Time bar (total: 21.1s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 99.7% | 0.3% | 0 |
| 0% | 99.7% | 0.3% | 1 |
| 0% | 99.7% | 0.3% | 2 |
| 0% | 99.7% | 0.3% | 3 |
| 0% | 99.7% | 0.3% | 4 |
| 0% | 99.7% | 0.3% | 5 |
| 0% | 99.7% | 0.3% | 6 |
| 0% | 99.7% | 0.3% | 7 |
| 0% | 99.7% | 0.3% | 8 |
| 0% | 99.7% | 0.3% | 9 |
| 0% | 99.7% | 0.3% | 10 |
| 0.6% | 99.1% | 0.3% | 11 |
| 1.8% | 98% | 0.3% | 12 |
| 2.6% | 97.1% | 0.3% | 13 |
| 4% | 95.7% | 0.3% | 14 |
Compiled 24 to 15 computations (37.5% saved)
| 1× | intervals |
| 16.0ms | 256× | body | 128 | valid |
| 1.0ms | 14× | body | 128 | invalid |
Compiled 53 to 35 computations (34% saved)
| 1× | egg-herbie |
| 920× | times-frac_binary64 |
| 593× | fma-def_binary64 |
| 507× | div-sub_binary64 |
| 484× | sub-neg_binary64 |
| 470× | neg-mul-1_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 15 | 23 |
| 1 | 25 | 21 |
| 2 | 50 | 21 |
| 3 | 93 | 21 |
| 4 | 157 | 21 |
| 5 | 270 | 21 |
| 6 | 423 | 21 |
| 7 | 724 | 21 |
| 8 | 1341 | 21 |
| 9 | 3898 | 21 |
| 10 | 4400 | 21 |
| 11 | 4952 | 21 |
1 alts after pruning (1 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 | 1 | 2 |
| Fresh | 1 | 0 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 2 | 1 | 3 |
| Status | Error | Program |
| ▶ | 23.4b | (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)) |
Compiled 80 to 41 computations (48.8% saved)
Found 3 expressions with local error:
| New | Error | Program |
| ✓ | 0.0b | (*.f64 z (-.f64 t a)) |
| ✓ | 0.3b | (fma.f64 x y (*.f64 z (-.f64 t a))) |
| ✓ | 22.6b | (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)) |
3 calls:
| 189.0ms | (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)) |
| 16.0ms | (fma.f64 x y (*.f64 z (-.f64 t a))) |
| 7.0ms | (*.f64 z (-.f64 t a)) |
| 1× | rewrite-expression-head |
| 31× | add-sqr-sqrt_binary64 |
| 29× | *-un-lft-identity_binary64 |
| 27× | add-cube-cbrt_binary64 |
| 18× | prod-diff_binary64 |
| 13× | distribute-lft-in_binary64 |
3 calls:
| 5.0ms | (*.f64 z (-.f64 t a)) |
| 2.0ms | (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)) |
| 0.0ms | (fma.f64 x y (*.f64 z (-.f64 t a))) |
| 1× | egg-herbie |
| 911× | associate-/l*_binary64 |
| 492× | fma-def_binary64 |
| 259× | +-commutative_binary64 |
| 206× | associate-+r+_binary64 |
| 151× | *-commutative_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 765 | 9527 |
| 1 | 2314 | 8862 |
| 2 | 5234 | 8862 |
8 alts after pruning (8 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 209 | 8 | 217 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 210 | 8 | 218 |
| Status | Error | Program |
| 24.0b | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) | |
| ▶ | 23.4b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))) |
| 28.6b | (-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))) | |
| 38.0b | (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (+.f64 (/.f64 (*.f64 a y) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y)))) | |
| 44.7b | (*.f64 (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)))) | |
| 23.4b | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) | |
| 40.9b | (/.f64 x (-.f64 1 z)) | |
| 28.3b | (-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))) |
Compiled 11389 to 4298 computations (62.3% saved)
Found 4 expressions with local error:
| New | Error | Program |
| ✓ | 0.0b | (*.f64 z (-.f64 b y)) |
| ✓ | 0.7b | (-.f64 (*.f64 y x) (*.f64 z a)) |
| ✓ | 12.9b | (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) |
| ✓ | 19.6b | (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y)))) |
4 calls:
| 138.0ms | (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y)))) |
| 76.0ms | (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) |
| 10.0ms | (-.f64 (*.f64 y x) (*.f64 z a)) |
| 7.0ms | (*.f64 z (-.f64 b y)) |
| 1× | rewrite-expression-head |
| 34× | add-sqr-sqrt_binary64 |
| 32× | *-un-lft-identity_binary64 |
| 30× | add-cube-cbrt_binary64 |
| 19× | prod-diff_binary64 |
| 13× | distribute-lft-in_binary64 |
4 calls:
| 7.0ms | (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) |
| 6.0ms | (*.f64 z (-.f64 b y)) |
| 5.0ms | (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y)))) |
| 3.0ms | (-.f64 (*.f64 y x) (*.f64 z a)) |
| 1× | egg-herbie |
| 943× | associate-/l*_binary64 |
| 454× | fma-def_binary64 |
| 211× | +-commutative_binary64 |
| 187× | sub-neg_binary64 |
| 170× | *-commutative_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 817 | 9849 |
| 1 | 2366 | 9124 |
| 2 | 5788 | 9124 |
8 alts after pruning (7 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 391 | 1 | 392 |
| Fresh | 1 | 6 | 7 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 392 | 8 | 400 |
| Status | Error | Program |
| 24.0b | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) | |
| ✓ | 23.4b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))) |
| 28.6b | (-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))) | |
| 38.0b | (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (+.f64 (/.f64 (*.f64 a y) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y)))) | |
| 44.7b | (*.f64 (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)))) | |
| 30.6b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 x (-.f64 1 z))) | |
| ▶ | 23.4b | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) |
| 28.3b | (-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))) |
Compiled 19431 to 5308 computations (72.7% saved)
Found 4 expressions with local error:
| New | Error | Program |
| 0.0b | (*.f64 z (-.f64 t a)) | |
| 0.3b | (fma.f64 x y (*.f64 z (-.f64 t a))) | |
| ✓ | 0.4b | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) |
| ✓ | 22.5b | (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))) |
2 calls:
| 407.0ms | (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))) |
| 183.0ms | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) |
| 1× | rewrite-expression-head |
| 84× | times-frac_binary64 |
| 52× | *-un-lft-identity_binary64 |
| 52× | add-sqr-sqrt_binary64 |
| 52× | add-cube-cbrt_binary64 |
| 16× | associate-/r*_binary64 |
2 calls:
| 4.0ms | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) |
| 2.0ms | (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))) |
| 1× | egg-herbie |
| 656× | +-commutative_binary64 |
| 547× | associate-+r+_binary64 |
| 293× | associate-/l*_binary64 |
| 280× | *-commutative_binary64 |
| 202× | associate-/r*_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1525 | 24218 |
| 1 | 5092 | 24218 |
8 alts after pruning (6 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 391 | 0 | 391 |
| Fresh | 0 | 6 | 6 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 1 | 1 |
| Total | 391 | 8 | 399 |
| Status | Error | Program |
| ▶ | 24.0b | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) |
| ✓ | 23.4b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))) |
| 28.6b | (-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))) | |
| 38.0b | (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (+.f64 (/.f64 (*.f64 a y) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y)))) | |
| 44.7b | (*.f64 (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)))) | |
| 30.6b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 x (-.f64 1 z))) | |
| ✓ | 23.4b | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) |
| 28.3b | (-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))) |
Compiled 29316 to 12143 computations (58.6% saved)
Found 4 expressions with local error:
| New | Error | Program |
| ✓ | 0.4b | (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) |
| ✓ | 8.1b | (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)) |
| ✓ | 9.5b | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) |
| ✓ | 19.1b | (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) |
4 calls:
| 523.0ms | (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) |
| 519.0ms | (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)) |
| 197.0ms | (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) |
| 196.0ms | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) |
| 1× | rewrite-expression-head |
| 54× | add-sqr-sqrt_binary64 |
| 41× | *-un-lft-identity_binary64 |
| 41× | cbrt-prod_binary64 |
| 41× | add-cube-cbrt_binary64 |
| 38× | times-frac_binary64 |
4 calls:
| 9.0ms | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) |
| 4.0ms | (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) |
| 3.0ms | (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)) |
| 1.0ms | (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) |
| 1× | egg-herbie |
| 595× | fma-def_binary64 |
| 376× | times-frac_binary64 |
| 194× | sub-neg_binary64 |
| 43× | unpow1/3_binary64 |
| 22× | exp-prod_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 3329 | 50611 |
| 1 | 5208 | 50611 |
8 alts after pruning (5 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 802 | 0 | 802 |
| Fresh | 0 | 5 | 5 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 2 | 2 |
| Total | 802 | 8 | 810 |
| Status | Error | Program |
| ✓ | 24.0b | (*.f64 (*.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a))))) (/.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))) |
| ✓ | 23.4b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 (-.f64 (*.f64 y x) (*.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))) |
| 28.6b | (-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))) | |
| 38.0b | (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (+.f64 (/.f64 (*.f64 a y) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y)))) | |
| 44.7b | (*.f64 (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y)))) | |
| 30.6b | (+.f64 (/.f64 (*.f64 t z) (+.f64 y (*.f64 z (-.f64 b y)))) (/.f64 x (-.f64 1 z))) | |
| ✓ | 23.4b | (/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))) |
| 28.3b | (-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))) |
Compiled 96801 to 42936 computations (55.6% saved)
Total 5.7b remaining (95.7%)
Threshold costs 0b (0%)
Compiled 84069 to 45894 computations (45.4% saved)
Compiled 23 to 14 computations (39.1% saved)
| 1× | egg-herbie |
| 19× | +-commutative_binary64 |
| 16× | *-commutative_binary64 |
| 14× | sub-neg_binary64 |
| 9× | neg-sub0_binary64 |
| 9× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 413 |
| 1 | 89 | 413 |
| 2 | 113 | 413 |
| 3 | 134 | 413 |
| 4 | 144 | 413 |
| 5 | 146 | 413 |
| 6 | 146 | 413 |
Compiled 285 to 71 computations (75.1% saved)
| 1× | intervals |
| 533.0ms | 8000× | body | 128 | valid |
| 27.0ms | 432× | body | 128 | invalid |
Compiled 622 to 236 computations (62.1% saved)
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