Details

sample635.0ms

Algorithm: halfpoints

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
4	2074
3	418
2	93
1	35
0	19

prune62.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize427.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
0.5b	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.7b	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

126×	`p16-times-frac`
117×	`p16-lft-identity-expand` `p16--un-lft-identity`
67×	`*p16-rgt-identity-expand`
38×	`p16-distribute-lft-out` `distribute-lft-out`
26×	`/p16-rgt-identity-expand`
19×	`associate-/r/`
15×	`associate-/r*`
14×	`distribute-rgt-out`
10×	`introduce-quire`
8×	`-p16-rgt-identity-expand` `associate-/l*`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-+r+` `insert-quire-fdp-add`
3×	`associate-+l+`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `distribute-lft1-in` `associate-*r/` `associate-+l-`
1×	`associate-*l/` `p16-flip--`

Counts

4 → 188

Calls

4 calls:

10.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
444.0ms	(+.p16 (/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
161.0ms	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
29.0ms	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.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 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
0.0ms	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

simplify2.8s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
3	3357
2	461
1	118
0	60

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize463.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))) (real->posit16 1.0))
0.2b	(/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha)))
0.6b	(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))
0.7b	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite663.0ms

Algorithm

rewrite-expression-head

Rules

461×	`p16-times-frac`
235×	`p16-lft-identity-expand` `p16--un-lft-identity`
233×	`*p16-rgt-identity-expand`
47×	`associate-/r/`
37×	`/p16-rgt-identity-expand`
20×	`associate-/r*`
19×	`associate-/l*`
15×	`p16-flip--`
8×	`introduce-quire`
6×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out`
3×	`distribute-rgt-out` `insert-quire-fdp-add` `associate-/l/`
2×	`associate-+l+` `associate-+r+`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `distribute-lft1-in` `associate-+l-`

Counts

4 → 305

Calls

4 calls:

419.0ms	(+.p16 (/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))) (real->posit16 1.0))
134.0ms	(/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha)))
75.0ms	(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))
15.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))) (real->posit16 1.0))
0.0ms	(/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha)))
0.0ms	(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))
0.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify2.9s

Counts

309 → 309

Iterations

Iter	Nodes
done	5001
3	4139
2	898
1	202
0	87

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize359.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2))))
0.2b	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 beta alpha) (.p16 i (real->posit16 2)))) (/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))
0.7b	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

21×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
18×	`p16-times-frac`
10×	`-p16-rgt-identity-expand`
8×	`+p16-lft-identity-expand` `introduce-quire` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
7×	`associate-+r-`
6×	`associate-+l+` `associate-/r` `associate-/l`
3×	`associate-+r+` `insert-quire-fdp-add` `associate-+l-` `associate-/l/`
2×	`distribute-rgt-in` `+-commutative` `distribute-lft-in` `associate-/r/`
1×	`insert-quire-add` `p16-flip--`

Counts

4 → 88

Calls

4 calls:

23.0ms	(+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2))))
10.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 beta alpha) (.p16 i (real->posit16 2)))) (/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
38.0ms	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))
40.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2))))
0.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 beta alpha) (.p16 i (real->posit16 2)))) (/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))

simplify2.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	1597
2	314
1	94
0	51

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize392.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2))))
0.2b	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 i (real->posit16 2))))) (/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))
0.7b	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

21×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
18×	`p16-times-frac`
10×	`-p16-rgt-identity-expand`
8×	`+p16-lft-identity-expand` `introduce-quire` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
7×	`associate-+r-`
6×	`associate-+l+` `associate-/r` `associate-/l`
3×	`associate-+r+` `insert-quire-fdp-add` `associate-+l-` `associate-/l/`
2×	`distribute-rgt-in` `+-commutative` `distribute-lft-in` `associate-/r/`
1×	`insert-quire-add` `p16-flip--`

Counts

4 → 88

Calls

4 calls:

23.0ms	(+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2))))
12.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 i (real->posit16 2))))) (/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
35.0ms	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))
8.0ms	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2))))
0.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 i (real->posit16 2))))) (/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (+.p16 alpha (real->posit16 2.0)) (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

simplify3.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5008
3	1499
2	314
1	95
0	52

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes1.1s

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	21
0	21

end0.0ms

sample14.5s

Algorithm: halfpoints