Details

sample188.0ms

Algorithm: halfpoints

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
2	16
1	14
0	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.3b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.3b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
1.1b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`introduce-quire`
10×	`p16-lft-identity-expand` `p16--un-lft-identity`
8×	`*p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`/p16-rgt-identity-expand` `insert-quire-fdp-sub`
4×	`associate--l+` `distribute-lft-out--`
3×	`p16-flip--` `associate-/l*`
2×	`associate--l-` `insert-quire-sub` `sub-neg` `associate--r+` `associate-/l/`
1×	`distribute-rgt-out--` `*-commutative` `associate--r-`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
4.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
5.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5016
3	984
2	189
1	76
0	41

prune651.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize248.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2) a)
0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
4.7b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`p16-lft-identity-expand` `+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `+p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-/l*`
2×	`associate--l+` `p16-flip--` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg`

Counts

4 → 35

Calls

4 calls:

9.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
6.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
1.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
0.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

simplify3.8s

Counts

39 → 39

Iterations

Iter	Nodes
done	5004
5	1606
4	336
3	116
2	55
1	43
0	28

prune595.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize207.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 a (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2))
0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
4.7b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`p16-lft-identity-expand` `+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `+p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-/r*`
2×	`associate--l+` `p16-flip--` `associate-/r/`
1×	`associate--l-` `insert-quire-sub` `sub-neg`

Counts

4 → 35

Calls

4 calls:

5.0ms	(/.p16 a (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
5.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
1.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 a (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
0.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

simplify3.0s

Counts

39 → 39

Iterations

Iter	Nodes
done	5028
5	1633
4	363
3	114
2	49
1	33
0	26

prune666.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize249.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.6b	(/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
1.2b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
2.9b	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

67×	`p16-lft-identity-expand` `p16--un-lft-identity`
51×	`p16-times-frac`
47×	`*p16-rgt-identity-expand`
40×	`distribute-lft-out--`
21×	`*-commutative`
20×	`associate-l` `difference-of-squares`
17×	`associate-/l*`
11×	`introduce-quire`
10×	`distribute-rgt-out--`
9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
7×	`-p16-rgt-identity-expand`
6×	`associate--l+` `/p16-rgt-identity-expand`
5×	`associate-r` `insert-quire-fdp-sub`
3×	`associate-/r*`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `p16-flip--` `associate--r+` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `sub-neg` `insert-quire-add` `associate-/r/` `associate-+l-` `associate--r-`

Counts

4 → 143

Calls

4 calls:

0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
47.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
7.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
12.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
0.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))

simplify1.6s

Counts

147 → 147

Iterations

Iter	Nodes
done	5007
3	1614
2	341
1	89
0	50

prune910.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.2b

regimes620.0ms

Accuracy

0% (0.6b remaining)

Error of 1.8b against oracle of 1.2b and baseline of 1.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample3.0s

Algorithm: halfpoints