Details

sample107.0ms

Algorithm: halfpoints

simplify4.2m

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
29	4588
28	4071
27	3600
26	3193
25	2769
24	2409
23	2118
22	1828
21	1545
20	1336
19	1156
18	982
17	815
16	683
15	584
14	493
13	382
12	305
11	253
10	204
9	151
8	116
7	95
6	82
5	61
4	50
3	41
2	33
1	22
0	12

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.4b	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.7b	(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

111×	`p16-lft-identity-expand` `p16--un-lft-identity`
89×	`*p16-rgt-identity-expand`
83×	`introduce-quire`
70×	`insert-quire-fdp-add`
63×	`p16-times-frac`
48×	`insert-quire-fdp-sub`
20×	`distribute-lft-out--`
19×	`associate-/r/` `/p16-rgt-identity-expand`
16×	`insert-quire-sub` `p16-distribute-lft-out` `distribute-lft-out`
10×	`distribute-rgt-out--`
9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`-p16-rgt-identity-expand`
7×	`p16-flip--`
6×	`associate-+l+` `associate-/r` `associate-/l`
5×	`insert-quire-add`
4×	`associate--l+`
2×	`associate-+r+` `sub-neg` `distribute-rgt-out` `associate--r+` `associate--r-` `associate-/l/`
1×	`associate--l-` `+-commutative` `associate-+r-` `associate-+l-`

Counts

4 → 205

Calls

4 calls:

3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
10.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
51.0ms	(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.0ms	(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))

simplify984.0ms

Counts

209 → 209

Iterations

Iter	Nodes
done	5050
3	1869
2	415
1	111
0	70

prune888.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize211.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1.0) (-.p16 x (real->posit16 1)))
16.1b	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (real->posit16 1.0) (/.p16 (real->posit16 2) x))
18.9b	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (real->posit16 1.0) (/.p16 (real->posit16 2) x)) (real->posit16 1) (/.p16 (real->posit16 1.0) (-.p16 x (real->posit16 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

18×	`p16-lft-identity-expand` `p16-times-frac` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
6×	`associate-/r` `/p16-rgt-identity-expand` `associate-/l`
3×	`associate-/r/`
2×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `associate-/l/`
1×	`p16-flip--`

Counts

4 → 51

Calls

4 calls:

3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
3.0ms	(/.p16 (real->posit16 1.0) (-.p16 x (real->posit16 1)))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (real->posit16 1.0) (/.p16 (real->posit16 2) x))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (real->posit16 1.0) (/.p16 (real->posit16 2) x)) (real->posit16 1) (/.p16 (real->posit16 1.0) (-.p16 x (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms	(/.p16 (real->posit16 1.0) (-.p16 x (real->posit16 1)))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (real->posit16 1.0) (/.p16 (real->posit16 2) x))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (real->posit16 1.0) (/.p16 (real->posit16 2) x)) (real->posit16 1) (/.p16 (real->posit16 1.0) (-.p16 x (real->posit16 1))))

simplify1.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5232
5	2825
4	623
3	255
2	118
1	42
0	31

prune384.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize136.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.4b	(-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.7b	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

66×	`p16-lft-identity-expand` `p16--un-lft-identity`
43×	`*p16-rgt-identity-expand`
24×	`distribute-lft-out--`
18×	`introduce-quire` `p16-times-frac`
16×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`/p16-rgt-identity-expand`
12×	`distribute-rgt-out--`
10×	`associate-/r/`
9×	`+p16-lft-identity-expand` `insert-quire-fdp-add` `+p16-rgt-identity-expand`
8×	`-p16-rgt-identity-expand`
6×	`associate-+r+` `associate-/r` `associate-/l`
4×	`associate--l+`
3×	`insert-quire-fdp-sub`
2×	`associate-+l+` `sub-neg` `distribute-rgt-out` `p16-flip--` `associate--r+` `associate--r-` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `insert-quire-add` `associate-+l-`

Counts

4 → 140

Calls

4 calls:

3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
8.0ms	(-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
48.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
3	2327
2	380
1	91
0	50

prune693.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize135.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.6b	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.8b	(-.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

187×	`p16-lft-identity-expand` `p16--un-lft-identity`
153×	`p16-times-frac`
113×	`*p16-rgt-identity-expand`
83×	`introduce-quire`
70×	`insert-quire-fdp-add`
48×	`insert-quire-fdp-sub`
32×	`p16-distribute-lft-out` `distribute-lft-out`
28×	`distribute-lft-out--`
25×	`associate-/r/` `/p16-rgt-identity-expand`
17×	`distribute-rgt-out`
16×	`insert-quire-sub`
10×	`-p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `p16-flip--` `+p16-rgt-identity-expand`
6×	`associate-/r` `associate-/l`
5×	`insert-quire-add`
3×	`associate--l-`
2×	`associate-+l+` `associate-+r+` `associate-+r-` `associate-+l-` `associate--r+` `associate-/l/`
1×	`+-commutative` `sub-neg` `distribute-rgt-out--` `associate--l+` `associate--r-`

Counts

4 → 248

Calls

4 calls:

3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
17.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
65.0ms	(-.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.0ms	(-.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x))

simplify2.0s

Counts

252 → 252

Iterations

Iter	Nodes
done	5024
3	3512
2	493
1	115
0	70

prune849.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

regimes121.0ms

Accuracy

0% (0.3b remaining)

Error of 1.0b against oracle of 0.7b and baseline of 1.0b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample1.6s

Algorithm: halfpoints