Details

sample348.0ms

Algorithm: halfpoints

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
4	3067
3	490
2	109
1	39
0	18

prune53.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize393.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.3b	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.4b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

468×	`p16-times-frac`
372×	`p16-lft-identity-expand` `p16--un-lft-identity`
338×	`*p16-rgt-identity-expand`
102×	`p16-distribute-lft-out` `distribute-lft-out`
80×	`associate-/l*`
51×	`distribute-rgt-out`
18×	`introduce-quire`
17×	`distribute-lft1-in`
14×	`insert-quire-fdp-add`
11×	`/p16-rgt-identity-expand`
10×	`-p16-rgt-identity-expand`
8×	`insert-quire-add`
6×	`associate-/r*` `+p16-lft-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
5×	`associate-+l-`
4×	`associate-+r+`
3×	`associate-+r-`
2×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 406

Calls

4 calls:

65.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
162.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
17.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
105.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify3.8s

Counts

410 → 410

Iterations

Iter	Nodes
done	5001
3	4067
2	517
1	116
0	55

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize495.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.2b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.4b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

783×	`p16-times-frac`
535×	`p16-lft-identity-expand` `p16--un-lft-identity`
493×	`*p16-rgt-identity-expand`
187×	`associate-l`
126×	`p16-distribute-lft-out` `distribute-lft-out`
64×	`associate-/l*`
63×	`distribute-rgt-out`
21×	`distribute-lft1-in`
16×	`/p16-rgt-identity-expand`
13×	`associate-r`
11×	`associate-/r/`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-/r*` `introduce-quire` `-p16-rgt-identity-expand`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-/l/`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 513

Calls

4 calls:

137.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
25.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
16.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
141.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify2.8s

Counts

517 → 517

Iterations

Iter	Nodes
done	5005
3	1468
2	471
1	144
0	58

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize438.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 beta alpha))) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.2b	(+.p16 alpha (+.p16 beta (*.p16 beta alpha)))
0.2b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.7b	(/.p16 (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 beta alpha))) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

783×	`p16-times-frac`
535×	`p16-lft-identity-expand` `p16--un-lft-identity`
493×	`*p16-rgt-identity-expand`
187×	`associate-l`
126×	`p16-distribute-lft-out` `distribute-lft-out`
64×	`associate-/l*`
63×	`distribute-rgt-out`
21×	`distribute-lft1-in`
16×	`/p16-rgt-identity-expand`
13×	`associate-r`
11×	`associate-/r/`
6×	`associate-/r*` `+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`introduce-quire`
3×	`associate-+r-`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`
1×	`+-commutative` `associate-+r+` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 509

Calls

4 calls:

84.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 beta alpha))) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
5.0ms	(+.p16 alpha (+.p16 beta (*.p16 beta alpha)))
15.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
70.0ms	(/.p16 (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 beta alpha))) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 beta alpha))) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.0ms	(+.p16 alpha (+.p16 beta (*.p16 beta alpha)))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.0ms	(/.p16 (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 beta alpha))) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify5.9s

Counts

513 → 513

Iterations

Iter	Nodes
done	5117
4	4807
3	1394
2	655
1	127
0	51

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize497.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.2b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.3b	(*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha))
0.7b	(.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

29×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
27×	`p16-times-frac`
16×	`associate-l`
14×	`/p16-rgt-identity-expand`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-/r` `+p16-lft-identity-expand` `+p16-rgt-identity-expand` `associate-/l`
5×	`associate-*r/`
4×	`introduce-quire` `associate-r` `-p16-rgt-identity-expand`
3×	`associate-*l/` `associate-/r/`
2×	`*-commutative` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

26.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
18.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
7.0ms	(*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha))
23.0ms	(.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha))
0.0ms	(.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)))

simplify4.7s

Counts

108 → 108

Iterations

Iter	Nodes
done	5311
3	4332
2	895
1	164
0	53

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes488.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	26

end0.0ms

sample6.3s

Algorithm: halfpoints