Details

sample107.0ms

Algorithm: halfpoints

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
3	28
2	26
1	19
0	14

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize183.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 re re) (.p16 im im))
0.3b	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.5b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.3b	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

11.0ms	(+.p16 (.p16 re re) (.p16 im im))
0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
3.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (.p16 re re) (.p16 im im))
0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
0.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

simplify8.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
5	2802
4	697
3	244
2	86
1	50
0	36

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize315.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 re re)) im im))) re)))
0.5b	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
1.3b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
4.4b	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

Calls

4 calls:

0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 re re)) im im))) re)))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
5.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
1.0ms	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 re re)) im im))) re)))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
0.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

simplify3.8s

Counts

34 → 34

Iterations

Iter	Nodes
done	5027
5	2145
4	413
3	130
2	50
1	34
0	26

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.7b

localize317.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.0b	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))
1.1b	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
2.7b	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

rewrite63.0ms

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 re re) (.p16 im im)))
23.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))
4.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
31.0ms	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
0.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
0.0ms	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

simplify2.2s

Counts

147 → 147

Iterations

Iter	Nodes
done	5007
3	1492
2	344
1	86
0	49

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize446.0ms

Local error

Found 4 expressions with local error:

1.0b	(/.p16 (.p16 (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re))
1.1b	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
1.1b	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
1.3b	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

33×	`p16-times-frac`
28×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
12×	`associate-r` `associate-l`
11×	`associate-/l*`
8×	`/p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-+l+` `*-commutative` `associate-/l/`
3×	`associate-/r*`
2×	`+-commutative` `insert-quire-add` `associate--l+` `associate-*r/` `p16-flip--` `associate-+l-`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-*l/` `associate-/r/`

Counts

4 → 100

Calls

4 calls:

33.0ms	(/.p16 (.p16 (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re))
7.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
7.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
6.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (.p16 (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
0.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
0.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

simplify3.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
4	2384
3	563
2	199
1	71
0	42

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.6b

regimes421.0ms

Accuracy

0% (0.4b remaining)

Error of 2.1b against oracle of 1.6b and baseline of 2.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	15
0	15

end0.0ms

sample2.5s

Algorithm: halfpoints