Details

sample79.0ms

Algorithm: halfpoints

simplify50.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2020
24	2020
23	1917
22	1649
21	1414
20	1220
19	1034
18	883
17	729
16	602
15	501
14	423
13	321
12	264
11	209
10	169
9	138
8	114
7	91
6	82
5	61
4	50
3	41
2	33
1	22
0	12

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize276.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.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))
0.6b	(+.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))))

rewrite527.0ms

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:

5.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
6.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
18.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
491.0ms	(+.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))))

simplify997.0ms

Counts

209 → 209

Iterations

Iter	Nodes
done	2001
3	2001
2	408
1	111
0	70

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize405.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.6b	(+.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
14.3b	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

34×	`p16-lft-identity-expand` `p16--un-lft-identity`
29×	`*p16-rgt-identity-expand`
27×	`p16-times-frac`
14×	`insert-quire-fdp-add`
9×	`/p16-rgt-identity-expand`
6×	`associate-/r` `associate-/r/` `associate-/l`
5×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`p16-distribute-lft-out` `distribute-lft-out`
3×	`introduce-quire`
2×	`associate-+l+` `associate-+r+` `distribute-rgt-out` `p16-flip--` `associate-/l/`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-+l-`

Counts

4 → 91

Calls

4 calls:

2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
16.0ms	(+.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))

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

simplify1.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	2049
6	2049
5	1578
4	570
3	328
2	156
1	60
0	44

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize257.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.3b	(-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.6b	(+.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)))

rewrite110.0ms

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)))
10.0ms	(-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
92.0ms	(+.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)))

simplify1.3s

Counts

144 → 144

Iterations

Iter	Nodes
done	2000
3	2000
2	370
1	91
0	50

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize242.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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)))
30.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
120.0ms	(-.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))

simplify1.1s

Counts

252 → 252

Iterations

Iter	Nodes
done	2000
3	2000
2	482
1	115
0	70

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.6b

regimes244.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample1.8s

Algorithm: halfpoints