Details

sample115.0ms

Algorithm: halfpoints

simplify4.1m

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
29	4637
28	4121
27	3647
26	3227
25	2804
24	2448
23	2156
22	1862
21	1576
20	1360
19	1176
18	998
17	828
16	696
15	595
14	497
13	386
12	309
11	256
10	205
9	152
8	117
7	96
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

localize145.0ms

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))))

rewrite61.0ms

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)))
8.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
45.0ms	(+.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))))

simplify454.0ms

Counts

209 → 209

Iterations

Iter	Nodes
done	5001
2	543
1	111
0	70

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

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) (+.p16 (real->posit16 1) x))
15.0b	(quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (real->posit16 1.0) (/.p16 (real->posit16 2) x))
22.0b	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (real->posit16 1.0) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (real->posit16 1.0))

rewrite13.0ms

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)))
10.0ms	(/.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))) (real->posit16 1.0) (/.p16 (real->posit16 2) x))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (real->posit16 1.0) (/.p16 (real->posit16 2) x)) (/.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))) (real->posit16 1.0) (/.p16 (real->posit16 2) x))
0.0ms	(quire16-mul-add (quire16-mul-sub (posit16->quire16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x))) (real->posit16 1.0) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (real->posit16 1.0))

simplify4.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	2856
2	187
1	45
0	33

prune428.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize148.0ms

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)))

rewrite52.0ms

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:

2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
5.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
7.0ms	(-.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
36.0ms	(+.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)))

simplify635.0ms

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	523
1	91
0	50

prune724.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize149.0ms

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))))
0.9b	(-.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))

rewrite77.0ms

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:

2.0ms	(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
14.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
53.0ms	(-.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))

simplify669.0ms

Counts

252 → 252

Iterations

Iter	Nodes
done	5001
2	653
1	115
0	70

prune912.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

regimes129.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample1.6s

Algorithm: halfpoints