000", "bit_rotate.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    table = (8, 1, -1, 0, 0, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 8}, {"input": 4, "output": 5}, {"input": 6, "output": 5}, {"input": 1, "output": 1}, {"input": 3, "output": 3}, {"input": 7, "output": 8}]

Current certified implementation:
```python
def transform(x):
    table = (8, 1, -1, 6, 0, 1)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_009", "parity_grid.protected.case_010", "parity_grid.protected.case_011"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 2, 5, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 2}, {"input": 3, "output": 6}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 2, 2, 1)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.


def transform(x):
    table = (5, -8, -1, -8, -6, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 5}, {"input": 4, "output": -4}, {"input": 6, "output": 5}, {"input": 1, "output": -7}, {"input": 3, "output": -3}, {"input": 7, "output": 3}]

Current certified implementation:
```python
def transform(x):
    table = (-8, -8, -1, -8, -6, -4)
    slot = ((x & 1) * 3 + (abs(x) // 3) % 3) % 6
    return x + table[slot]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["parity_grid.protected.case_000", "parity_grid.protected.case_001", "parity_grid.protected.case_002"]

Produce the next complete implementation.


def transform(x):
    shifts = (3, 2, 1, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 4}, {"input": 3, "output": 3}]

Current certified implementation:
```python
def transform(x):
    shifts = (3, 2, 3, 5)
    x = x & 31
    s = shifts[x & 3] % 5
    return (((x << s) | (x >> (5 - s))) & 31) if s else x
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["bit_rotate.protected.case_006", "bit_rotate.protected.case_007", "bit_rotate.protected.case_008"]

Produce the next complete implementation.