Details

sample1.2s

Algorithm: halfpoints

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5014
3	1591
2	264
1	60
0	19

prune61.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize373.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
1.5b	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
3.4b	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

58×	`p16-times-frac`
36×	`/p16-rgt-identity-expand`
29×	`associate-/r/`
28×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
24×	`difference-of-squares`
11×	`associate-l/` `associate-r/`
8×	`associate-/r` `introduce-quire` `difference-of-sqr-1` `-p16-rgt-identity-expand` `associate-/l`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-+r+`
5×	`associate-/l/`
3×	`associate-+l+`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-`
1×	`distribute-rgt-in` `distribute-lft-in` `p16-flip--`

Counts

4 → 127

Calls

4 calls:

8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
3.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
7.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
6.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	5008
2	937
1	172
0	69

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.8b

localize420.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.7b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
1.4b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

478×	`p16-times-frac`
339×	`p16-lft-identity-expand` `p16--un-lft-identity`
323×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
48×	`p16-distribute-lft-out` `distribute-lft-out`
44×	`/p16-rgt-identity-expand`
42×	`distribute-rgt-out--`
38×	`associate-/r/`
37×	`associate-/r*`
24×	`distribute-rgt-out` `associate-/l*`
8×	`distribute-lft1-in`
5×	`associate-/l/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
1×	`associate-*r/` `p16-flip--`

Counts

4 → 404

Calls

4 calls:

77.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
94.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
32.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
23.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.0s

Counts

408 → 408

Iterations

Iter	Nodes
done	5007
2	947
1	167
0	71

prune2.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.5b

localize1.1s

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.7b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.9b	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

301×	`p16-times-frac`
226×	`p16-lft-identity-expand` `p16--un-lft-identity`
222×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
42×	`distribute-rgt-out--`
37×	`associate-/r*`
24×	`/p16-rgt-identity-expand`
18×	`associate-/r/`
17×	`associate-/l*`
12×	`p16-distribute-lft-out` `distribute-lft-out`
6×	`distribute-rgt-out`
5×	`associate-/l/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
2×	`distribute-lft1-in`
1×	`associate-l/` `associate-r/` `p16-flip--`

Counts

4 → 280

Calls

4 calls:

78.0ms	(/.p16 (.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
73.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
7.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
24.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.7s

Counts

284 → 284

Iterations

Iter	Nodes
done	5000
2	982
1	155
0	63

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.5b

localize533.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.8b	(.p16 (/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (.p16 (real->posit16 2) i) (+.p16 alpha beta))) (/.p16 (real->posit16 1.0) (-.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)) (real->posit16 1.0))))
0.9b	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b	(/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

78×	`p16-lft-identity-expand` `p16--un-lft-identity`
74×	`*p16-rgt-identity-expand`
73×	`p16-times-frac`
41×	`associate-r`
25×	`associate-/r*`
18×	`distribute-lft-out--`
13×	`associate-l`
12×	`p16-distribute-lft-out` `/p16-rgt-identity-expand` `distribute-lft-out`
9×	`distribute-rgt-out--`
6×	`+p16-lft-identity-expand` `distribute-rgt-out` `associate-/r/` `+p16-rgt-identity-expand`
4×	`introduce-quire` `-p16-rgt-identity-expand` `associate-/l*` `associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft1-in` `associate-l/` `associate-r/`
1×	`p16-flip--` `*-commutative`

Counts

4 → 157

Calls

4 calls:

77.0ms	(/.p16 (.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
57.0ms	(.p16 (/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (.p16 (real->posit16 2) i) (+.p16 alpha beta))) (/.p16 (real->posit16 1.0) (-.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)) (real->posit16 1.0))))
13.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
20.0ms	(/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.4s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	967
1	171
0	62

prune1.7s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 0.4b

regimes2.2s

Accuracy

0% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
0	29

end0.0ms

sample31.3s

Algorithm: halfpoints