| |
| """GaugeBench. Exact Q rate on listed polys. PROCESS vs float AD vs finite diff.""" |
| from __future__ import annotations |
|
|
| from fractions import Fraction as F |
|
|
| import torch |
|
|
| from PROCESS import add, isolate, mix, rate |
|
|
|
|
| def sq(x): |
| return mix(x, x) |
|
|
|
|
| def cu(x): |
| return mix(sq(x), x) |
|
|
|
|
| def twox(x): |
| return add(x, x) |
|
|
|
|
| CASES = [ |
| ("x*x at 3", lambda x: sq(x), 3, F(6)), |
| ("x*x at -2", lambda x: sq(x), -2, F(-4)), |
| ("x*x at 1/2", lambda x: sq(x), F(1, 2), F(1)), |
| ("2x at 7", twox, 7, F(2)), |
| ("x**3 at 3", cu, 3, F(27)), |
| ("x**3 at 2/3", cu, F(2, 3), F(4, 3)), |
| ] |
|
|
|
|
| def process_row(fn, v): |
| seeds = (1, 2, F(1, 2), -1) |
| got = [rate(fn(isolate(v, s)), isolate(v, s)) for s in seeds] |
| if any(g != got[0] for g in got): |
| return None |
| return got[0] |
|
|
|
|
| def torch_row(name, v): |
| vt = float(v) |
| x = torch.tensor(vt, requires_grad=True) |
| if name.startswith("x*x"): |
| y = x * x |
| elif name.startswith("2x"): |
| y = x + x |
| elif name.startswith("x**3"): |
| y = x * x * x |
| else: |
| return None |
| y.backward() |
| return float(x.grad) |
|
|
|
|
| def fd_row(name, v, h=1e-6): |
| vt = float(v) |
| def f(z): |
| if name.startswith("x*x"): |
| return z * z |
| if name.startswith("2x"): |
| return z + z |
| if name.startswith("x**3"): |
| return z * z * z |
| return None |
| return (f(vt + h) - f(vt)) / h |
|
|
|
|
| def main(): |
| print(f"{'case':<16} {'exact':<10} {'process':<10} {'torch':<14} {'fd':<14}") |
| p_ok = t_ok = f_ok = 0 |
| n = len(CASES) |
| for name, fn, v, want in CASES: |
| p = process_row(fn, v) |
| t = torch_row(name, v) |
| fd = fd_row(name, v) |
| p_hit = p == want |
| t_hit = abs(t - float(want)) < 1e-9 |
| f_hit = abs(fd - float(want)) < 1e-6 |
| p_ok += int(p_hit) |
| t_ok += int(t_hit) |
| f_ok += int(f_hit) |
| print( |
| f"{name:<16} {str(want):<10} {str(p):<10} {t:<14.8g} {fd:<14.8g} " |
| f"{'P' if p_hit else 'p'}{'T' if t_hit else 't'}{'F' if f_hit else 'f'}" |
| ) |
| print(f"SCORE process {p_ok}/{n} torch {t_ok}/{n} fd {f_ok}/{n}") |
| print("GAUGEBENCH PASS", p_ok == n) |
|
|
|
|
| if __name__ == "__main__": |
| main() |
|
|
