Details

sample1.4s

Algorithm: halfpoints

simplify983.0ms

Counts

1 → 1

Iterations

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

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize272.0ms

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)))
3.5b	(/.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))))

rewrite48.0ms

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:

15.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
6.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) 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)))
11.0ms	(/.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))))

simplify1.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	2010
3	2010
2	937
1	172
0	69

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.0b

localize341.0ms

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)))
0.6b	(/.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)))
1.3b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite191.0ms

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:

86.0ms	(/.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)))
71.0ms	(/.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)))
11.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
15.0ms	(/.p16 (.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 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

simplify1.2s

Counts

408 → 408

Iterations

Iter	Nodes
done	2081
3	2081
2	997
1	166
0	71

prune2.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 0.6b

localize533.0ms

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

rewrite115.0ms

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:

53.0ms	(/.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 i (+.p16 (+.p16 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 (real->posit16 2) i)))
14.0ms	(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
12.0ms	(/.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 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) 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)))

simplify860.0ms

Counts

258 → 258

Iterations

Iter	Nodes
done	2042
3	2042
2	930
1	141
0	63

prune2.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.6b

localize724.0ms

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

rewrite226.0ms

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:

106.0ms	(/.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)))
56.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (+.p16 alpha beta)) (*.p16 (real->posit16 2) i)))
28.0ms	(/.p16 (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta) (+.p16 alpha (+.p16 beta 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 (.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 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta) (+.p16 alpha (+.p16 beta i)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.2s

Counts

258 → 258

Iterations

Iter	Nodes
done	2060
3	2060
2	852
1	130
0	61

prune2.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 0.5b

regimes3.0s

Accuracy

0% (0.9b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	31
0	31

end0.0ms

sample32.1s

Algorithm: halfpoints