Details

sample227.0ms

Algorithm: halfpoints

simplify771.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2098
4	2098
3	490
2	109
1	39
0	18

prune112.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize363.0ms

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))))

rewrite356.0ms

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:

55.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
125.0ms	(/.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))))
20.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
142.0ms	(/.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))))

simplify1.3s

Counts

410 → 410

Iterations

Iter	Nodes
done	2028
3	2028
2	517
1	116
0	55

prune21.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize555.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

468×	`p16-times-frac`
358×	`p16-lft-identity-expand` `p16--un-lft-identity`
326×	`*p16-rgt-identity-expand`
96×	`p16-distribute-lft-out` `distribute-lft-out`
80×	`associate-/l*`
48×	`distribute-rgt-out`
16×	`distribute-lft1-in`
11×	`/p16-rgt-identity-expand`
8×	`introduce-quire` `-p16-rgt-identity-expand`
6×	`associate-/r*` `associate-/r/`
5×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`insert-quire-add` `associate-+l-`
2×	`+-commutative` `associate-+l+` `associate-+r+` `associate-/l/`
1×	`associate-+r-` `insert-quire-fdp-add`

Counts

4 → 376

Calls

4 calls:

8.0ms	(+.p16 (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)
75.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
66.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

380 → 380

Iterations

Iter	Nodes
done	2013
3	2013
2	504
1	121
0	61

prune20.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize597.0ms

Local error

Found 4 expressions with local error:

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

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

439×	`p16-times-frac`
228×	`p16-lft-identity-expand` `p16--un-lft-identity`
226×	`*p16-rgt-identity-expand`
36×	`/p16-rgt-identity-expand`
31×	`associate-/r/`
24×	`introduce-quire`
19×	`associate-/r` `insert-quire-fdp-add` `associate-/l`
8×	`-p16-rgt-identity-expand`
6×	`p16-distribute-lft-out` `distribute-lft-out`
5×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-+r-`
3×	`distribute-rgt-out` `associate-/l/`
2×	`associate-+l+` `associate-+l-`
1×	`+-commutative` `associate-+r+` `insert-quire-add` `distribute-lft1-in`

Counts

4 → 291

Calls

4 calls:

11.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) alpha) beta))
135.0ms	(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)) (/.p16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (*.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0)))))
49.0ms	(+.p16 (*.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0)))
90.0ms	(/.p16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.1s

Counts

295 → 295

Iterations

Iter	Nodes
done	2007
3	2007
2	530
1	137
0	63

prune16.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize506.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

49×	`p16-times-frac`
46×	`p16-lft-identity-expand` `p16--un-lft-identity`
44×	`*p16-rgt-identity-expand`
24×	`introduce-quire`
19×	`insert-quire-fdp-add`
16×	`associate-/l*`
13×	`associate-r`
12×	`/p16-rgt-identity-expand`
8×	`-p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
6×	`p16-distribute-lft-out` `distribute-lft-out`
4×	`associate-+r-` `associate-/r*`
3×	`distribute-rgt-out` `associate-l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-l/` `associate-r/` `associate-+l-` `associate-/l/`
1×	`+-commutative` `associate-+r+` `insert-quire-add` `distribute-lft1-in` `*-commutative`

Counts

4 → 131

Calls

4 calls:

101.0ms	(/.p16 (real->posit16 1.0) (+.p16 (*.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0))))
25.0ms	(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) alpha) beta)) (.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha)) (/.p16 (real->posit16 1.0) (+.p16 (.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0))))))
69.0ms	(+.p16 (*.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0)))
33.0ms	(.p16 (+.p16 (.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha)) (/.p16 (real->posit16 1.0) (+.p16 (*.p16 beta alpha) (+.p16 (+.p16 beta alpha) (real->posit16 1.0)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify850.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	2018
3	2018
2	550
1	150
0	57

prune7.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes634.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	25

end0.0ms

sample5.9s

Algorithm: halfpoints