Details

sample166.0ms

Algorithm: halfpoints

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
3	28
2	26
1	19
0	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize265.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
0.1b	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
0.4b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

151×	`p16-lft-identity-expand` `p16--un-lft-identity`
111×	`*p16-rgt-identity-expand`
105×	`p16-times-frac`
50×	`p16-distribute-lft-out` `distribute-lft-out`
35×	`distribute-rgt-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
15×	`associate-/r*`
12×	`introduce-quire`
10×	`distribute-lft1-in`
8×	`-p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`insert-quire-fdp-add`
4×	`associate-+r+`
3×	`associate-+l+` `associate-/l/`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-+l-`
1×	`p16-flip--`

Counts

4 → 233

Calls

4 calls:

142.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
15.0ms	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
81.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
25.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.4s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
3	1588
2	266
1	64
0	41

prune917.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize187.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
0.1b	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.4b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

101×	`p16-lft-identity-expand` `p16--un-lft-identity`
91×	`*p16-rgt-identity-expand`
78×	`p16-times-frac`
30×	`p16-distribute-lft-out` `distribute-rgt-out` `distribute-lft-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
10×	`distribute-lft1-in`
8×	`introduce-quire` `-p16-rgt-identity-expand`
6×	`associate-/r*` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-+r-`
3×	`associate-+r+` `insert-quire-fdp-add` `associate-/l/`
2×	`+-commutative` `associate-+l+`
1×	`insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 182

Calls

4 calls:

33.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
4.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
16.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
14.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
3	1426
2	220
1	54
0	36

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize247.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta)) (real->posit16 1.0)) (real->posit16 2.0))
0.1b	(+.p16 (+.p16 (real->posit16 2.0) alpha) beta)
0.4b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta)) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

101×	`p16-lft-identity-expand` `p16--un-lft-identity`
91×	`*p16-rgt-identity-expand`
78×	`p16-times-frac`
30×	`p16-distribute-lft-out` `distribute-rgt-out` `distribute-lft-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
10×	`distribute-lft1-in` `introduce-quire`
8×	`-p16-rgt-identity-expand`
6×	`associate-/r*` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`insert-quire-add` `associate-+l-`
3×	`associate-+l+` `insert-quire-fdp-add` `associate-/l/`
2×	`+-commutative` `associate-+r+`
1×	`associate-+r-` `p16-flip--`

Counts

4 → 184

Calls

4 calls:

158.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta)) (real->posit16 1.0)) (real->posit16 2.0))
20.0ms	(+.p16 (+.p16 (real->posit16 2.0) alpha) beta)
95.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta)) (real->posit16 1.0))
47.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.7s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
3	1266
2	242
1	67
0	44

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize327.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0)))) (real->posit16 1.0)) (real->posit16 2.0))
0.4b	(+.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0)))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))))
5.7b	(quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

100×	`p16-lft-identity-expand` `p16--un-lft-identity`
90×	`*p16-rgt-identity-expand`
78×	`p16-times-frac`
30×	`p16-distribute-lft-out` `distribute-rgt-out` `distribute-lft-out`
27×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
10×	`distribute-lft1-in`
7×	`introduce-quire`
6×	`associate-/r*`
5×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`insert-quire-fdp-add` `associate-/l/`
2×	`associate-+l+` `associate-+r+`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 170

Calls

4 calls:

16.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0)))) (real->posit16 1.0)) (real->posit16 2.0))
25.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0)))) (real->posit16 1.0))
5.0ms	(/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))))
0.0ms	(quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0)))) (real->posit16 1.0)) (real->posit16 2.0))
0.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0)))) (real->posit16 1.0))
0.0ms	(/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))))
0.0ms	(quire16-mul-add (quire16-mul-add (posit16->quire16 (real->posit16 2.0)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))

simplify2.1m

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
5	3461
4	1072
3	585
2	192
1	52
0	36

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes268.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
0	15

end0.0ms

sample4.8s

Algorithm: halfpoints