Details

sample86.0ms

Algorithm: halfpoints

simplify5.5m

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
31	4854
30	4480
29	3983
28	3473
27	3156
26	2815
25	2501
24	2204
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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize151.0ms

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))
0.8b	(+.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))))

rewrite67.0ms

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:

2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
9.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
50.0ms	(+.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))))

simplify1.4s

Counts

209 → 209

Iterations

Iter	Nodes
done	5007
3	2469
2	408
1	111
0	70

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize238.0ms

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 (real->posit16 1) x))
15.0b	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
22.5b	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (real->posit16 1.0))

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:

2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
4.0ms	(/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (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 (real->posit16 1) x))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (real->posit16 1.0))

simplify2.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
5	2686
4	1017
3	381
2	141
1	45
0	33

prune481.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize262.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (*.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1))))
15.0b	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
25.5b	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (real->posit16 1) (*.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1)))) (+.p16 (real->posit16 1) x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`/p16-rgt-identity-expand`
6×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`distribute-rgt-in` `distribute-lft-in` `+p16-lft-identity-expand` `-p16-rgt-identity-expand` `associate-*r/` `associate-/r/` `+p16-rgt-identity-expand`
3×	`p16-times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`sub-neg` `introduce-quire` `associate-*l/` `p16-flip--` `associate--r-`
1×	`associate-/r` `-commutative` `associate-/l/`

Counts

4 → 46

Calls

4 calls:

4.0ms	(*.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1)))
2.0ms	(/.p16 (real->posit16 1) (*.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1))))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (real->posit16 1) (*.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1)))) (+.p16 (real->posit16 1) x))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5001
3	1063
2	197
1	86
0	44

prune702.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize237.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))
0.2b	(/.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (-.p16 x (real->posit16 1)))
15.0b	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
25.5b	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (-.p16 x (real->posit16 1))) (+.p16 (real->posit16 1) x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

84×	`p16-times-frac`
52×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
16×	`associate-/l*`
9×	`/p16-rgt-identity-expand`
7×	`associate-/r/`
6×	`associate-/r*`
2×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `associate-/l/`
1×	`p16-flip--`

Counts

4 → 91

Calls

4 calls:

4.0ms	(/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))
6.0ms	(/.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (-.p16 x (real->posit16 1)))
0.0ms	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 2) x) (real->posit16 1.0)) (/.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (-.p16 x (real->posit16 1))) (+.p16 (real->posit16 1) x))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

95 → 95

Iterations

Iter	Nodes
done	5002
3	1380
2	482
1	84
0	43

prune548.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes151.0ms

Accuracy

0% (0.2b 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

sample1.7s

Algorithm: halfpoints