Details

sample329.0ms

Algorithm: halfpoints

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2098
4	2098
3	490
2	109
1	39
0	18

prune81.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize368.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.2b	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.3b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.8b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

468×	`p16-times-frac`
372×	`p16-lft-identity-expand` `p16--un-lft-identity`
338×	`*p16-rgt-identity-expand`
102×	`p16-distribute-lft-out` `distribute-lft-out`
80×	`associate-/l*`
51×	`distribute-rgt-out`
18×	`introduce-quire`
17×	`distribute-lft1-in`
14×	`insert-quire-fdp-add`
11×	`/p16-rgt-identity-expand`
10×	`-p16-rgt-identity-expand`
8×	`insert-quire-add`
6×	`associate-/r*` `+p16-lft-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
5×	`associate-+l-`
4×	`associate-+r+`
3×	`associate-+r-`
2×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 406

Calls

4 calls:

58.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
105.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
14.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
124.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify1.2s

Counts

410 → 410

Iterations

Iter	Nodes
done	2028
3	2028
2	517
1	116
0	55

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize627.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)))
0.3b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) alpha) beta))
0.3b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.8b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

429×	`p16-times-frac`
317×	`p16-lft-identity-expand` `p16--un-lft-identity`
291×	`*p16-rgt-identity-expand`
187×	`associate-l`
78×	`p16-distribute-lft-out` `distribute-lft-out`
39×	`distribute-rgt-out`
22×	`associate-/l*`
13×	`distribute-lft1-in` `associate-r` `/p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
6×	`associate-/r*` `introduce-quire` `-p16-rgt-identity-expand`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-/l/`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 345

Calls

4 calls:

71.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)))
10.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) alpha) beta))
11.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
110.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) alpha) beta))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify1.7s

Counts

349 → 349

Iterations

Iter	Nodes
done	2026
4	2026
3	1369
2	382
1	136
0	57

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize508.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (.p16 (+.p16 (+.p16 beta (+.p16 alpha (.p16 beta alpha))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))
0.3b	(+.p16 beta (+.p16 alpha (*.p16 beta alpha)))
0.3b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.8b	(.p16 (+.p16 (+.p16 beta (+.p16 alpha (.p16 beta alpha))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

33×	`p16-lft-identity-expand` `p16--un-lft-identity`
31×	`*p16-rgt-identity-expand`
21×	`p16-times-frac`
19×	`associate-l`
13×	`associate-r`
11×	`/p16-rgt-identity-expand`
6×	`associate-/r*` `p16-distribute-lft-out` `+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out`
4×	`introduce-quire` `associate-/l*` `associate-/l/`
3×	`associate-+r-` `distribute-rgt-out` `associate-/r/`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`+-commutative` `associate-+r+` `distribute-lft1-in` `*-commutative`

Counts

4 → 103

Calls

4 calls:

22.0ms	(/.p16 (.p16 (+.p16 (+.p16 beta (+.p16 alpha (.p16 beta alpha))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))
8.0ms	(+.p16 beta (+.p16 alpha (*.p16 beta alpha)))
21.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
37.0ms	(.p16 (+.p16 (+.p16 beta (+.p16 alpha (.p16 beta alpha))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (.p16 (+.p16 (+.p16 beta (+.p16 alpha (.p16 beta alpha))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(+.p16 beta (+.p16 alpha (*.p16 beta alpha)))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(.p16 (+.p16 (+.p16 beta (+.p16 alpha (.p16 beta alpha))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))))

simplify2.7s

Counts

107 → 107

Iterations

Iter	Nodes
done	2012
4	2012
3	1985
2	383
1	105
0	43

prune2.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize429.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0))))
0.3b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.3b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)))

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

9499×	`p16-times-frac`
4834×	`p16-lft-identity-expand` `p16--un-lft-identity`
4558×	`*p16-rgt-identity-expand`
828×	`p16-distribute-lft-out` `distribute-lft-out`
414×	`distribute-rgt-out`
251×	`associate-/r*` `associate-/r/`
241×	`/p16-rgt-identity-expand`
138×	`distribute-lft1-in`
19×	`associate-/l*`
6×	`introduce-quire` `-p16-rgt-identity-expand`
5×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l/`
2×	`associate-+r+`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 2939

Calls

4 calls:

163.0ms	(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0))))
23.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
10.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
70.0ms	(/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0))))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)))

simplify2.7s

Counts

2943 → 2943

Iterations

Iter	Nodes
done	2008
3	2008
2	551
1	152
0	66

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes768.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	25
1	25
0	23

end0.0ms

sample7.1s

Algorithm: halfpoints