Details

sample1.8s

Algorithm: halfpoints

simplify5.8s

Counts

1 → 1

Iterations

Iter	Nodes
4	15340
3	1591
2	264
1	60
0	19

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize347.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
1.5b	(/.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)))
3.6b	(/.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))))

rewrite29.0ms

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:

9.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
4.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
7.0ms	(/.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)))
6.0ms	(/.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))))

simplify6.2s

Counts

131 → 131

Iterations

Iter	Nodes
3	10742
2	936
1	172
0	69

prune7.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 1.0b

localize423.0ms

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)))
0.7b	(/.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)))
1.4b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
1.5b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite281.0ms

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:

99.0ms	(/.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)))
119.0ms	(/.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)))
27.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
21.0ms	(/.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 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 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify4.4s

Counts

408 → 408

Iterations

Iter	Nodes
3	7161
2	917
1	168
0	71

prune19.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.7b

localize446.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.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 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.2b	(/.p16 (+.p16 i (+.p16 alpha beta)) (+.p16 (+.p16 alpha beta) (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0))))
1.5b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite103.0ms

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:

57.0ms	(/.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)))
3.0ms	(/.p16 i (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
23.0ms	(/.p16 (+.p16 i (+.p16 alpha beta)) (+.p16 (+.p16 alpha beta) (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0))))
12.0ms	(/.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 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (+.p16 i (+.p16 alpha beta)) (+.p16 (+.p16 alpha beta) (+.p16 (*.p16 i (real->posit16 2)) (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)))

simplify2.2s

Counts

294 → 294

Iterations

Iter	Nodes
3	4455
2	884
1	145
0	63

prune15.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.5b

localize693.0ms

Local error

Found 4 expressions with local error:

0.8b	(.p16 (/.p16 (+.p16 (.p16 (+.p16 (+.p16 i alpha) beta) i) (.p16 beta alpha)) (+.p16 (.p16 i (real->posit16 2)) (+.p16 alpha beta))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0)))))
0.8b	(/.p16 i (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.2b	(/.p16 (+.p16 i (+.p16 alpha beta)) (+.p16 (+.p16 alpha beta) (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0))))
1.5b	(/.p16 (+.p16 (.p16 (+.p16 (+.p16 i alpha) beta) i) (.p16 beta alpha)) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))

rewrite105.0ms

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:

30.0ms	(.p16 (/.p16 (+.p16 (.p16 (+.p16 (+.p16 i alpha) beta) i) (.p16 beta alpha)) (+.p16 (.p16 i (real->posit16 2)) (+.p16 alpha beta))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0)))))
8.0ms	(/.p16 i (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
42.0ms	(/.p16 (+.p16 i (+.p16 alpha beta)) (+.p16 (+.p16 alpha beta) (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0))))
19.0ms	(/.p16 (+.p16 (.p16 (+.p16 (+.p16 i alpha) beta) i) (.p16 beta alpha)) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify4.8s

Counts

170 → 170

Iterations

Iter	Nodes
4	6431
3	1447
2	446
1	133
0	57

prune10.5s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.5b

regimes2.6s

Accuracy

0% (1.0b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 1.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
1	28
0	28

end0.0ms

sample30.7s

Algorithm: halfpoints