Details

sample292.0ms

Algorithm: halfpoints

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	18
3	18
2	17
1	15
0	10

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize264.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (.p16 b_2 b_2) (.p16 a c))
0.3b	(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c)))) a)
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c)))
1.5b	(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

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

series1.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify49.3s

Counts

73 → 73

Iterations

Iter	Nodes
4	25291
3	1835
2	304
1	81
0	44

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.7b

localize176.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))) a)
0.4b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
1.5b	(-.p16 (neg.p16 b_2) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))))
5.7b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

3.0ms	(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
3.0ms	(-.p16 (neg.p16 b_2) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))))
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify16.3s

Counts

55 → 55

Iterations

Iter	Nodes
4	13003
3	978
2	166
1	51
0	33

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.7b

localize328.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 a (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)))
0.4b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)))
1.5b	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c))) b_2)
5.7b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) a c)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/r` `p16-lft-identity-expand` `p16-*-un-lft-identity`
6×	`*p16-rgt-identity-expand`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out--`
2×	`associate-+l+` `associate-/r/`
1×	`+-commutative` `insert-quire-add` `distribute-rgt-out--` `p16-flip--` `associate-+l-`

Counts

4 → 39

Calls

4 calls:

5.0ms	(/.p16 a (-.p16 (real->posit16 0.0) (+.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)))
3.0ms	(+.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)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 a (-.p16 (real->posit16 0.0) (+.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)

simplify12.9s

Counts

43 → 43

Iterations

Iter	Nodes
5	2841
4	565
3	192
2	80
1	44
0	27

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

localize207.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.3b	(/.p16 a (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
1.5b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
10.0ms	(/.p16 a (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))
1.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
7.0ms	(+.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 a (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))
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)

simplify3.9s

Counts

61 → 61

Iterations

Iter	Nodes
4	7915
3	924
2	236
1	75
0	38

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.6b

regimes585.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
1	11
0	11

end0.0ms

sample3.5s

Algorithm: halfpoints