Details

sample395.0ms

Algorithm: halfpoints

simplify1.1s

Counts

1 → 1

Iterations

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

prune63.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize270.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.3b	(/.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))))
0.4b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite356.0ms

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:

59.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
151.0ms	(/.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))))
17.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
111.0ms	(/.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))))

simplify1.5s

Counts

410 → 410

Iterations

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

prune20.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize1000.0ms

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))
0.4b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite232.0ms

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:

58.0ms	(.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)))
19.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) alpha) beta))
16.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
131.0ms	(/.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))))

simplify1.3s

Counts

349 → 349

Iterations

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

prune17.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize688.0ms

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 alpha (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) beta))))
0.3b	(/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) beta)))
0.4b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite249.0ms

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:

76.0ms	(.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 alpha (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) beta))))
9.0ms	(/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) beta)))
16.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
130.0ms	(/.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 alpha (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) beta))))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) 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))))

simplify1.8s

Counts

349 → 349

Iterations

Iter	Nodes
done	2035
4	2035
3	1981
2	445
1	137
0	57

prune19.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize370.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0))))
0.4b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

2445×	`p16-times-frac`
1466×	`p16-lft-identity-expand` `p16--un-lft-identity`
1362×	`*p16-rgt-identity-expand`
312×	`p16-distribute-lft-out` `distribute-lft-out`
193×	`associate-/l*`
156×	`distribute-rgt-out`
83×	`associate-/r*`
52×	`distribute-lft1-in`
24×	`/p16-rgt-identity-expand`
23×	`associate-/r/`
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 → 1123

Calls

4 calls:

78.0ms	(/.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
70.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0))))
8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
65.0ms	(/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.8s

Counts

1127 → 1127

Iterations

Iter	Nodes
done	2000
3	2000
2	401
1	125
0	58

prune56.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes448.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	23

end0.0ms

sample6.5s

Algorithm: halfpoints