Time bar (total: 14.9s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 99.8% | 0.2% | 0 |
| 0% | 99.8% | 0.2% | 1 |
| 0% | 99.8% | 0.2% | 2 |
| 0% | 99.8% | 0.2% | 3 |
| 0% | 99.8% | 0.2% | 4 |
| 0% | 99.8% | 0.2% | 5 |
| 0% | 99.8% | 0.2% | 6 |
| 0% | 99.8% | 0.2% | 7 |
| 0% | 99.8% | 0.2% | 8 |
| 18.7% | 76.4% | 4.9% | 9 |
| 18.7% | 76.4% | 4.9% | 10 |
| 21.8% | 72.5% | 5.7% | 11 |
| 21.8% | 69.8% | 8.4% | 12 |
| 32.7% | 46.6% | 20.7% | 13 |
| 32.7% | 46.6% | 20.7% | 14 |
Compiled 24 to 20 computations (16.7% saved)
| 1× | intervals |
| 59.0ms | 256× | body | 128 | valid |
| 28.0ms | 134× | body | 128 | nan |
Compiled 51 to 43 computations (15.7% saved)
| 1× | egg-herbie |
| 564× | fma-def_binary64 |
| 527× | associate-/r/_binary64 |
| 522× | fma-neg_binary64 |
| 484× | unswap-sqr_binary64 |
| 458× | associate-/l/_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 29 |
| 1 | 33 | 27 |
| 2 | 63 | 27 |
| 3 | 165 | 27 |
| 4 | 492 | 27 |
| 5 | 1679 | 27 |
| 6 | 3655 | 27 |
| 7 | 4950 | 27 |
| 8 | 5043 | 27 |
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 |
| ▶ | 11.0b | (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
Compiled 85 to 67 computations (21.2% saved)
Found 4 expressions with local error:
| New | Error | Program |
| ✓ | 0.3b | (pow.f64 (/.f64 Om Omc) 2) |
| ✓ | 0.4b | (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) |
| ✓ | 0.5b | (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
| ✓ | 10.0b | (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) |
4 calls:
| 685.0ms | (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) |
| 427.0ms | (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) |
| 35.0ms | (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
| 23.0ms | (pow.f64 (/.f64 Om Omc) 2) |
| 1× | rewrite-expression-head |
| 143× | add-sqr-sqrt_binary64 |
| 108× | times-frac_binary64 |
| 98× | *-un-lft-identity_binary64 |
| 70× | difference-of-squares_binary64 |
| 49× | add-cube-cbrt_binary64 |
4 calls:
| 27.0ms | (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) |
| 23.0ms | (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) |
| 6.0ms | (pow.f64 (/.f64 Om Omc) 2) |
| 1.0ms | (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
| 1× | egg-herbie |
| 968× | fma-def_binary64 |
| 483× | times-frac_binary64 |
| 368× | associate-/l*_binary64 |
| 208× | *-commutative_binary64 |
| 144× | +-commutative_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 775 | 21028 |
| 1 | 2091 | 17483 |
| 2 | 4849 | 17362 |
| 3 | 5175 | 17362 |
7 alts after pruning (7 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 302 | 7 | 309 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 303 | 7 | 310 |
| Status | Error | Program |
| ▶ | 11.0b | (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) |
| 44.6b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))) | |
| 23.3b | (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) | |
| 44.3b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t))) | |
| 12.2b | (*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) | |
| 23.4b | (asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))) | |
| 11.1b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
Compiled 18214 to 13434 computations (26.2% saved)
Found 4 expressions with local error:
| New | Error | Program |
| 0.3b | (pow.f64 (/.f64 Om Omc) 2) | |
| 0.4b | (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) | |
| ✓ | 0.5b | (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) |
| ✓ | 10.0b | (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) |
2 calls:
| 715.0ms | (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) |
| 38.0ms | (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) |
| 1× | rewrite-expression-head |
| 4× | add-sqr-sqrt_binary64 |
| 3× | *-un-lft-identity_binary64 |
| 3× | sqrt-prod_binary64 |
| 3× | add-cube-cbrt_binary64 |
| 3× | pow1_binary64 |
2 calls:
| 2.0ms | (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) |
| 1.0ms | (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) |
| 1× | egg-herbie |
| 516× | fma-def_binary64 |
| 396× | times-frac_binary64 |
| 338× | associate-/r*_binary64 |
| 333× | associate-*l*_binary64 |
| 255× | associate-/l*_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 471 | 11719 |
| 1 | 1445 | 9757 |
| 2 | 5224 | 9757 |
7 alts after pruning (7 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 269 | 1 | 270 |
| Fresh | 0 | 6 | 6 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 270 | 7 | 277 |
| Status | Error | Program |
| ▶ | 11.0b | (expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) |
| 23.4b | (asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))) | |
| 23.3b | (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) | |
| 44.3b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t))) | |
| 44.6b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))) | |
| 12.2b | (*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) | |
| 11.1b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
Compiled 17118 to 12889 computations (24.7% saved)
Found 4 expressions with local error:
| New | Error | Program |
| 0.3b | (pow.f64 (/.f64 Om Omc) 2) | |
| 0.4b | (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) | |
| 0.5b | (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) | |
| 10.0b | (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) |
7 alts after pruning (6 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 270 | 0 | 270 |
| Fresh | 0 | 6 | 6 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 270 | 7 | 277 |
| Status | Error | Program |
| ✓ | 11.0b | (expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) |
| 23.4b | (asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))) | |
| 23.3b | (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) | |
| 44.3b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t))) | |
| 44.6b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))) | |
| 12.2b | (*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) | |
| ▶ | 11.1b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
Compiled 17632 to 13407 computations (24% saved)
Found 4 expressions with local error:
| New | Error | Program |
| 0.3b | (pow.f64 (/.f64 Om Omc) 2) | |
| ✓ | 0.5b | (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) |
| ✓ | 0.5b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
| ✓ | 10.1b | (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) |
3 calls:
| 388.0ms | (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) |
| 20.0ms | (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) |
| 19.0ms | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
| 1× | rewrite-expression-head |
| 155× | sqrt-prod_binary64 |
| 148× | add-sqr-sqrt_binary64 |
| 116× | times-frac_binary64 |
| 103× | *-un-lft-identity_binary64 |
| 70× | difference-of-squares_binary64 |
3 calls:
| 14.0ms | (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) |
| 1.0ms | (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) |
| 0.0ms | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) |
| 1× | egg-herbie |
| 818× | fma-def_binary64 |
| 433× | times-frac_binary64 |
| 377× | associate-/r*_binary64 |
| 291× | associate-/l*_binary64 |
| 202× | associate-*l/_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 645 | 19365 |
| 1 | 1761 | 16645 |
| 2 | 4923 | 16520 |
| 3 | 5188 | 16520 |
10 alts after pruning (9 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 298 | 6 | 304 |
| Fresh | 2 | 3 | 5 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 1 | 1 |
| Total | 301 | 10 | 311 |
| Status | Error | Program |
| 44.9b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l))))) | |
| 44.6b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))) | |
| 12.2b | (*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) | |
| 45.0b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l)))) | |
| 11.1b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/2))) | |
| 44.3b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))) | |
| 47.6b | (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (*.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 l 3) (*.f64 (pow.f64 t 3) (*.f64 2 (sqrt.f64 2)))) -1/8))))) | |
| ✓ | 11.0b | (expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) |
| 44.3b | (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t))) | |
| 11.2b | (asin.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) |
Compiled 17813 to 13257 computations (25.6% saved)
Total 0.4b remaining (43.7%)
Threshold costs 0.4b (43.7%)
Compiled 35741 to 29006 computations (18.8% saved)
Compiled 7 to 5 computations (28.6% saved)
| 1× | egg-herbie |
| 15× | *-commutative_binary64 |
| 12× | +-commutative_binary64 |
| 12× | sub-neg_binary64 |
| 10× | neg-sub0_binary64 |
| 10× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 118 |
| 1 | 57 | 118 |
| 2 | 81 | 118 |
| 3 | 103 | 118 |
| 4 | 117 | 118 |
| 5 | 123 | 118 |
| 6 | 124 | 118 |
| 7 | 122 | 118 |
Compiled 81 to 58 computations (28.4% saved)
| 1× | intervals |
| 979.0ms | 8000× | body | 128 | valid |
| 531.0ms | 4556× | body | 128 | nan |
Compiled 404 to 318 computations (21.3% saved)
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