Details

sample1.2s

Algorithm: halfpoints

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2011
4	2011
3	1591
2	264
1	60
0	19

prune82.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize266.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
1.4b	(/.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)))
3.3b	(/.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))))

rewrite38.0ms

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`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-+r+`
2×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-`
1×	`p16-flip--`

Counts

4 → 124

Calls

4 calls:

8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
13.0ms	(/.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)))
7.0ms	(/.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 alpha beta) (*.p16 (real->posit16 2) 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))))

simplify1.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	2008
3	2008
2	873
1	149
0	58

prune5.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.8b

localize446.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.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)))
0.7b	(/.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)))
1.2b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
1.3b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite330.0ms

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:

112.0ms	(/.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)))
138.0ms	(/.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)))
27.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
37.0ms	(/.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 (.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 (.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)))

simplify1.9s

Counts

408 → 408

Iterations

Iter	Nodes
done	2004
3	2004
2	952
1	167
0	71

prune20.2s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 0.5b

localize679.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.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 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 i (real->posit16 2))))
1.0b	(/.p16 (+.p16 (+.p16 beta i) alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))
1.3b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite666.0ms

Algorithm

rewrite-expression-head

Rules

291×	`p16-times-frac`
210×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
84×	`distribute-lft-out--`
42×	`distribute-rgt-out--`
23×	`/p16-rgt-identity-expand`
21×	`associate-/r*`
19×	`associate-/l*`
18×	`associate-/r/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l/`
1×	`p16-flip--`

Counts

4 → 254

Calls

4 calls:

527.0ms	(/.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)))
61.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 i (real->posit16 2))))
43.0ms	(/.p16 (+.p16 (+.p16 beta i) alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))
25.0ms	(/.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 (.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 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 i (real->posit16 2))))
0.0ms	(/.p16 (+.p16 (+.p16 beta i) alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.6s

Counts

258 → 258

Iterations

Iter	Nodes
done	2000
3	2000
2	862
1	147
0	63

prune14.0s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 0.4b

localize845.0ms

Local error

Found 4 expressions with local error:

0.7b	(.p16 (/.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 alpha (+.p16 (.p16 i (real->posit16 2)) beta))) (/.p16 (real->posit16 1.0) (+.p16 (*.p16 i (real->posit16 2)) (-.p16 (+.p16 alpha beta) (real->posit16 1.0)))))
0.9b	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 i (real->posit16 2))))
1.0b	(/.p16 (+.p16 (+.p16 beta i) alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))
1.3b	(/.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 alpha (+.p16 (*.p16 i (real->posit16 2)) beta)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

36×	`p16-times-frac`
35×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
13×	`associate-r` `associate-l`
11×	`/p16-rgt-identity-expand`
9×	`associate-/r*`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand` `associate-/l*`
5×	`associate-/r/`
4×	`introduce-quire` `-p16-rgt-identity-expand`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`
1×	`associate-l/` `associate-r/` `*-commutative`

Counts

4 → 103

Calls

4 calls:

49.0ms	(.p16 (/.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 alpha (+.p16 (.p16 i (real->posit16 2)) beta))) (/.p16 (real->posit16 1.0) (+.p16 (*.p16 i (real->posit16 2)) (-.p16 (+.p16 alpha beta) (real->posit16 1.0)))))
57.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 i (real->posit16 2))))
44.0ms	(/.p16 (+.p16 (+.p16 beta i) alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))
11.0ms	(/.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 alpha (+.p16 (*.p16 i (real->posit16 2)) beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.4s

Counts

107 → 107

Iterations

Iter	Nodes
done	2019
4	2019
3	1950
2	528
1	139
0	57

prune6.9s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 0.4b

regimes2.6s

Accuracy

0% (0.9b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	30
0	30

end0.0ms

sample30.3s

Algorithm: halfpoints