Details

sample709.0ms

Algorithm: halfpoints

simplify1.8s

Counts

1 → 1

Iterations

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

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize517.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))
0.2b	(+.p16 (/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
0.2b	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
1.3b	(/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))))

rewrite616.0ms

Algorithm

rewrite-expression-head

Rules

451×	`associate-l`
352×	`p16-lft-identity-expand` `p16--un-lft-identity`
308×	`p16-times-frac`
168×	`*p16-rgt-identity-expand`
126×	`associate-r`
110×	`p16-distribute-lft-out` `distribute-lft-out`
56×	`associate-+r+`
42×	`*-commutative`
28×	`associate-/r*`
25×	`distribute-rgt-out`
24×	`/p16-rgt-identity-expand`
20×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
16×	`distribute-rgt-in` `distribute-lft-in`
15×	`associate-/r/`
14×	`associate-+l+`
11×	`associate-/l*`
10×	`+-commutative` `-p16-rgt-identity-expand`
8×	`introduce-quire` `associate-*l/`
7×	`associate-+r-` `associate-*r/`
4×	`distribute-lft1-in` `associate-/l/`
3×	`insert-quire-fdp-add` `associate-+l-`
1×	`insert-quire-add` `p16-flip--`

Counts

4 → 500

Calls

4 calls:

45.0ms	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))
435.0ms	(+.p16 (/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
21.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
79.0ms	(/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.9s

Counts

504 → 504

Iterations

Iter	Nodes
done	5000
2	2574
1	387
0	117

prune3.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize322.0ms

Local error

Found 4 expressions with local error:

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

rewrite513.0ms

Algorithm

rewrite-expression-head

Rules

125×	`p16-lft-identity-expand` `p16--un-lft-identity`
69×	`p16-times-frac`
65×	`*p16-rgt-identity-expand`
44×	`p16-distribute-lft-out` `associate-l` `distribute-lft-out`
23×	`associate-/r*`
20×	`associate-+r+`
13×	`distribute-rgt-out`
12×	`+p16-lft-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
10×	`associate-+l+` `-p16-rgt-identity-expand`
8×	`introduce-quire` `associate-r`
7×	`associate-+r-`
6×	`associate-/r/` `associate-/l*`
4×	`+-commutative`
3×	`distribute-lft1-in` `insert-quire-fdp-add` `associate-+l-` `associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`insert-quire-add` `p16-flip--`

Counts

4 → 203

Calls

4 calls:

369.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (real->posit16 1.0))
21.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
50.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
60.0ms	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.1s

Counts

207 → 207

Iterations

Iter	Nodes
done	5031
3	1673
2	403
1	111
0	58

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize356.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

146×	`p16-lft-identity-expand` `p16--un-lft-identity`
144×	`p16-times-frac`
89×	`*p16-rgt-identity-expand`
39×	`associate-/r*`
32×	`p16-distribute-lft-out` `associate-l` `distribute-lft-out`
18×	`associate-+r+`
15×	`associate-/r/` `/p16-rgt-identity-expand`
14×	`associate-/l*`
8×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-+r-`
5×	`associate-/l/`
4×	`associate-+l+` `distribute-rgt-out` `introduce-quire`
3×	`+-commutative`
2×	`associate-+l-` `remove-double-div.p16`
1×	`p16-flip--`

Counts

4 → 219

Calls

4 calls:

22.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
110.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha)))
40.0ms	(/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha))
32.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.6s

Counts

223 → 223

Iterations

Iter	Nodes
done	5001
3	1559
2	335
1	96
0	52

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize524.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha (.p16 (real->posit16 2) i)) (+.p16 (real->posit16 2.0) beta)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (real->posit16 1.0))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha (*.p16 (real->posit16 2) i)) (+.p16 (real->posit16 2.0) beta)) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 (+.p16 alpha (*.p16 (real->posit16 2) i)) (+.p16 (real->posit16 2.0) beta)) (+.p16 beta alpha))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

386×	`p16-lft-identity-expand` `p16--un-lft-identity`
360×	`p16-times-frac`
217×	`*p16-rgt-identity-expand`
116×	`p16-distribute-lft-out` `distribute-lft-out`
66×	`associate-/r*`
44×	`associate-l`
41×	`associate-/l*`
31×	`distribute-rgt-out`
28×	`associate-/r/`
19×	`/p16-rgt-identity-expand`
11×	`remove-double-div.p16`
8×	`+p16-lft-identity-expand` `introduce-quire` `associate-r` `+p16-rgt-identity-expand`
6×	`associate-+l+` `-p16-rgt-identity-expand`
5×	`associate-/l/`
3×	`distribute-lft1-in` `insert-quire-fdp-add`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 415

Calls

4 calls:

680.0ms	(+.p16 (.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha (.p16 (real->posit16 2) i)) (+.p16 (real->posit16 2.0) beta)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (real->posit16 1.0))
175.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha (*.p16 (real->posit16 2) i)) (+.p16 (real->posit16 2.0) beta)) (+.p16 beta alpha)))
72.0ms	(/.p16 (+.p16 (+.p16 alpha (*.p16 (real->posit16 2) i)) (+.p16 (real->posit16 2.0) beta)) (+.p16 beta alpha))
62.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.8s

Counts

419 → 419

Iterations

Iter	Nodes
done	5004
3	1736
2	349
1	112
0	56

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

regimes1.2s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	25
0	25

end0.0ms

sample13.4s

Algorithm: halfpoints