Details

sample1.2s

Algorithm: halfpoints

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
3	1711
2	279
1	60
0	19

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize314.0ms

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)))
1.2b	(/.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)))
3.0b	(/.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))))

rewrite61.0ms

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:

23.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
6.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
14.0ms	(/.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)))
13.0ms	(/.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))))

simplify1.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	982
1	172
0	69

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.7b

localize362.0ms

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

rewrite252.0ms

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:

93.0ms	(/.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)))
116.0ms	(/.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)))
16.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
20.0ms	(/.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)))

simplify1.6s

Counts

408 → 408

Iterations

Iter	Nodes
done	5010
2	1082
1	166
0	71

prune2.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.4b

localize458.0ms

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)))
0.8b	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.1b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 (real->posit16 2) i)) (+.p16 alpha beta)))
1.2b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

318×	`p16-times-frac`
251×	`p16-lft-identity-expand` `p16--un-lft-identity`
227×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
42×	`distribute-rgt-out--`
30×	`associate-/r*`
23×	`/p16-rgt-identity-expand`
19×	`associate-/l*`
18×	`associate-/r/`
16×	`p16-distribute-lft-out` `distribute-lft-out`
4×	`+p16-lft-identity-expand` `distribute-rgt-out` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l/`
1×	`p16-flip--`

Counts

4 → 290

Calls

4 calls:

87.0ms	(/.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)))
14.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
55.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 (real->posit16 2) i)) (+.p16 alpha beta)))
13.0ms	(/.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 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 (real->posit16 2) i)) (+.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)))

simplify1.9s

Counts

294 → 294

Iterations

Iter	Nodes
done	5001
2	891
1	137
0	59

prune2.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.3b

localize622.0ms

Local error

Found 4 expressions with local error:

0.7b	(.p16 (/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha (.p16 (real->posit16 2) i)) beta)) (/.p16 (real->posit16 1.0) (+.p16 (-.p16 (*.p16 (real->posit16 2) i) (real->posit16 1.0)) (+.p16 alpha beta))))
0.8b	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.1b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 (real->posit16 2) i)) (+.p16 alpha beta)))
1.2b	(/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha (*.p16 (real->posit16 2) i)) beta))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

109×	`p16-lft-identity-expand` `p16--un-lft-identity`
90×	`p16-times-frac`
67×	`*p16-rgt-identity-expand`
40×	`associate-r`
28×	`p16-distribute-lft-out` `distribute-lft-out`
18×	`associate-/r*`
13×	`associate-l`
11×	`/p16-rgt-identity-expand`
7×	`distribute-rgt-out`
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 → 166

Calls

4 calls:

32.0ms	(.p16 (/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha (.p16 (real->posit16 2) i)) beta)) (/.p16 (real->posit16 1.0) (+.p16 (-.p16 (*.p16 (real->posit16 2) i) (real->posit16 1.0)) (+.p16 alpha beta))))
13.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
56.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 (real->posit16 2) i)) (+.p16 alpha beta)))
25.0ms	(/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha (*.p16 (real->posit16 2) i)) beta))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.1s

Counts

170 → 170

Iterations

Iter	Nodes
done	5040
3	2156
2	549
1	141
0	55

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.3b

regimes1.8s

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	28
0	28

end0.0ms

sample28.7s

Algorithm: halfpoints