def transform(x):
    bias = (5, -6, 5, -7, 2)
    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": -5}, {"input": 1, "output": 0}, {"input": 2, "output": 6}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    bias = (5, -6, 5, 6, 2)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["quadratic_residue.protected.case_000", "quadratic_residue.protected.case_001", "quadratic_residue.protected.case_002", "quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_006", "quadratic_residue.protected.case_007", "quadratic_residue.protected.case_008", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011"]

Produce the next complete implementation.

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


def transform(x):
    bias = (-5, -6, 5, -7, 2)
    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": -5}, {"input": 1, "output": 0}, {"input": 2, "output": 6}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    bias = (5, -6, 5, -7, 2)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_000", "quadratic_residue.protected.case_001", "quadratic_residue.protected.case_002", "quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_006", "quadratic_residue.protected.case_007", "quadratic_residue.protected.case_008"]

Produce the next complete implementation.

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


def transform(x):
    bias = (-5, -6, 2, -7, 2)
    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": -5}, {"input": 1, "output": 0}, {"input": 2, "output": 6}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    bias = (-5, -6, 5, -7, 2)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_006", "quadratic_residue.protected.case_007", "quadratic_residue.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    bias = (-5, -6, -4, -7, 2)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-5, -1, 2, -7, 2)
    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": -5}, {"input": 1, "output": 0}, {"input": 2, "output": 6}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    bias = (-5, -6, 2, -7, 2)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005"]

Produce the next complete implementation.

def transform(x):
    bias = (3, -6, 2, -7, 2)
    return x * x + bias[x % 5]


def transform(x):
    factor = (2, 4, 8, 9, 4)
    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": 2}, {"input": 2, "output": 16}, {"input": 3, "output": 27}, {"input": -1, "output": 25}]

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

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

Produce the next complete implementation.

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


def transform(x):
    factor = (2, 2, 8, 9, 4)
    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": 2}, {"input": 2, "output": 16}, {"input": 3, "output": 27}, {"input": -1, "output": 25}]

Current certified implementation:
```python
def transform(x):
    factor = (2, 4, 8, 9, 4)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005"]

Produce the next complete implementation.

def transform(x):
    factor = (2, 9, 8, 9, 4)
    return (x * factor[x % 5]) % 29


def transform(x):
    masks = (12, 9, 4, 1)
    return x ^ masks[x & 3]

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

Current certified implementation:
```python
def transform(x):
    masks = (13, 9, 4, 1)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (1, 9, 4, 1)
    return x ^ masks[x & 3]


def transform(x):
    masks = (12, 9, 4, 13)
    return x ^ masks[x & 3]

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

Current certified implementation:
```python
def transform(x):
    masks = (12, 9, 4, 1)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (12, 9, 4, 5)
    return x ^ masks[x & 3]


def transform(x):
    masks = (12, 9, 14, 13)
    return x ^ masks[x & 3]

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

Current certified implementation:
```python
def transform(x):
    masks = (12, 9, 4, 13)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (5, 9, 14, 13)
    return x ^ masks[x & 3]


def transform(state):
    delta = (5, 1, 6, 4)
    return (state + delta[state & 3]) % 17

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(state) 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": 8}, {"input": 3, "output": 8}]

Current certified implementation:
```python
def transform(state):
    delta = (5, 1, 1, 4)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (5, 1, 4, 4)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (3, 1, 6, 4)
    return (state + delta[state & 3]) % 17

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(state) 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": 8}, {"input": 3, "output": 8}]

Current certified implementation:
```python
def transform(state):
    delta = (5, 1, 6, 4)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (3, 6, 6, 5)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (3, 1, 6, 5)
    return (state + delta[state & 3]) % 17

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(state) 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": 8}, {"input": 3, "output": 8}]

Current certified implementation:
```python
def transform(state):
    delta = (3, 1, 6, 4)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (3, 1, 6, 3)
    return (state + delta[state & 3]) % 17


def transform(x):
    delta = (-5, 5, 7, 7, -6, -6)
    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": -5}, {"input": 1, "output": -4}, {"input": 2, "output": 4}, {"input": 3, "output": 10}, {"input": 4, "output": 12}, {"input": 5, "output": -1}]

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

Sanitized verifier feedback:
passed_count=6
failed_count=12
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", "lookup_delta.protected.case_012", "lookup_delta.protected.case_013", "lookup_delta.protected.case_014"]

Produce the next complete implementation.

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


def transform(x):
    delta = (-5, 5, 7, 7, 8, -6)
    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": -5}, {"input": 1, "output": -4}, {"input": 2, "output": 4}, {"input": 3, "output": 10}, {"input": 4, "output": 12}, {"input": 5, "output": -1}]

Current certified implementation:
```python
def transform(x):
    delta = (-5, 5, 7, 7, -6, -6)
    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_012", "lookup_delta.protected.case_013", "lookup_delta.protected.case_014"]

Produce the next complete implementation.

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


def transform(x):
    delta = (-5, -5, 7, 7, 8, -6)
    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": -5}, {"input": 1, "output": -4}, {"input": 2, "output": 4}, {"input": 3, "output": 10}, {"input": 4, "output": 12}, {"input": 5, "output": -1}]

Current certified implementation:
```python
def transform(x):
    delta = (-5, 5, 7, 7, 8, -6)
    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_006", "lookup_delta.protected.case_007", "lookup_delta.protected.case_008"]

Produce the next complete implementation.

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


def transform(x):
    delta = (-5, -5, 2, 7, 8, -6)
    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": -5}, {"input": 1, "output": -4}, {"input": 2, "output": 4}, {"input": 3, "output": 10}, {"input": 4, "output": 12}, {"input": 5, "output": -1}]

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


def transform(x):
    table = (7, 7, -7, -1, 4)
    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": -5}, {"input": 2, "output": 9}, {"input": 4, "output": -3}, {"input": 6, "output": 8}, {"input": 8, "output": 0}]

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

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_003", "signed_bucket.protected.case_004", "signed_bucket.protected.case_005", "signed_bucket.protected.case_009", "signed_bucket.protected.case_010", "signed_bucket.protected.case_011", "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, 4, -7, -1, 4)
    return x + table[(abs(x) // 2) % 5]


def transform(x):
    table = (-5, 7, -7, -1, 4)
    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": -5}, {"input": 2, "output": 9}, {"input": 4, "output": -3}, {"input": 6, "output": 8}, {"input": 8, "output": 0}]

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

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_009", "signed_bucket.protected.case_010", "signed_bucket.protected.case_011", "signed_bucket.protected.case_012", "signed_bucket.protected.case_013", "signed_bucket.protected.case_014"]

Produce the next complete implementation.

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


def transform(x):
    table = (-5, 7, -7, -1, -8)
    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": -5}, {"input": 2, "output": 9}, {"input": 4, "output": -3}, {"input": 6, "output": 8}, {"input": 8, "output": 0}]

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

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

Produce the next complete implementation.

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


def transform(x):
    table = (-5, 7, -7, 2, -8)
    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": -5}, {"input": 2, "output": 9}, {"input": 4, "output": -3}, {"input": 6, "output": 8}, {"input": 8, "output": 0}]

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

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

Produce the next complete implementation.

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


def transform(x):
    offsets = (4, 4, -2, 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": -23}, {"input": -3, "output": 4}, {"input": 3, "output": -3}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (-1, 4, -2, 6)
    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_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"]

Produce the next complete implementation.

def transform(x):
    offsets = (4, 4, -6, -7)
    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 = (4, 4, -6, 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": -23}, {"input": -3, "output": 4}, {"input": 3, "output": -3}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (4, 4, -2, 6)
    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_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"]

Produce the next complete implementation.

def transform(x):
    offsets = (4, 4, -6, -3)
    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 = (4, 7, -6, 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": -23}, {"input": -3, "output": 4}, {"input": 3, "output": -3}, {"input": 27, "output": 33}]

Current certified implementation:
```python
def transform(x):
    offsets = (4, 4, -6, 6)
    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_003", "piecewise_bias.protected.case_004", "piecewise_bias.protected.case_005"]

Produce the next complete implementation.

def transform(x):
    offsets = (-8, 7, -6, 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):
    bias = (-2, 0, 7, 0, -6)
    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": 1}, {"input": 2, "output": 11}, {"input": 3, "output": 9}, {"input": -1, "output": 1}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, 0, 7, 3, -6)
    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, 0, -6, 3, -6)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-2, 0, 7, 0, 0)
    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": 1}, {"input": 2, "output": 11}, {"input": 3, "output": 9}, {"input": -1, "output": 1}]

Current certified implementation:
```python
def transform(x):
    bias = (-2, 0, 7, 0, -6)
    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, 0, 7, 0, 5)
    return x * x + bias[x % 5]


def transform(x):
    factor = (8, 7, 2, 9, 8)
    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": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 15}, {"input": -1, "output": 24}]

Current certified implementation:
```python
def transform(x):
    factor = (8, 7, 3, 9, 8)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["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 = (5, 7, 3, 9, 8)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (8, 7, 2, 9, 5)
    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": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 15}, {"input": -1, "output": 24}]

Current certified implementation:
```python
def transform(x):
    factor = (8, 7, 2, 9, 8)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005", "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 = (8, 7, 2, 9, 9)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (8, 7, 2, 5, 5)
    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": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 15}, {"input": -1, "output": 24}]

Current certified implementation:
```python
def transform(x):
    factor = (8, 7, 2, 9, 5)
    return (x * factor[x % 5]) % 29
```

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

Produce the next complete implementation.

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


def transform(x):
    factor = (8, 2, 2, 5, 5)
    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": 2}, {"input": 2, "output": 4}, {"input": 3, "output": 15}, {"input": -1, "output": 24}]

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

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005"]

Produce the next complete implementation.

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


def transform(x):
    masks = (8, 12, 1, 2)
    return x ^ masks[x & 3]

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": 12}, {"input": 1, "output": 11}, {"input": 2, "output": 14}, {"input": 3, "output": 1}]

Current certified implementation:
```python
def transform(x):
    masks = (8, 12, 1, 3)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (8, 12, 1, 12)
    return x ^ masks[x & 3]


def transform(x):
    masks = (8, 12, 12, 2)
    return x ^ masks[x & 3]

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": 12}, {"input": 1, "output": 11}, {"input": 2, "output": 14}, {"input": 3, "output": 1}]

Current certified implementation:
```python
def transform(x):
    masks = (8, 12, 1, 2)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["xor_mask.protected.case_000", "xor_mask.protected.case_001", "xor_mask.protected.case_002", "xor_mask.protected.case_003", "xor_mask.protected.case_004", "xor_mask.protected.case_005", "xor_mask.protected.case_006", "xor_mask.protected.case_007", "xor_mask.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    masks = (8, 12, 1, 5)
    return x ^ masks[x & 3]


def transform(x):
    masks = (12, 12, 12, 2)
    return x ^ masks[x & 3]

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": 12}, {"input": 1, "output": 11}, {"input": 2, "output": 14}, {"input": 3, "output": 1}]

Current certified implementation:
```python
def transform(x):
    masks = (8, 12, 12, 2)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["xor_mask.protected.case_000", "xor_mask.protected.case_001", "xor_mask.protected.case_002", "xor_mask.protected.case_003", "xor_mask.protected.case_004", "xor_mask.protected.case_005"]

Produce the next complete implementation.

def transform(x):
    masks = (12, 10, 6, 2)
    return x ^ masks[x & 3]


def transform(x):
    masks = (12, 10, 12, 2)
    return x ^ masks[x & 3]

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": 12}, {"input": 1, "output": 11}, {"input": 2, "output": 14}, {"input": 3, "output": 1}]

Current certified implementation:
```python
def transform(x):
    masks = (12, 12, 12, 2)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (12, 1, 12, 2)
    return x ^ masks[x & 3]


def transform(state):
    delta = (1, 3, 4, 6)
    return (state + delta[state & 3]) % 17

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(state) 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": 4}, {"input": 2, "output": 8}, {"input": 3, "output": 5}]

Current certified implementation:
```python
def transform(state):
    delta = (1, 1, 4, 6)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (1, 6, 4, 6)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (1, 3, 6, 6)
    return (state + delta[state & 3]) % 17

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(state) 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": 4}, {"input": 2, "output": 8}, {"input": 3, "output": 5}]

Current certified implementation:
```python
def transform(state):
    delta = (1, 3, 4, 6)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (2, 6, 6, 6)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (2, 3, 6, 6)
    return (state + delta[state & 3]) % 17

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(state) 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": 4}, {"input": 2, "output": 8}, {"input": 3, "output": 5}]

Current certified implementation:
```python
def transform(state):
    delta = (1, 3, 6, 6)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (3, 3, 6, 6)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (2, 3, 6, 2)
    return (state + delta[state & 3]) % 17

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(state) 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": 4}, {"input": 2, "output": 8}, {"input": 3, "output": 5}]

Current certified implementation:
```python
def transform(state):
    delta = (2, 3, 6, 6)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (3, 3, 6, 6)
    return (state + delta[state & 3]) % 17


def transform(x):
    delta = (-3, 3, -5, -4, 2, -8)
    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": -3}, {"input": 1, "output": 4}, {"input": 2, "output": -3}, {"input": 3, "output": -1}, {"input": 4, "output": 6}, {"input": 5, "output": -2}]

Current certified implementation:
```python
def transform(x):
    delta = (-3, 3, 2, -4, 2, -8)
    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_015", "lookup_delta.protected.case_016", "lookup_delta.protected.case_017"]

Produce the next complete implementation.

def transform(x):
    delta = (-3, 3, 8, -4, 2, -8)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (-3, 3, -5, -4, 2, -7)
    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": -3}, {"input": 1, "output": 4}, {"input": 2, "output": -3}, {"input": 3, "output": -1}, {"input": 4, "output": 6}, {"input": 5, "output": -2}]

Current certified implementation:
```python
def transform(x):
    delta = (-3, 3, -5, -4, 2, -8)
    return x + delta[abs(x) % 6]
```

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

Produce the next complete implementation.

def transform(x):
    delta = (0, 3, -5, -4, 2, -7)
    return x + delta[abs(x) % 6]


def transform(x):
    table = (-6, 2, 2, -4, 3)
    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": -6}, {"input": 2, "output": 4}, {"input": 4, "output": -3}, {"input": 6, "output": 2}, {"input": 8, "output": 2}]

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

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_006", "signed_bucket.protected.case_007", "signed_bucket.protected.case_008", "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, 2, 2, -4, 3)
    return x + table[(abs(x) // 2) % 5]


def transform(x):
    table = (-6, 2, -7, -4, 3)
    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": -6}, {"input": 2, "output": 4}, {"input": 4, "output": -3}, {"input": 6, "output": 2}, {"input": 8, "output": 2}]

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

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

Produce the next complete implementation.

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


def transform(x):
    table = (-6, 2, -7, -4, -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": -6}, {"input": 2, "output": 4}, {"input": 4, "output": -3}, {"input": 6, "output": 2}, {"input": 8, "output": 2}]

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


def transform(x):
    if x < -6: return x + (0)
    if x < 0: return x + (-5)
    if x < 6: return x + (-5)
    return x + (-1)

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": 1}, {"input": 3, "output": 12}, {"input": 27, "output": 26}]

Current certified implementation:
```python
def transform(x):
    if x < -6: return x + (0)
    if x < 0: return x + (-5)
    if x < 6: return x + (-5)
    return x + (8)
```

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):
    if x < -6: return x + (0)
    if x < 0: return x + (-5)
    if x < 6: return x + (-5)
    return x + (1)


def transform(x):
    if x < -6: return x + (0)
    if x < 0: return x + (-5)
    if x < 6: return x + (9)
    return x + (-1)

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": 1}, {"input": 3, "output": 12}, {"input": 27, "output": 26}]

Current certified implementation:
```python
def transform(x):
    if x < -6: return x + (0)
    if x < 0: return x + (-5)
    if x < 6: return x + (-5)
    return x + (-1)
```

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_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"]

Produce the next complete implementation.

def transform(x):
    if x < -6: return x + (-7)
    if x < 0: return x + (-5)
    if x < 6: return x + (9)
    return x + (3)


def transform(x):
    if x < -6: return x + (-7)
    if x < 0: return x + (-5)
    if x < 6: return x + (9)
    return x + (-1)

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": 1}, {"input": 3, "output": 12}, {"input": 27, "output": 26}]

Current certified implementation:
```python
def transform(x):
    if x < -6: return x + (0)
    if x < 0: return x + (-5)
    if x < 6: return x + (9)
    return x + (-1)
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
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"]

Produce the next complete implementation.

def transform(x):
    if x < -6: return x + (-7)
    if x < 0: return x + (4)
    if x < 6: return x + (9)
    return x + (-9)


def transform(x):
    if x < -6: return x + (-7)
    if x < 0: return x + (4)
    if x < 6: return x + (9)
    return x + (-1)

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": 1}, {"input": 3, "output": 12}, {"input": 27, "output": 26}]

Current certified implementation:
```python
def transform(x):
    if x < -6: return x + (-7)
    if x < 0: return x + (-5)
    if x < 6: return x + (9)
    return x + (-1)
```

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

Produce the next complete implementation.

def transform(x):
    if x < -6: return x + (-7)
    if x < 0: return x + (-5)
    if x < 6: return x + (-8)
    return x + (-1)


def transform(x):
    offsets = (9, -5, -6, 8, 1)
    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": -7}, {"input": 1, "output": -4}, {"input": 2, "output": -1}, {"input": 3, "output": 11}, {"input": -1, "output": 6}]

Current certified implementation:
```python
def transform(x):
    offsets = (9, 2, -6, 8, 1)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
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_006", "residue_bias.protected.case_007", "residue_bias.protected.case_008", "residue_bias.protected.case_012", "residue_bias.protected.case_013", "residue_bias.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    offsets = (9, 2, -6, -1, 1)
    return x + offsets[x % 5]


def transform(x):
    offsets = (9, -5, -3, 8, 1)
    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": -7}, {"input": 1, "output": -4}, {"input": 2, "output": -1}, {"input": 3, "output": 11}, {"input": -1, "output": 6}]

Current certified implementation:
```python
def transform(x):
    offsets = (9, -5, -6, 8, 1)
    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_006", "residue_bias.protected.case_007", "residue_bias.protected.case_008", "residue_bias.protected.case_012", "residue_bias.protected.case_013", "residue_bias.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    offsets = (9, -5, -3, 2, 1)
    return x + offsets[x % 5]


def transform(x):
    offsets = (9, -5, -3, 8, 7)
    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": -7}, {"input": 1, "output": -4}, {"input": 2, "output": -1}, {"input": 3, "output": 11}, {"input": -1, "output": 6}]

Current certified implementation:
```python
def transform(x):
    offsets = (9, -5, -3, 8, 1)
    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_012", "residue_bias.protected.case_013", "residue_bias.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    offsets = (9, 8, -3, 8, 7)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-7, -5, -3, 8, 7)
    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": -7}, {"input": 1, "output": -4}, {"input": 2, "output": -1}, {"input": 3, "output": 11}, {"input": -1, "output": 6}]

Current certified implementation:
```python
def transform(x):
    offsets = (9, -5, -3, 8, 7)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002"]

Produce the next complete implementation.

def transform(x):
    offsets = (4, -5, -3, 8, 7)
    return x + offsets[x % 5]


def transform(x):
    bias = (-7, 5, 0, -5, -3)
    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": -7}, {"input": 1, "output": 6}, {"input": 2, "output": 4}, {"input": 3, "output": 11}, {"input": -1, "output": 5}]

Current certified implementation:
```python
def transform(x):
    bias = (-7, -4, 0, -5, -3)
    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 = (-7, 7, 0, -5, -3)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-7, 5, 0, 2, -3)
    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": -7}, {"input": 1, "output": 6}, {"input": 2, "output": 4}, {"input": 3, "output": 11}, {"input": -1, "output": 5}]

Current certified implementation:
```python
def transform(x):
    bias = (-7, 5, 0, -5, -3)
    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 = (-7, -5, 0, 2, -3)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-7, 5, 0, 2, 4)
    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": -7}, {"input": 1, "output": 6}, {"input": 2, "output": 4}, {"input": 3, "output": 11}, {"input": -1, "output": 5}]

Current certified implementation:
```python
def transform(x):
    bias = (-7, 5, 0, 2, -3)
    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 = (-7, 5, 0, 6, -3)
    return x * x + bias[x % 5]


def transform(x):
    factor = (3, 1, 5, 6, 5)
    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": 1}, {"input": 2, "output": 18}, {"input": 3, "output": 18}, {"input": -1, "output": 24}]

Current certified implementation:
```python
def transform(x):
    factor = (3, 1, 5, 7, 5)
    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 = (9, 1, 9, 6, 5)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (3, 1, 9, 6, 5)
    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": 1}, {"input": 2, "output": 18}, {"input": 3, "output": 18}, {"input": -1, "output": 24}]

Current certified implementation:
```python
def transform(x):
    factor = (3, 1, 5, 6, 5)
    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 = (3, 9, 9, 6, 5)
    return (x * factor[x % 5]) % 29


def transform(x):
    masks = (11, 13, 10, 7)
    return x ^ masks[x & 3]

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": 11}, {"input": 1, "output": 12}, {"input": 2, "output": 8}, {"input": 3, "output": 0}]

Current certified implementation:
```python
def transform(x):
    masks = (11, 13, 1, 7)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (11, 14, 1, 7)
    return x ^ masks[x & 3]


def transform(x):
    masks = (11, 13, 10, 3)
    return x ^ masks[x & 3]

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": 11}, {"input": 1, "output": 12}, {"input": 2, "output": 8}, {"input": 3, "output": 0}]

Current certified implementation:
```python
def transform(x):
    masks = (11, 13, 10, 7)
    return x ^ masks[x & 3]
```

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

Produce the next complete implementation.

def transform(x):
    masks = (11, 13, 10, 2)
    return x ^ masks[x & 3]


def transform(state):
    delta = (4, 2, 4, 1)
    return (state + delta[state & 3]) % 17

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(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

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

Current certified implementation:
```python
def transform(state):
    delta = (4, 2, 2, 1)
    return (state + delta[state & 3]) % 17
```

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

Produce the next complete implementation.

def transform(state):
    delta = (4, 2, 3, 1)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (4, 2, 4, 2)
    return (state + delta[state & 3]) % 17

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(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

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

Current certified implementation:
```python
def transform(state):
    delta = (4, 2, 4, 1)
    return (state + delta[state & 3]) % 17
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["fsm_delta.protected.case_000", "fsm_delta.protected.case_001", "fsm_delta.protected.case_002", "fsm_delta.protected.case_003", "fsm_delta.protected.case_004", "fsm_delta.protected.case_005", "fsm_delta.protected.case_009", "fsm_delta.protected.case_010", "fsm_delta.protected.case_011"]

Produce the next complete implementation.

def transform(state):
    delta = (4, 2, 3, 2)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (4, 6, 4, 2)
    return (state + delta[state & 3]) % 17

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(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

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

Current certified implementation:
```python
def transform(state):
    delta = (4, 2, 4, 2)
    return (state + delta[state & 3]) % 17
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["fsm_delta.protected.case_000", "fsm_delta.protected.case_001", "fsm_delta.protected.case_002", "fsm_delta.protected.case_003", "fsm_delta.protected.case_004", "fsm_delta.protected.case_005"]

Produce the next complete implementation.

def transform(state):
    delta = (4, 2, 4, 6)
    return (state + delta[state & 3]) % 17


def transform(state):
    delta = (5, 6, 4, 2)
    return (state + delta[state & 3]) % 17

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(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

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

Current certified implementation:
```python
def transform(state):
    delta = (4, 6, 4, 2)
    return (state + delta[state & 3]) % 17
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["fsm_delta.protected.case_000", "fsm_delta.protected.case_001", "fsm_delta.protected.case_002"]

Produce the next complete implementation.

def transform(state):
    delta = (5, 2, 4, 2)
    return (state + delta[state & 3]) % 17


def transform(x):
    table = (-7, -8, 5, -4, 2)
    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": -6}, {"input": 4, "output": 9}, {"input": 6, "output": 2}, {"input": 8, "output": 16}]

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

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_009", "signed_bucket.protected.case_010", "signed_bucket.protected.case_011", "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, -8, 2, -4, 8)
    return x + table[(abs(x) // 2) % 5]


def transform(x):
    table = (-7, -8, 5, -4, 8)
    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": -6}, {"input": 4, "output": 9}, {"input": 6, "output": 2}, {"input": 8, "output": 16}]

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


def transform(x):
    table = (3, -8, 5, -4, 8)
    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": -6}, {"input": 4, "output": 9}, {"input": 6, "output": 2}, {"input": 8, "output": 16}]

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

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002"]

Produce the next complete implementation.

def transform(x):
    table = (3, -8, 5, -4, -6)
    return x + table[(abs(x) // 2) % 5]


def transform(x):
    offsets = (3, -3, -5, 2)
    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": -32}, {"input": -3, "output": -6}, {"input": 3, "output": 0}, {"input": 27, "output": 24}]

Current certified implementation:
```python
def transform(x):
    offsets = (3, 8, -5, 2)
    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 = (3, 3, -5, 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 = (-5, -3, -5, 2)
    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": -32}, {"input": -3, "output": -6}, {"input": 3, "output": 0}, {"input": 27, "output": 24}]

Current certified implementation:
```python
def transform(x):
    offsets = (3, -3, -5, 2)
    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 = (-5, -5, -5, 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 = (-5, -3, -5, -3)
    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": -32}, {"input": -3, "output": -6}, {"input": 3, "output": 0}, {"input": 27, "output": 24}]

Current certified implementation:
```python
def transform(x):
    offsets = (-5, -3, -5, 2)
    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, 4, -3, -3)
    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 = (-5, -3, -3, -3)
    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": -32}, {"input": -3, "output": -6}, {"input": 3, "output": 0}, {"input": 27, "output": 24}]

Current certified implementation:
```python
def transform(x):
    offsets = (-5, -3, -5, -3)
    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_006", "piecewise_bias.protected.case_007", "piecewise_bias.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    offsets = (-5, 4, -3, -3)
    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 = (5, -3, 2, 2, 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": 5}, {"input": 1, "output": -2}, {"input": 2, "output": 7}, {"input": 3, "output": 5}, {"input": -1, "output": 4}]

Current certified implementation:
```python
def transform(x):
    offsets = (5, -3, 2, 2, 9)
    return x + offsets[x % 5]
```

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

Produce the next complete implementation.

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


def transform(x):
    offsets = (5, -3, 5, 2, 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": 5}, {"input": 1, "output": -2}, {"input": 2, "output": 7}, {"input": 3, "output": 5}, {"input": -1, "output": 4}]

Current certified implementation:
```python
def transform(x):
    offsets = (5, -3, 2, 2, 5)
    return x + offsets[x % 5]
```

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

Produce the next complete implementation.

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


def transform(x):
    bias = (7, 7, -3, 0, 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": 7}, {"input": 1, "output": -6}, {"input": 2, "output": 1}, {"input": 3, "output": 14}, {"input": -1, "output": 7}]

Current certified implementation:
```python
def transform(x):
    bias = (1, 7, -3, 0, 1)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["quadratic_residue.protected.case_000", "quadratic_residue.protected.case_001", "quadratic_residue.protected.case_002", "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 = (-5, 7, -3, 0, 1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (7, 7, -3, 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": 7}, {"input": 1, "output": -6}, {"input": 2, "output": 1}, {"input": 3, "output": 14}, {"input": -1, "output": 7}]

Current certified implementation:
```python
def transform(x):
    bias = (7, 7, -3, 0, 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 = (7, 7, -1, 0, 1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (7, -7, -3, 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": 7}, {"input": 1, "output": -6}, {"input": 2, "output": 1}, {"input": 3, "output": 14}, {"input": -1, "output": 7}]

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

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "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, 7, -3, 5, 1)
    return x * x + bias[x % 5]


def transform(x):
    bias = (7, -7, -3, 5, 6)
    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": 7}, {"input": 1, "output": -6}, {"input": 2, "output": 1}, {"input": 3, "output": 14}, {"input": -1, "output": 7}]

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


def transform(x):
    factor = (2, 3, 8, 7, 8)
    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": 6}, {"input": 2, "output": 6}, {"input": 3, "output": 21}, {"input": -1, "output": 20}]

Current certified implementation:
```python
def transform(x):
    factor = (3, 3, 8, 7, 8)
    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_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_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (2, 3, 8, 9, 8)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (2, 3, 3, 7, 8)
    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": 6}, {"input": 2, "output": 6}, {"input": 3, "output": 21}, {"input": -1, "output": 20}]

Current certified implementation:
```python
def transform(x):
    factor = (2, 3, 8, 7, 8)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["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_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

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


def transform(x):
    factor = (2, 3, 3, 7, 9)
    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": 6}, {"input": 2, "output": 6}, {"input": 3, "output": 21}, {"input": -1, "output": 20}]

Current certified implementation:
```python
def transform(x):
    factor = (2, 3, 3, 7, 8)
    return (x * factor[x % 5]) % 29
```

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

Produce the next complete implementation.

def transform(x):
    factor = (2, 3, 5, 7, 9)
    return (x * factor[x % 5]) % 29