Details

sample294.0ms

Algorithm: halfpoints

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	16
2	16
1	14
0	10

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize172.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.3b	(sqrt.p16 (-.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)
1.2b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

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

series1.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify10.0s

Counts

57 → 57

Iterations

Iter	Nodes
4	9276
3	1003
2	203
1	72
0	39

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize236.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
0.3b	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2) a)
1.2b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2)
5.4b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)

rewrite25.0ms

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:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
7.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2) a)
16.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2)
1.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2m

Counts

39 → 39

Iterations

Iter	Nodes
6	5937
5	1681
4	332
3	114
2	53
1	41
0	28

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.4b

localize282.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.3b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.4b	(/.p16 a (-.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)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

3.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
3.0ms	(/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
3.0ms	(-.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	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(/.p16 a (-.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)

simplify12.4s

Counts

57 → 57

Iterations

Iter	Nodes
4	9160
3	936
2	182
1	63
0	37

prune2.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.4b

localize327.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (/.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)) a)
0.5b	(/.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))
0.9b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
2.6b	(-.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))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`p16-times-frac`
21×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
20×	`associate-/l*`
9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`difference-of-squares`
7×	`introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand`
6×	`associate--l+`
3×	`associate-/r*` `associate-/l/`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `p16-flip--` `associate-/r/` `associate--r+`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `sub-neg` `insert-quire-add` `associate-+l-` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 91

Calls

4 calls:

13.0ms	(/.p16 (/.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)) a)
7.0ms	(/.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))
3.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
7.0ms	(-.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	(/.p16 (/.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)) 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))

simplify13.0s

Counts

95 → 95

Iterations

Iter	Nodes
4	15040
3	1998
2	469
1	115
0	59

prune3.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 1.2b

regimes858.0ms

Accuracy

0% (0.5b remaining)

Error of 1.7b against oracle of 1.2b and baseline of 1.7b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	10
0	10

end0.0ms

sample3.4s

Algorithm: halfpoints