def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, 5, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=9
failed_count=9
failed_obligation_ids=["lookup_delta.protected.case_003", "lookup_delta.protected.case_004", "lookup_delta.protected.case_005", "lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (-4, 5, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, 5, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=9
failed_count=9
failed_obligation_ids=["lookup_delta.protected.case_003", "lookup_delta.protected.case_004", "lookup_delta.protected.case_005", "lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (4, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, 5, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=9
failed_count=9
failed_obligation_ids=["lookup_delta.protected.case_003", "lookup_delta.protected.case_004", "lookup_delta.protected.case_005", "lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (-6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (6, -8, 4, -7, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (1, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (-7, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, -4, -6, -4)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (-8, -8, 6, 5, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 6, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]
```

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

Produce the next complete implementation.

def transform(x):
    delta = (6, -8, -6, 5, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 6, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]
```

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

Produce the next complete implementation.

def transform(x):
    delta = (-4, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (6, -8, 6, 5, -6, -4)
    return x + delta[abs(x) % 6]

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": 6}, {"input": 1, "output": -7}, {"input": 2, "output": 8}, {"input": 3, "output": 8}, {"input": 4, "output": -2}, {"input": 5, "output": 1}]

Current certified implementation:
```python
def transform(x):
    delta = (6, -8, 4, 5, -6, -4)
    return x + delta[abs(x) % 6]
```

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

Produce the next complete implementation.

def transform(x):
    delta = (-5, -8, 6, 5, -6, -4)
    return x + delta[abs(x) % 6]


def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -1, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_003", "residue_bias.protected.case_004", "residue_bias.protected.case_005", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-1, 8, 7, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -1, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_003", "residue_bias.protected.case_004", "residue_bias.protected.case_005", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-1, -1, -9, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -1, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_003", "residue_bias.protected.case_004", "residue_bias.protected.case_005", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-1, -3, -3, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -1, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_003", "residue_bias.protected.case_004", "residue_bias.protected.case_005", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (3, -3, -6, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-6, -3, 7, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-1, -3, 8, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (3, -3, 4, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (3, -3, 9, -3, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -3, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (3, -3, 7, 2, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -3, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (3, 1, 7, -6, -5)
    return x + offsets[x % 5]


def transform(x):
    offsets = (3, -3, 7, -3, -5)
    return x + offsets[x % 5]

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": 3}, {"input": 1, "output": -2}, {"input": 2, "output": 9}, {"input": 3, "output": 0}, {"input": -1, "output": -6}]

Current certified implementation:
```python
def transform(x):
    offsets = (3, -3, 7, -6, -5)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (3, 9, 7, -3, -5)
    return x + offsets[x % 5]


def transform(x):
    factor = (4, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 1, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=1
failed_count=14
failed_obligation_ids=["mod_product.protected.case_000", "mod_product.protected.case_002", "mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 7, 4, 6, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=4
failed_count=11
failed_obligation_ids=["mod_product.protected.case_000", "mod_product.protected.case_002", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (3, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=4
failed_count=11
failed_obligation_ids=["mod_product.protected.case_000", "mod_product.protected.case_002", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 7, 4, 6, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=4
failed_count=11
failed_obligation_ids=["mod_product.protected.case_000", "mod_product.protected.case_002", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 4, 4, 6, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=4
failed_count=11
failed_obligation_ids=["mod_product.protected.case_000", "mod_product.protected.case_002", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 3, 4, 6, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 8, 4, 6, 3)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 5, 4, 6, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 5, 4, 6, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 2)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 2, 4, 4, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 8, 4, 5, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 9, 4, 6, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 4, 4, 4, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 6, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 7, 7, 4, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 7, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 8, 8, 4, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 7, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 8, 4, 4, 3)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 7, 4, 7)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 12}, {"input": -1, "output": 22}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 4, 4, 7)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 8, 7, 4, 8)
    return (x * factor[x % 5]) % 29


def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, 1, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, -6, 2, 7, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, 1, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-3, 1, 2, 7, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, 1, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-1, -4, 2, 7, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, 1, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-4, -4, 2, 5, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, -4, 2, -2, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, 1, 2, 7, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, -7, 2, 5, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 7, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, 6, 2, 5, -5)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -5)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, -4, 2, 5, -6)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -5)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, -2, 2, 5, -1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, -4, 2, 5, -5)
    return x * x + bias[x % 5]

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": -2}, {"input": 1, "output": -3}, {"input": 2, "output": 6}, {"input": 3, "output": 14}, {"input": -1, "output": -4}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, -4, 2, 5, -1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-2, -3, 2, 5, -5)
    return x * x + bias[x % 5]


def transform(x):
    offsets = (-4, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-4, -4, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=0
failed_count=12
failed_obligation_ids=["piecewise_bias.protected.case_000", "piecewise_bias.protected.case_001", "piecewise_bias.protected.case_002", "piecewise_bias.protected.case_003", "piecewise_bias.protected.case_004", "piecewise_bias.protected.case_005", "piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-4, 0, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-4, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["piecewise_bias.protected.case_000", "piecewise_bias.protected.case_001", "piecewise_bias.protected.case_002", "piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-4, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-4, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["piecewise_bias.protected.case_000", "piecewise_bias.protected.case_001", "piecewise_bias.protected.case_002", "piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-4, 7, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-4, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["piecewise_bias.protected.case_000", "piecewise_bias.protected.case_001", "piecewise_bias.protected.case_002", "piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-7, 3, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-4, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["piecewise_bias.protected.case_000", "piecewise_bias.protected.case_001", "piecewise_bias.protected.case_002", "piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-7, -6, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-7, -2, -7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-9, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (6, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, 7, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["piecewise_bias.protected.case_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008", "piecewise_bias.protected.case_009", "piecewise_bias.protected.case_010", "piecewise_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (5, -2, -1, 6)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, 6)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

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

Produce the next complete implementation.

def transform(x):
    offsets = (-7, -2, -1, -2)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, 6)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

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

Produce the next complete implementation.

def transform(x):
    offsets = (-7, -2, 5, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


def transform(x):
    offsets = (-7, -2, -1, 6)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]

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": -27, "output": -34}, {"input": -3, "output": -5}, {"input": 3, "output": 2}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, -2, -1, -5)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]
```

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

Produce the next complete implementation.

def transform(x):
    offsets = (-7, -2, -3, 6)
    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3
    return x + offsets[bucket]


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


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

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": -3}, {"input": 2, "output": 3}, {"input": 4, "output": 8}, {"input": 6, "output": 8}, {"input": 8, "output": 3}]

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

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 6, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 4, 2, 3, 3)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 6, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 4, 6, 4, 3)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 6, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 4, 9, 6, 3)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 6, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 4, 9, 4, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (4, 4, 9, 3, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 4, 9, 3, 7)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (4, 4, 9, 3, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 8, 9, 3, 3)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (4, 4, 9, 3, 2)
    return (x * factor[x % 5]) % 29

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": 0}, {"input": 1, "output": 4}, {"input": 2, "output": 18}, {"input": 3, "output": 9}, {"input": -1, "output": 27}]

Current certified implementation:
```python
def transform(x):
    factor = (4, 4, 9, 3, 3)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (4, 5, 9, 3, 2)
    return (x * factor[x % 5]) % 29


def transform(x):
    delta = (-7, -7, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]

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

Current certified implementation:
```python
def transform(x):
    delta = (-7, -6, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_003", "lookup_delta.protected.case_004", "lookup_delta.protected.case_005", "lookup_delta.protected.case_012", "lookup_delta.protected.case_013", "lookup_delta.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    delta = (-7, 2, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (-7, -7, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]

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

Current certified implementation:
```python
def transform(x):
    delta = (-7, -6, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_003", "lookup_delta.protected.case_004", "lookup_delta.protected.case_005", "lookup_delta.protected.case_012", "lookup_delta.protected.case_013", "lookup_delta.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    delta = (-7, -6, 1, -5, -7, -8)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (-7, -7, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]

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

Current certified implementation:
```python
def transform(x):
    delta = (-7, -6, 1, -5, -7, -5)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_003", "lookup_delta.protected.case_004", "lookup_delta.protected.case_005", "lookup_delta.protected.case_012", "lookup_delta.protected.case_013", "lookup_delta.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    delta = (-7, -7, 1, -5, -7, 6)
    return x + delta[abs(x) % 6]