Details

sample257.0ms

Algorithm: halfpoints

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
2	16
1	14
0	10

prune61.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize187.0ms

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)

rewrite14.0ms

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:

4.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
3.0ms	(/.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)))
4.0ms	(-.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)

simplify1.4s

Counts

57 → 57

Iterations

Iter	Nodes
done	5001
3	989
2	197
1	74
0	39

prune782.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize254.0ms

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)) c a))) b_2) a)
0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2)
3.7b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)

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-/l*`
2×	`associate--l+` `p16-flip--` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg`

Counts

4 → 35

Calls

4 calls:

6.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
4.0ms	(-.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)

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

simplify4.0s

Counts

39 → 39

Iterations

Iter	Nodes
done	5002
5	1606
4	336
3	116
2	55
1	43
0	28

prune537.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize180.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

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:

2.0ms	(/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
3.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
2.0ms	(-.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 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
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 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify1.9s

Counts

57 → 57

Iterations

Iter	Nodes
done	5005
3	1139
2	189
1	64
0	37

prune700.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.3b

localize254.0ms

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 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))
1.1b	(-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2)
1.8b	(/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
12×	`p16-times-frac`
7×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
6×	`/p16-rgt-identity-expand`
4×	`associate-/l*` `difference-of-squares`
3×	`associate-/r*`
2×	`associate-+l+` `associate-+r+` `associate--l+` `p16-flip--` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `associate-/r/` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 69

Calls

4 calls:

12.0ms	(+.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))
2.0ms	(-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2)
8.0ms	(/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))

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

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5003
3	2091
2	310
1	82
0	46

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.2b

regimes422.0ms

Accuracy

0% (0.4b remaining)

Error of 1.7b against oracle of 1.3b and baseline of 1.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample3.3s

Algorithm: halfpoints