Time bar (total: 17.1s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 28.1% | 71.9% | 0 |
| 0% | 28.1% | 71.9% | 1 |
| 0% | 28.1% | 71.9% | 2 |
| 7% | 21.1% | 71.9% | 3 |
| 17.5% | 10.5% | 71.9% | 4 |
| 21.1% | 7% | 71.9% | 5 |
| 22.8% | 5.3% | 71.9% | 6 |
| 23.2% | 4.8% | 71.9% | 7 |
| 23.7% | 4.4% | 71.9% | 8 |
| 24.6% | 3.5% | 71.9% | 9 |
| 25.1% | 3% | 71.9% | 10 |
| 25.8% | 2.3% | 71.9% | 11 |
| 26.3% | 1.8% | 71.9% | 12 |
| 26.6% | 1.5% | 71.9% | 13 |
| 26.9% | 1.2% | 71.9% | 14 |
Compiled 43 to 28 computations (34.9% saved)
| 1.4s | 6694× | body | 128 | valid |
| 419.0ms | 557× | body | 512 | valid |
| 312.0ms | 671× | body | 1024 | valid |
| 74.0ms | 279× | body | 256 | valid |
| 31.0ms | 55× | body | 2048 | valid |
Compiled 118 to 76 computations (35.6% saved)
| 1× | egg-herbie |
| 847× | times-frac_binary64 |
| 817× | distribute-rgt-in_binary64 |
| 748× | distribute-lft-in_binary64 |
| 537× | div-sub_binary64 |
| 535× | fma-neg_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 43 |
| 1 | 34 | 39 |
| 2 | 110 | 37 |
| 3 | 435 | 37 |
| 4 | 1672 | 37 |
| 5 | 2494 | 37 |
| 6 | 3358 | 37 |
| 7 | 5392 | 37 |
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 2 | 2 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 0 | 3 | 3 |
| Status | Error | Program |
| 22.8b | (/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2) | |
| ▶ | 19.0b | (/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2) |
Compiled 180 to 106 computations (41.1% saved)
Found 3 expressions with local error:
| New | Error | Program |
| ✓ | 0.0b | (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) |
| ✓ | 11.2b | (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) |
| ✓ | 17.8b | (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) |
3 calls:
| 556.0ms | (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) |
| 308.0ms | (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) |
| 25.0ms | (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) |
| 1× | rewrite-expression-head |
| 13× | *-un-lft-identity_binary64 |
| 13× | add-sqr-sqrt_binary64 |
| 10× | add-cbrt-cube_binary64 |
| 10× | add-exp-log_binary64 |
| 7× | add-cube-cbrt_binary64 |
3 calls:
| 8.0ms | (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) |
| 6.0ms | (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) |
| 0.0ms | (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) |
| 1× | egg-herbie |
| 561× | +-commutative_binary64 |
| 490× | fma-def_binary64 |
| 487× | associate-+r+_binary64 |
| 392× | *-commutative_binary64 |
| 294× | associate-*r/_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1400 | 19973 |
| 1 | 5450 | 19973 |
4 alts after pruning (4 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 202 | 3 | 205 |
| Fresh | 0 | 1 | 1 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 203 | 4 | 207 |
| Status | Error | Program |
| 50.6b | (/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2) | |
| ▶ | 11.1b | (/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2) |
| 22.8b | (/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2) | |
| 52.6b | (/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2) |
Compiled 24695 to 15944 computations (35.4% saved)
Found 3 expressions with local error:
| New | Error | Program |
| ✓ | 0.1b | (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) |
| ✓ | 0.3b | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) |
| ✓ | 11.2b | (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) |
3 calls:
| 585.0ms | (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) |
| 327.0ms | (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) |
| 53.0ms | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) |
| 1× | rewrite-expression-head |
| 166× | times-frac_binary64 |
| 156× | *-un-lft-identity_binary64 |
| 116× | add-sqr-sqrt_binary64 |
| 78× | add-cube-cbrt_binary64 |
| 24× | associate-/l*_binary64 |
3 calls:
| 11.0ms | (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) |
| 5.0ms | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) |
| 0.0ms | (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) |
| 1× | egg-herbie |
| 490× | fma-def_binary64 |
| 477× | associate-+r+_binary64 |
| 326× | associate-*r/_binary64 |
| 177× | associate-/l*_binary64 |
| 171× | associate-/r*_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1591 | 25853 |
| 1 | 5046 | 25853 |
4 alts after pruning (4 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 296 | 2 | 298 |
| Fresh | 1 | 2 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 298 | 4 | 302 |
| Status | Error | Program |
| ▶ | 11.1b | (/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2) |
| 50.6b | (/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2) | |
| 52.6b | (/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2) | |
| 11.1b | (/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2) |
Compiled 30279 to 18745 computations (38.1% saved)
Found 4 expressions with local error:
| New | Error | Program |
| 0.1b | (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) | |
| 0.3b | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) | |
| ✓ | 2.0b | (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) |
| ✓ | 2.8b | (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) |
2 calls:
| 520.0ms | (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) |
| 328.0ms | (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) |
| 1× | rewrite-expression-head |
| 139× | times-frac_binary64 |
| 123× | *-un-lft-identity_binary64 |
| 92× | add-sqr-sqrt_binary64 |
| 82× | associate-*r*_binary64 |
| 59× | add-cube-cbrt_binary64 |
2 calls:
| 25.0ms | (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) |
| 16.0ms | (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) |
| 1× | egg-herbie |
| 404× | +-commutative_binary64 |
| 361× | *-commutative_binary64 |
| 354× | fma-def_binary64 |
| 349× | associate-+r+_binary64 |
| 271× | associate-*r/_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1236 | 21338 |
| 1 | 4728 | 21233 |
| 2 | 5013 | 21233 |
5 alts after pruning (5 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 505 | 2 | 507 |
| Fresh | 0 | 3 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 506 | 5 | 511 |
| Status | Error | Program |
| ▶ | 11.1b | (/.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) 2) |
| 50.6b | (/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2) | |
| 27.9b | (/.f64 (/.f64 (fma.f64 (pow.f64 (+.f64 beta alpha) 2) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) -1) (fma.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) -1)) 2) | |
| 52.6b | (/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2) | |
| 11.1b | (/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2) |
Compiled 48820 to 29876 computations (38.8% saved)
Found 4 expressions with local error:
| New | Error | Program |
| ✓ | 0.2b | (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) |
| ✓ | 0.3b | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) |
| ✓ | 2.0b | (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) |
| ✓ | 2.8b | (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))) |
4 calls:
| 2.5s | (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))) |
| 1.5s | (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) |
| 381.0ms | (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) |
| 70.0ms | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) |
| 1× | rewrite-expression-head |
| 154× | times-frac_binary64 |
| 144× | *-un-lft-identity_binary64 |
| 113× | add-sqr-sqrt_binary64 |
| 82× | associate-*r*_binary64 |
| 72× | add-cube-cbrt_binary64 |
4 calls:
| 24.0ms | (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) |
| 5.0ms | (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) |
| 1.0ms | (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) |
| 0.0ms | (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))) |
| 1× | egg-herbie |
| 1155× | fma-def_binary64 |
| 457× | times-frac_binary64 |
| 14× | cube-mult_binary64 |
| 14× | unpow3_binary64 |
| 13× | unpow2_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 3255 | 68432 |
| 1 | 5234 | 68432 |
5 alts after pruning (4 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 345 | 0 | 345 |
| Fresh | 0 | 4 | 4 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 345 | 5 | 350 |
| Status | Error | Program |
| ✓ | 11.1b | (/.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) 2) |
| 50.6b | (/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2) | |
| 27.9b | (/.f64 (/.f64 (fma.f64 (pow.f64 (+.f64 beta alpha) 2) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) -1) (fma.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) -1)) 2) | |
| 52.6b | (/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2) | |
| 11.1b | (/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2) |
Compiled 90497 to 61843 computations (31.7% saved)
Total 1.4b remaining (92.8%)
Threshold costs 0b (0%)
Compiled 21880 to 15248 computations (30.3% saved)
Compiled 28 to 16 computations (42.9% saved)
| 1× | egg-herbie |
| 7× | +-commutative_binary64 |
| 5× | *-commutative_binary64 |
| 2× | sub-neg_binary64 |
| 1× | neg-sub0_binary64 |
| 1× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 99 |
| 1 | 42 | 99 |
| 2 | 47 | 99 |
| 3 | 49 | 99 |
| 4 | 50 | 99 |
| 5 | 50 | 99 |
Compiled 359 to 207 computations (42.3% saved)
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